Trigeminal ganglion contrast enhancement (TGCE) is reported to be a normal and a common finding on magnetic resonance imaging studies of dogs, cats and humans. The intent of the present study was to describe the anatomical characteristics of the trigeminal ganglion, its surrounding structures, and histological features that are relevant to explain or hypothesize on the reason for TGCE on T1-weighted post-contrast MRI studies of the brain in dogs.Eight dog cadavers were dissected to study the anatomy of the trigeminal ganglion. The presence and anatomy of vessels was studied by dissection and by histological techniques. Two trigeminal ganglia were isolated and stained with hematoxylin–eosin (HE). Two other trigeminal ganglia included in the trigeminal canal and trigeminal cavity were decalcified with formic acid/formalin for 12 weeks and stained with HE to study the related vessels. Additionally, a corrosion cast was obtained from a separate canine specimen.Leptomeninges and a subarachnoid space were identified at the level of the trigeminal nerve roots and the trigeminal ganglion. No subarachnoid space was identified and leptomeninges were no longer present at the level of the three trigeminal nerve branches. Small arterial vessels ran to and supplied the trigeminal ganglion, passing through the dura mater. No venous plexus was visualized at the level of the trigeminal ganglion in the dissections. A complex arterial vascular network was identified within the leptomeningeal covering of the trigeminal ganglion and was best appreciated in the corrosion cast. Histological examination revealed small-to moderate-sized blood vessels located in the epineurium around the ganglion; from there a multitude of arterioles penetrated into the perineurium. Small endoneurial branches and capillaries penetrated the ganglion and the trigeminal nerve branches.Limitations to this study include the limited number of canine specimens included and the lack of electron microscopy to further support current hypotheses included in our discussion. In conclusion, this study provides further support to the theory that TGCE in dogs may be due an incomplete blood-nerve barrier or blood-ganglion barrier at the interface between the central nervous system and the peripheral nervous system. Magnetic resonance imaging (MRI) studies of the canine and feline head offers clinicians the opportunity to diagnose a plethora of disorders affecting the brain, cranial nerves and surrounding structures. Publications describing normal findings, so-called pseudolesions, and anatomical features regarding, for instance, cranial nerves exiting from the cranium provide a valuable resource for comparison to pathological states . A numbeIt is valuable for clinicians to be aware of this normal finding, as it may be mistaken for an abnormality (pseudolesion), and it be mistakenly thought of as a pathologic process affecting the trigeminal ganglion . As for cadaveric studies in dogs would be useful to determine whether a perineural venous plexus is present, paralleling what has been documented in humans’  cranial nerves and MRI observations , 10. Suc humans’ , no studThe objective of this study was to describe the anatomical characteristics of the trigeminal ganglion, its surrounding structures, and histological features that are relevant to explain or hypothesize the cause for TGCE on T1-weighted post-contrast MRI studies of the brain in dogs. In the discussion, we include a brief literature review regarding TGCE and hypothesize on the reason for TGCE in dogs based on this review and our findings.Eight adult dog cadavers were dissected to study the anatomy of the trigeminal ganglion. The cadavers used came from the dissection room of the Anatomy Unit of the Veterinary Faculty of the Universitat Autónoma de Barcelona. The dogs were euthanized for medical reasons unrelated to the central nervous system (CNS) and donated by owners following the approved donation program of the University and used for anatomical dissections. All the specimens were dissected by one author (VAG).3 beagles 1 German shepherd 1 golden retriever 1 Border collie 2 mixed breeds Dog breeds included:Cadavers were fixed with a 10% formaldehyde buffered solution injected via the common carotid artery. The cadavers were then preserved for a few weeks (variable) at 4–6°C. The heads of the eight dogs were isolated by atlantooccipital decapitation.Dorsal craniotomies were performed on 5 heads . The brains were removed by gross dissection.The other heads  were transversally sectioned.For each, dissection of the trigeminal ganglion and related structures was performed from that point forward with the use of stereomicroscopy and microsurgical equipment.The presence and anatomy of vessels was studied by dissection and by histological techniques. Two trigeminal ganglia were isolated and stained with hematoxylin–eosin (HE). Two other trigeminal ganglia included in the trigeminal canal and trigeminal cavity were decalcified with formic acid/formalin for 12 weeks and stained with HE to study the related vessels. Additionally, a corrosion cast was obtained from a separate, additional (ninth) canine specimen  injecting araldite mixed with red die  through the carotid artery. Briefly, the injected anatomical sample has been dissected and corroded in a basic solution of pancreatin at 37°C that destroys the muscles and ligaments while preserving the vascular mold.From the ventrolateral aspect of the brain stem, trigeminal nerve roots course rostrally through the trigeminal canal formed by the petrosal crest . At is rLeptomeninges and a subarachnoid space  were identified at the level of the trigeminal nerve roots and the trigeminal ganglion . SpecifiSmall arterial vessels, coming from the basilar artery, ran to and supplied the trigeminal ganglion, passing through the dura mater . FurtherHistological examination revealed small-to moderate-sized blood vessels located in the epineurium around the ganglion . From thIn this canine cadaveric and histological study, we describe the presence of complex vascular networks around the trigeminal ganglion in dog specimens. When contrast medium (commonly gadolinium-based) is administered to canine patients undergoing MRI studies of the brain, the presence of vascular structures must be taken into account when assessing TGCE. In theory, enhancement of vascular structures might be mistaken for TGCE, especially when contrast- and spatial resolution are suboptimal. Indeed, a human cadaveric study described the presence of a perineural/periganglionic vascular plexus and postulated that contrast enhancement is the reason for apparent TGCE . The autPublications from human studies have, without additional evidence, taken the results of either or both of these studies , 11 intoOur findings of a rich and complex vascular supply to the trigeminal ganglion contrast the findings in the human cadaveric study reported by Williams et al. . In thatThe presence of tight junctions and non-fenestrated endothelium characterizes the BNB . But thiWhatever the reasons may be, the fact that the BGB is incomplete is evidenced and supported by the finding that the trigeminal ganglion is not the only ganglion reported to show contrast enhancement on MRI in humans. Indeed, other ganglia reported to show contrast enhancement on MRI in humans include lumbar spinal DRG , geniculThe clinical importance of TGCE as normal feature on MRI studies deserves to be stressed here. Diagnosis of pathological states of the trigeminal ganglion should not solely be based on contrast-enhancement, though it may well be that contrast-enhancement of, for example, trigeminal ganglionitis or neoplasia affecting the trigeminal ganglion is different from normal TGCE. However, there are no specific reports quantifying the extent of TGCE in pathological versus normal states in dogs. Reports documenting MRI-based diagnoses of trigeminal neuritis focus on contrast-enhancement as well as increased size . ReportsOur findings of leptomeninges and a subarachnoid space . Written informed consent was not obtained from the owners for the participation of their animals in this study because they were donated by owners following the approved donation program of the University and used for anatomical dissections.KS: Conceptualization, Formal analysis, Writing – original draft, Writing – review & editing. EG: Conceptualization, Formal analysis, Writing – review & editing. MP: Conceptualization, Formal analysis, Investigation, Methodology, Writing – review & editing. VA: Visualization, Writing – review & editing, Conceptualization, Formal analysis, Investigation, Methodology.The author(s) declare financial support was received for the research, authorship, and/or publication of this article. The publication fee was covered by IVC Evidensia’s fund for publication of peer-reviewed scientific articles.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The head-related transfer functions (HRTFs) describe the acoustic path transfer functions between sound sources in the free-field and the listener’s ear canal. They enable the evaluation of the sound perception of a human being and the creation of immersive virtual acoustic environments that can be reproduced over headphones or loudspeakers. HRTFs are strongly individual and they can be measured by in-ear microphones worn by real subjects. However, standardized HRTFs can also be measured using artificial head simulators which standardize the body dimensions. In this paper, a comparative analysis of HRTF measurement using in-ear microphones is presented. The results obtained with in-ear microphones are compared with the HRTFs measured with a standard head and torso simulator, investigating different positions of the microphones and of the sound source and employing two different types of microphones. Finally, the HRTFs of five real subjects are measured and compared with the ones measured by the microphones in the ear of a standard mannequin. The head-related transfer functions (HRTFs) are mathematical functions that represent the acoustic path between a sound source and the ears of a listener in the frequency domain. These functions can be expressed also in the time domain under the name of head-related impulse responses (HRIRs). Humans can perceive the direction and the distance of a sound source by evaluating the differences in sound between the ears. These differences are represented by the localization cues, such as interaural time difference (ITD), interaural level difference (ILD), and spectral cues, that are contained in the HRTFs . For thiThe HRTFs are strongly individual because they depends on the shape of head, pinnae, and torso that are different for each human being. However, mannequins with standardized dimensions can be used to generate standardized HRTFs . StandarSeveral perceptual studies have aimed at evaluating how the use of individual HRTFs enables a high fidelity of the binaural rendering ,19,20, rAnother important aspect of individual HRTFs measurements is the microphone position ,21. ActuIn this context, this paper presents a new comparative analysis of two different in-ear miniature microphone systems positioned inside the ear canal for the HRTF measurement. Taking into account different positions of a sound source , two analyses have been carried out. A comparison between the HRTFs obtained with the proposed systems and the HRTFs measured by a standard binaural mannequin is performed first, then an analysis of several HRTFs measured considering real subjects is reported. The former is performed to study the performance of the acquisition systems and the effect of the microphones positions with respect to the ear canal. The latter is performed to evaluate the performance of these two different systems considering real subject ear’s shape. All these analyses have been performed in terms of objective evaluations.The paper is organized as follows. The head-related impulse responses (HRIRs) can be measured using several approaches that can be divided into two groups, deconvolution methods and adaptive filtering techniques . The decHRTF measurements could be affected by several problems, such as non-linear distortions of the electro-acoustic systems, environmental noises, reflections from the environments, sound source characteristics, and temperature variations ,54. The For the comparative analysis proposed in this paper, the measurements have been carried out in a semi-anechoic environment with professional equipment and low levels of input signals to reduce possible distortions introduced by the system. The impulse responses have been measured using the sweep signal. Further details on the hardware setup and the acquisition chain are reported in the next section.Focusing on in-ear microphones, the sensors used must be as small as possible, indeed this is important for two main reasons; first, since the sensor is placed inside the ear canal, a small device could be installed without being too much annoying for the subject, then, a small form factor is also important in order to minimize any modification in the ear form which can degrade the quality of the measured responses. Another important aspect of the microphone is its frequency response, which should be as flat as possible at least until 10 kHz. For this analysis, the HRTF measurements have been carried out with two different microphones, i.e., the Knowles FG-23329-D65 and the Sennheiser MKE2-EW Gold. The HRTFs measured with the two microphones are compared with the ones measured with the Brüel & Kjær head and torso simulator (HATS) Type 4128C, i.e., a binaural mannequin used as a reference and shown in For the Brüel & Kjær HATS simulator, For the Knowles microphone, For the Sennheiser microphone, The non-linearities that the measurement system may introduce have been evaluated by calculating the total harmonic distortion (THD) on a tone at 1 kHz. The THD is defined as the percentage ratio between the power of all harmonics and the power of the fundamental frequency. The THD values obtained with the three microphones are reported in the following:The highest distortion is obtained with the Knowles microphone and it is lower than lared in . The sweA comparison between the HRTFs measured with the in-ear miniature microphones placed in different points on the B&K mannequin ear canal and the HRTFs measured by the internal microphone of mannequin considering different positions of the sound source see ;A comparison of individual HRTFs measured on five real subjects with the two in-ear microphones for different positions of the sound source see .Two types of experiments have been carried out, in particular:The two microphones have been settled on the left ear of the mannequin and of the subjects by means of a hook fixed on earplugs, as shown in For an objective evaluation, the HRTFs measured with the in-ear microphones are evaluated in terms of frequency magnitude response and log-spectral distance (LSD)  considerThe first experiment aims at analyzing the differences between the HRTFs measured with the mannequin and the HRTFs measured with the in-ear microphones settled on the dummy ear. The in-ear microphones have been placed in the mannequin ear considering four different positions, as shown in The aim of this experiment is to investigate how much the microphone position influences the HRTF measurement and the results are shown in  kHz cf. a,b. In f kHz cf. . In thiscies cf. c,d. Howecies cf. . For thed P4 cf. e,f, resud P4 cf. . Finallylues cf. g,h. For lues cf. . These rThe second experiment involves five real subjects wearing alternatively the two in-ear microphones, as shown in In this paper, a comparative analysis of HRTFs measurement procedures is presented. In more detail, the HRTFs measured with two different in-ear microphones  are analyzed and compared with the HRTFs measured with a standard binaural mannequin. As first step, the influence of the microphone position on the frequency responses is investigated using the mannequin’s ear. Then, individual HRTFs of five real subjects are measured and compared among them. The experimental results have proven that the HRTFs are similar at low frequencies when different types of microphones are involved. In addition, the position of the microphone influences the HRTFs above 4 kHz. The experiments have shown that it is difficult to define the best position for the in-ear microphone. In fact, the analysis of the LSD values has reported that the best location of the microphone varies with the loudspeaker position and is not always the same. However, the Sennheiser microphone enables the obtaining of frequency responses more similar to the ones measured by the dummy head. Finally, the individual HRTFs measured on real subjects have shown how the frequency responses change with different ears. Furthermore, in this case, the Sennheiser microphone has produced HRTFs more similar to the mannequin and more similar among the five subjects. However, the worst performance of Knowles are compensated by the price that is one order of magnitude lower than Sennheiser microphone. Future works will investigate the effectiveness of the different HRTF measurements through subjective tests, evaluating the immersive perception. The subjective tests will examine the influence of the microphone position on the listening experience and will subjectively investigate the difference between personalized and standardized HRTFs.


Nowadays, usable plastic materials with defined properties are created by blending additives into the base polymer. This is the main task of compounding on co-rotating twin-screw extruders. The thermal and mechanical stress occurring in the process leads to a mostly irreversible damage to the material. Consequently, the properties of the polymer melt and the subsequent product are affected. The material degradation of polypropylene (PP) on a 28 mm twin-screw extruder has already been studied and modeled at Kunststofftechnik Paderborn. In this work, the transferability of the previous results to other machine sizes and polypropylene compounds were investigated experimentally. Therefore, pure polypropylene was processed with screw diameters of 25 mm and 45 mm. Furthermore, polypropylene compounds with titanium dioxide as well as carbon fibers were considered on a 28 mm extruder. In the course of the evaluation of the pure polypropylene, the melt flow rates of the samples were measured and the molar masses were calculated on this basis. The compounds were analyzed by gel permeation chromatography. As in the previous investigations, high rotational speeds, low throughputs and high melt temperatures lead to a higher material degradation. In addition, it is illustrated that the previously developed model for the calculation of material degradation is generally able to predict the degradation even for different machine sizes by adjusting the process coefficients. In summary, this article shows that compounders can use the recommendations for action and the calculation model for the material degradation of polypropylene, irrespective of the machine size, to design processes that are gentle on the material. To produce usable plastics, the properties of the materials must be specifically modified. This is conducted during compounding on co-rotating twin-screw extruders. Additives such as fillers, fibers or colors are mixed with the base polymer. Besides the desired melting and homogenization of the components, the thermal and mechanical stress in the extruder causes mostly irreversible damage to the material. The occurring damage mechanisms can be divided into purely thermal, thermal–oxidative, thermal–mechanical and hydrolytic degradation. These reactions usually run simultaneously and lead to different types of damage. Mainly, chain scission results in a reduction in the molar mass and a change in the molar mass distribution. This influences the rheological properties of the melt in the process as well as the mechanical properties such as the tensile strength of the end product. Moreover, color or odor changes may occur ,2,3.The evaluation of the material degradation caused by the compounding process, which is usually only possible retrospectively, is associated with a high economic and time expenditure, since a suitable operating point must first be detected using a try and error procedure. This problem led to the objective of a research project carried out at Kunststofftechnik Paderborn (KTP). It pursues the development of recommendations for gentle processing as well as mathematical modeling to describe the material degradation of market-dominating polypropylene on the co-rotating twin-screw extruder.The literature already contains several studies on the material degradation of PP on single- or twin-screw extruders. Pongratz , for exaIn previous research projects at the KTP, the material degradation of polyolefins on the single-screw extruder ,11,12 anWithin the research project on the material degradation of PP on the twin-screw extruder, basic investigations were first carried out ,16. Two The left side of the equation contains the weight-average molar mass to be calculated, 2) and carbon fibers (CF). The measuring methods used to determine the material degradation are then presented, as well as recommendations for gentle processing. In addition, it is illustrated that the introduced calculation model is also generally transferable to varying plant sizes.This article explains the further investigations to verify the previously developed recommendations for gentle processing and the applicability of the model to varying machine sizes and PP compounds. For this purpose, the following section first explains the tests carried out on pure polypropylene on a 25 mm and 45 mm extruder, as well as studies on compounds with titanium dioxide  and 45 mm (Barmag Saurer BTS-PET-045/40D) were used to investigate the transferability of the developed degradation model to other machine sizes. The PP compounds were processed on a ZE 28 BluePower twin-screw extruder from KraussMaffei with a screw diameter of 28 mm. Since the screw configuration can be assumed to have a small influence on the material degradation according to the findings of the previous studies, only one screw configuration was considered for each setup . The conGravimetric feeding and a water bath were used for all experimental investigations. The cooled extrudates were granulated with the help of a strand pelletizer. A comprehensive examination of the influence of the process parameters’ rotational speed, and the throughput and barrel temperature on material degradation was ensured by full-factorial test designs. Three different rotational speeds and three different throughputs were varied for each investigation according to To assess the effects of the temperature configuration on material degradation, low, medium and high barrel temperatures were considered in each investigation . While tAs already described in section one, processing on the twin-screw extruder leads to molar mass degradation and thus to a reduction in melt viscosity. Knowledge of the quickly measurable and evaluable melt flow rate as a dimension for the viscosity therefore allows conclusions about the occurred material degradation. For this reason, the melt mass flow-rate (MFR) and the melt volume flow-rate (MVR) of the taken granulate samples were measured according to  using a For the evaluation of the preliminary basic investigations carried out on the 28 mm extruder, the measured MFR values were converted into weight-average molar masses by using a model developed by Bremner et al. . To veriSince the calculation with Equation (2) is only suitable for pure polymers, the PP compounds were analyzed by GPC. This provides the advantage that the molar mass distribution is determined in addition to the weight-average molar mass. Essentially, the measurement conditions corresponded to those of the previously performed verification.The results of the further investigations largely correspond to those of the basic investigations on the 28 mm extruder. An increase in screw speed with otherwise constant parameters generally increases material degradation on all twin-screw extruder sizes. The reasons for this are the higher mechanical stress due to the increasing shear rates and the associated increased temperature of the material, which, for example, outweigh the material-protecting effect of the reducing residence time . In addi2 compound (a–c) and the PP/CF compound (d–f) are shown for different rotational speeds, throughputs and mass temperatures. The chain scissions caused by the processing on the twin-screw extruder leads to a shift of the distribution curves into the range of lower molar mass. Higher stress on the material due to high rotational speeds, low throughputs or high melt temperatures results in increased chain scissions and thus in a more significant displacement of the molar mass distribution.The effect of the individual process parameters on the PP compounds is illustrated in As explained, an increase in speed causes a higher shear stress, which in turn causes a higher mechanical degradation. Here, a deformation of the bond angles and the bond distance and consequently a breakage of the molecular chain occurs. Due to the structural viscosity of PP, the higher shear stress also causes the chains to stretch and align more, so that less energy is required for the flow. This reduces the effects of mechanical damage when the rotational speed is steadily increased. The higher the shear stress and the resulting dissipation, the more the melt heats up. This heating primarily causes chain scissions through the purely thermal and especially the thermal-oxidative degradation of the material. In terms of the pure thermal degradation, PP is relatively stable. However, it reacts easily with oxygen and radicals and therefore has only a low resistance to thermal-oxidative degradation. The thermal-oxidative degradation proceeds autocatalytically, meaning the initially slow reaction is accelerated by the formation of hydroperoxides and their decomposition into radicals. In addition, the thermal-oxidative degradation is accelerated by primary radicals which are formed during mechanical degradation. The increase in rotational speed also reduces the residence time of the material in the extruder, which is gentle on the material. Since the damaging effects associated with the increase in rotational speed dominate, an overall rise in material degradation takes place ,23.With increased throughput comes a reduction in the residence time of the material in the extruder. This particularly reduces the mechanical degradation. The higher filling level in the channel also has a positive effect. In combination with the shorter residence time, it leads to a lower melt temperature. As a result, the purely thermal and thermal-oxidative degradation is reduced. The latter is also decreased; due to a high filling level, less oxygen is available for the oxidation of the melt. Accordingly, the higher the throughput, the lower the material degradation. Raising the barrel temperature leads to a higher mass temperature. This in turn boosts the purely thermal as well as the thermal-oxidative degradation. At the same time, a higher mass temperature is accompanied by a lower viscosity, which reduces the mechanical degradation. However, overall, there is a clear increase in material degradation. In general, the material degradation is increased by high rotational speeds, low throughputs and high melt temperatures.w at the particular operating point and the weight-average initial molar mass Mw,0. If no material degradation occurred, this molar mass quotient equals one. The higher the material degradation, the more the molar mass quotient approaches zero. For pure PP on the 25 mm extruder, all modeled values show an upward deviation according to The result of the modeling with Equation (1) is the ratio of the reduced weight-average molar mass MAn adjustment of the process coefficients of the model according to 2 and PP/CF compounds were produced on a 28 mm twin-screw extruder. For the pure PP, the melt flow rates were measured and the molar masses were calculated. Since the calculation of the molar mass from the MFR is only suitable for pure polymers, the compounds were analyzed by GPC. The results correspond to the findings obtained for the 28 mm extruder and to the conclusions in the literature [From the previously conducted investigations on the material degradation of PP on a 28 mm twin-screw extruder, recommendations for gentle processing have already been derived. Additionally, a mathematical model for describing the material degradation was developed and implemented in the SIGMA simulation software. In this work, further experimental investigations were carried out to ensure the transferability of the previous results to other machine sizes as well as PP compounds. On the one hand, pure PP was processed on a 25 mm and a 45 mm twin-screw extruder. On the other hand, PP/TiO


Validation experiments were carried out on two different types of displacement sensors to benchmark the performance of the proposed method compared to the polynomial models and the the non-smoothing cubic spline. The results show that the proposed method with the new modified Akaike Information Criterion stands out compared to the other linearization methods and can improve the residual nonlinearity by over 50% compared to the standard polynomial model. After being linearized via the proposed method, the residual nonlinearities reach as low as ±0.0311% F.S. , for the 1.5 mm range chromatic confocal displacement sensor, and ±0.0047% F.S., for the 100 mm range laser triangulation displacement sensor.A noise-resistant linearization model that reveals the true nonlinearity of the sensor is essential for retrieving accurate physical displacement from the signals captured by sensing electronics. In this paper, we propose a novel information-driven smoothing spline linearization method, which innovatively integrates one new and three standard information criterions into a smoothing spline for the high-precision displacement sensors’ linearization. Using theoretical analysis and Monte Carlo simulation, the proposed linearization method is demonstrated to outperform traditional polynomial and spline linearization methods for high-precision displacement sensors with a low noise to range ratio in the 10 Sensors are the fundamental components in modern mechatronic systems, which typically transform a physical/chemical/biological variable into an interpretable signal for human or electronic processors. The general information flow of sensors could be summarized into an information encoding–decoding process: input physical values are encoded into electronic or mechanical signals and then decoded by signal processing modules to output the measurement value. According to the types of their input and output values, sensors can be categorized into different types such as displacement sensors, force sensors, pressure sensors, strain sensors, temperature sensors, etc. . While t(1)Nonlinearity measurement: measure the discrete nonlinearity deviations of the sensor using a traceable instrument with higher accuracy;(2)Nonlinearity reconstruction: construct an accurate mathematical model of nonlinearity from the discrete measurement data;(3)Nonlinearity correction: implement a real-time or off-line correction of the new measurement results using the constructed linearization model.Among the above-mentioned sensors, displacement sensors are a typical type of physical sensor which measure the change in length unit and cover wide measurement applications such as position, motion, profile, vibration, and deformation . TypicalA comprehensive review for the implementation of calibration systems for high-precision displacement sensors could be found in the literature . CurrentFor nonlinearity measurements, Seppä et al. established a novel linearization system that can correct sub-fringe periodic nonlinearity of heterodyne laser interferometers via a capacitive sensor and achieved picometer-level repeatability ; Giusca For the implementation of nonlinearity correction algorithms, Erdem compared the computational performance of six linearization algorithms on microcontrollers with a nonlinear optical displacement sensor and offered insights into the selection and implementation of an optimal linearization algorithm ; BouheddThe aforementioned works have covered the first and third steps for linearization. However, the second step regarding nonlinearity reconstruction has remained insufficiently explored in terms of how to construct a linearization model that best reveals the nonlinear characteristics of the displacement sensors from small amounts of nonlinearity measurement data while also adequately addressing the noise. Conventionally, polynomial models (PL) are adopted as standard methods for linearization ,27,28,29Attempts have been made by researchers to use data-driven machine learning approaches like the piecewise linear model (PWL) ,32,33,34Apart from PWL, ANN methods have exhibited high potential in sensor linearization. Marques et al. explored the application of ANN in compensating the nonlinearities for arbitrary types of sensors and successfully reduced the nonlinearity error of a negative temperature coefficient resistor sensor from ±3.33% F.S. to ±0.42% F.S. over a 60 °C range ; AnandanAdvanced curve models with enhanced local controllability, such as Bezier curves ,40 and SAn overview of the literature related to sensor linearization is presented in In this paper, we propose a novel information-driven linearization method by integrating smoothing spline with three standard information criterions and one newly devised criterion adapted for high-precision displacement sensors. The newly proposed method is different from conventional methods in that it can automatically select the best model parameter from the information in the data and the model itself, such as the number of data points, the residual sum of squares of fitting results, and most importantly, the freedom of the model. In this way, it can handle rough nonlinearity characteristics and can balance between underfitting and overfitting for noisy nonlinearity measurement data without human intervention. Verification and comparison experiments were carried out on two types of self-developed high-precision displacement sensors to validate the accuracy and repeatability of the proposed method. The results demonstrate that the smoothing spline linearization model constructed using the new modified Akaike information criterion stands out compared to that constructed from other information criterions and outperforms the standard polynomial model and the non-smoothing spline model in managing noise and local fluctuations.The remainder of this paper are arranged as follows. To compensate the systematic errors without overfitting the random noise, a good linearization model must be constructed to deal with the trade-off between goodness of fit and overfitting. Here, the theory foundations of three types of linearization methods are introduced: (1) the polynomial model, (2) the non-smoothing spline, and (3) the newly proposed smoothing spline linearization method constructed from the Bayesian information criterion, the Akaike information criterion, the corrected Akaike information criterion, and the new modified Akaike information criterion.x and interferometer data y, their generalized form could be expressed as: k, a group of Polynomial regressions are the standard method for linearization. Given input displacement sensor data The traditional polynomial model is powerful in generating a moderate fitting model with few coefficients ,44,45, bn basis functions m:Spline is a smooth curve controlled by a series of knots and is smoothly conjugated by piecewise polynomials . When usEquation  from [47Unlike the polynomial model, for which any local change would affect all the coefficients, spline is composed of a series of polynomial functions, with each part covering a certain range of the input data. This characteristic allows the spline model to fit the data with a much lower order than the polynomial model. The insensitivity to local undulation due to its piecewise structure makes spline a better choice for fitting local rough models than the polynomial. However, the “pass-all-data” characteristic of spline also makes it prone to overfitting the data, which can result in an overly complex model that is sensitive to noise. Consequently, improvements must be taken when using spline for linearization to ensure that the model accurately captures the underlying behavior of the data, while avoiding overfitting the noise.n data points and order m can be expressed as Equation  , which itimizing . TherefoFor smoothing splines, it is desired to find the best EDF that can predict the measurement results as close to the laser interferometers measurements as possible without over fitting the random noise of the measurement data. The key is to devise a suitable and concrete criterion for model selection . To tackCriterion strategy 1: The smoothing spline by the Bayesian Information Criterion (SP-BIC).k is the number of parameters of the model , n is the number of unique sample points in the dataset, and k. For discrete measurements, the The Bayesian information criterion (BIC) is a pervasively adopted model selection metric in statistics derived by Gideon E. Schwartz in 1978 ,58. The k-dimensional coefficients’ vector, In Equation , θi are Criterion strategy 2: The smoothing spline by the Akaike Information Criterion (SP-AIC).k with different penalty terms:The Akaike information criterion (AIC) was formulated by Hirotugu Akaike in 1974  for statFor normally distributed errors, the proposed smoothing spline linearization model with EDF selected by AIC could be expressed as:Criterion strategy 3: The smoothing spline by the corrected Akaike Information Criterion (SP-AICc).The corrected Akaike information criterion (AICc) is a variation of AIC to address the potential bias of AIC when the sample size is small. The AICc is the most widely adopted and most representative variation of the AICc criterion . It is dThe AICc criterion introduces a penalty function that is more stringent than the AIC, which favors models with fewer EDF for the same dataset. This criterion is particularly useful in applications like ecology engineering where the data are sparse and the noise is large, as it helps prevent the selection of overly complex models. However, for applications such as displacement sensors, the noise is significantly smaller compared to the input signal. In such a condition, the AICc might over-penalize the model, leading to suboptimal fitting results. This problem also exists for other similar information criterions like the Hannan–Quinn Information Criterion (HQIC) . Here, wCriterion strategy 4: The smoothing spline by the new Modified Akaike Information Criterion (SP-MAIC).−5 range. The measurement data are therefore fine observations of the system’s nonlinearity characteristics. In contrast to applications like in ecology, these applications have a low noise–signal ratio. In such low-noise applications, it is possible for the BIC, AIC, and AICc metric to select an over-simplified model due to excessive penalty, thus restricting the improvement of linearization accuracy. More information from the measurement data should be incorporated into the linearization model to make better predictions compared to large noise datasets. Hereby, the adjustment coefficient is introduced to alleviate the penalty term in AIC, where the new modified Akaike information criterion (MAIC) is formulated by:For high-precision displacement sensors like chromatic confocal displacement sensors and laser triangulation displacement sensors, the relative ratio between the root mean square of its measurement noise and its measurement range is small and typically in the 10k is small, the penalty term coefficient k increases, the penalty term also increases quickly to exclude overfitted models. Note that k is always smaller than n because the coefficients of the linearization model would never exceed the number of measurement data for fitting.It is noteworthy that the aim of MAIC differs from that of the AICc criterion, as well as other derived criterions, in that while the AICc endeavors to construct simpler models to mitigate overfitting, the MAIC is specifically designed to construct a more intricate and accurate model that effectively accommodates the high-precision characteristics of displacement sensors. This is accomplished by adopting a more moderate penalty term. In Equation , when k Compared to BIC, AIC, and AICc, the MAIC metric allows for higher EDF to raise the information adopted for constructing the smoothing spline linearization model. For measurement data with normally distributed noise, the proposed smoothing spline linearization model in RSS form is expressed by:−5 noise to range ratio.It is important to clarify that this paper does not propose the BIC, AIC, and AICc, which are widely-adopted standard criterions. Rather, this paper novelly integrates these information criterions into the construction of the smoothing spline model to optimize the smoothing parameter for sensor linearization, at the same time proposing the MAIC criterion with alleviated penalization to adapt to the linearization of high-precision displacement sensors with a typical 10The preceding section establishes the theoretical foundation for constructing linearization models. A precise measurement of the nonlinearities of displacement sensors is essential to ensure an optimal linearization performance of these models. To achieve accurate and traceable measurement results, the displacement sensors must be calibrated using a traceable displacement measurement instrument with higher measurement accuracy. The laser interferometers are regarded as the standard traceable length reference . They caThe basic principle of the designed linearization system is illustrated in For displacement sensors, the reference position is the zero-reading point after linearization and is defined by a reference distance starting from the front of the displacement sensor. After the standard target is moved to the reference position, the reading of the laser interferometer is set to zero to create an absolute calibration coordinate so the fitted linearization model would have a zero crossing at the point. The detailed workflow of the nonlinearity measurement system is arranged as follows:Step 1: Fix the standard target to the motion table. Mount the displacement sensor and the laser interferometer to different sides of the workpiece. Move the target to the reference positions of the displacement sensor and create absolute calibration coordinates by setting the reading of the laser interferometer to zero;Step 2: Move the motion table to near the end of the displacement measuring range. Record the data of the nonlinearized displacement sensor and the interferometer each time the standard target moves forward by a predefined calibration step;Step 3: Feed the nonlinearity data to the linearization model and apply the model to the displacement sensor;Step 4: Repeat the measurements. Record the data of both the displacement sensor and the interferometer each time the target moves by a predefined verification step;Step 5: Evaluate the residual linearity errors by calculating the deviation between the displacement sensor reading and the laser interferometer reading.Note that the measured nonlinearity data in this process are physical observations of the true nonlinearity of displacement sensors coupled with random errors such as photon detective noise and electrical noise. After the nonlinearity data are measured along the sensing range, the linearization follows the cross-validation approach, as illustrated in This systematic approach facilitates the linearization of displacement sensors and enables a detailed comparision of the performance of the linearization methods. A comparative analysis of the theoretical and practical aspects of these linearization methods is presented in the subsequent section.In this section, the theoretical performance of the four proposed information-driven linearization methods as well as the standard polynomial model and the non-smoothing spline model are evaluated from three key aspects: the local undulation of the targeted model, the noise level of the sampling dataset, and the number of samples in the measurement data. Among the three factors, the robustness to the local undulation and resistance to noise are critical metrics implying the reliability and adaptability of linearization methods.AFactor 1. The local undulation : The local undulation refers to the local variability exhibited by a model function. Intuitively, the freedom of a model decides its complexity, which is positively correlated to its capability to handle local undulation. Compared to polynomial models, the information-driven smoothing splines are more effective to handle local undulation because they allow for higher freedom and can approximate the local undulations better via piecewise reconstruction.NFactor 2. The noise level : The noise-resistant capabilities of a linearization method is essential for achieving good linearization results. Ideally, a linearization model should demonstrate consistent high performance across different noise levels. This is key in physical applications since noise levels vary from one condition to another. For the proposed information-driven linearization methods, their superiority compared to the non-smoothing spline lie in the ability to adapt to the noise data, and thus, can achieve better linearization accuracy.PFactor 3. The number of sampling points : The number of sampling points could also influence the linearization results. As a general rule, more sampling points can furnish linearization models with more physical information to achieve better linearization results. Nevertheless, in practical conditions, the number of sampling points is commonly restricted to the hundreds, considering the time and effort required for measurement. Too many samples could also lead to overfitting. This trade-off must be balanced to avoid overfitting.From the above analysis, it could be summarized in principle that the superiority of the proposed information-driven SP-MAIC lies in its ability to adopt a larger EDF to construct a more complex model , by using a milder penalty term, with the ability to deal with noisy data (compared to the non-smoothing spline method), by introducing the penalty term to avoid overfitting noise characteristics. To validate this, Monte Carlo simulations are conducted to compare the performance of the linearization methods in the following part of this section.Monte Carlo simulation is a known computational technique that involves using repeated random sampling to simulate the behavior of complex systems or processes . To theoAnd the expression of the constructed sigmoid function (SF) is:For Equations  and 17)17), the In Based on the above settings, the Monte Carlo simulations are carried out according to the following steps:A and a fixed sampling point P, x are evenly sampled from the input range of the nonlinear function;Step 1. For a fixed local undulation x via the nonlinear function;Step 2. The theoretical output N is generated and added to the theoretical output y, which, together with the sampled x, are used as nonlinearity measurements;Step 3. A Gaussian noise sequence with standard deviation x and y and then estimate the output Step 4. The linearization methods in y and calculating the root mean squared error (RMSE).Step 5. The performance of the linearization methods are evaluated by comparing the output of the linearization model Step 6. Steps 3–5 are repeated a hundred times, each time with different random noise, to implement the Monte Carlo simulation. The average RMSE errors converge during the simulation and are calculated as the performance of the linearization model.A and the sampling points P as required.Step 7. To estimate the performance under different local undulation and sampling points, steps 2–6 are carried out after changing the local undulation Following the above simulation workflow, the conducted simulation and the simulated performance of the linearization methods are given as follows:(1) Simulated Performance on the Local Undulation.A, the number of sampling points and the noise level must be fixed to implement single-variable analysis. Without compromising generality, the number of sampling points is set to 200 as a representative case to sufficiently capture the nonlinearities of the function curves in To verify the performance of the linearization methods under different local undulation In Among the spline models, the SP-FEDF model exhibits a higher residual error than the proposed information-driven smoothing spline models, which is the result of its overfitting of noise. (2) Simulated Performance on the Noise Level.In this simulation, the number of samples is set to 200 in alignment with the choice in the preceding simulation and the local undulation is set to 10 to model highly varying local nonlinearity change, as illustrated in From Among the smoothing spline models, SP-MAIC outperform the other three proposed information-driven models in general according to (3) Simulated Performance on the Number of SamplesA further simulation is conducted to verify the performance of the linearization methods with a different number of samples. In accordance with the parameter choices in the previous two simulations, the local undulation is set to 10 and the noise level is set to one. The results are plotted in In this simulation, the range of the number of samples is strategically chosen from 200 to 1000 via 50-step high-precision displacement sensor linearization, where hundreds of samples are sufficient for capturing their nonlinearities while balancing the duration for the nonlinearity measurement process. While a larger number of samples typically improves the linearization outcomes, it also introduces potential drift due to the long measurement period. Assume that the measurement of each point requires five seconds, so a range of 200 to 1000 samples results in a duration of 16.7 to 83.3 min, which is reasonable for practical applications.From From the simulation results presented above, it can be summarized that compared to the polynomial and SP-FEDF models, the proposed information-driven smoothing spline linearization methods exhibit higher resilience to both noise and local undulation in principle. Among the smoothing spline linearization methods constructed from four different criterions, SP-MAIC demonstrates the best performance compared to others by allowing for a more complex model with a higher EDF. This conforms to the analysis conducted in The changing trends of the select EDF in the three simulations are also worth noting here. The EDFs selected by the proposed smoothing spline linearization methods with four criterions increase as the local undulation and numbers of sampling points increase, but decrease as the noise level increases. This further demonstrates the adaptability and versatility for the proposed methods—they can automatically adapt the constructed linearization model to the local undulation, the noise level, and the number of samples without human intervention, driven by information like the number of samples, the residual sum squared of fitting, and the freedom of the model from the input data and the constructed model only.To verify the performance of the four proposed information-driven linearization methods, experiments were conducted on two types of self-developed displacement sensors including a chromatic confocal displacement sensor (CCDS), with a 1.5 mm range, and a laser triangulation displacement sensor (LTDS), with a 100 mm range. The LTDS and CCDS are chosen because they are both prevalent high-precision industrial applicable sensors with intrinsic optoelectronic nonlinearities that must be linearized before practical use, while they differ in terms of accuracy and range.Two linearization calibration system were developed based on the scheme in In this experiment, the linearization methods were verified on the self-developed chromatic confocal sensor. −5 mm and the noise–range ratio is 5.86 × 10−5, considering the 1.5 mm measurement range of the CCDS.Static measurement of noise was also conducted on the system to check the distribution of the sensor noise. After the standard plane mirror was moved into the sensing range and was kept static, the reading of CCDS was recorded at a 1 kHz rate for a 10 s period to obtain 10,000 static readings. The distribution probabilities of the readings, as shown in In the model fitting stage, one group of measurement data was used for fitting and another was used for validating the fitted model. The same Gaussian noise as that in the static measurement was incorporated into the linearization model to check the performance of the fitting algorithm under noise.At each EDF, the fitted RMSE, BIC, AIC, AICc, and MAIC were calculated. Here, the degree of freedom for the horizontal axis in From To demonstrate the versatility of the proposed linearization methods on different displacement sensors, experiments were also carried out on a self-developed laser triangulation displacement sensor as shown in In this setup, an API XD5 laser interferometer  was adopted, which is also traceable to the SI length unit via NIST. A standard ceramic plate was used as the standard target, to guarantee good scattering ability, and a long-range linear stage driven by servo motors is adopted. −3 mm and the variance–range ratio was 1.243 × 10−5. The change trend of evaluation criterions for polynomials and for smoothing spline was calculated and shown in Linearization results of the polynomial linearization methods, the proposed information-driven smoothing spline linearization methods with four different criterions , and the non-smoothing spline (SP-FEDF) are compared in this section on the two types of high-precision displacement sensors. Both the residual nonlinearity RMSE  and PV  are adopted to benchmark the performance of the linearization methods.The residual error of all the selected models on the validation dataset along the ±0.75 mm valid sensing range are shown in Similar to the data for CCDS, The linearization results are presented in detail in From the linearization results across the three groups of repeated tests for the CCDS in In Additionally, it is noteworthy that the difference in linearization results between polynomial linearization, smoothing spline linearization, and the proposed non-smoothing spline linearization method with different information criterions in the experiments is not as distinguishable as in the simulation. From the bar charts in From the experimental data in To sum up, a novel information-driven smoothing spline linearization method integrated with three standard and one new information criterion had been proposed in this paper for linearization of high-precision sensors, among which the SP-MAIC constructed from the new MAIC criterion achieved the best linearization performance. Verification experiments had been conducted to compare the proposed method with the standard polynomial model and the non-smoothing spline model. The test results on two different kinds of self-developed sensors verified that the SP-MAIC demonstrated consistent best performance over other models and reduced the nonlinearities of the CCDS and the LTDS to ±0.0311% F.S. and ±0.0047% F.S., respectively. The residual errors were significantly decreased by over 50% compared to that by the best-fit polynomial model. Intrinsically, this work exploited the possible application of statistical methods like information criterions in improving traditional engineering applications, such as displacement sensor linearization, and could be further extended to the linearization and compensation of other physical systems. By combining smoothing spline with information criterions, this paper provides a generic and highly adaptable linearization method with the capability of managing intricate nonlinearities and noise, which could find broader applications in linearizing various complex and noisy systems.While this paper focuses on the novel construction of smoothing spline linearization models via penalized information criterions for displacement sensors, the possible noise–range ratio of the sensor as to where the proposed metric performs best and how they can be adapted to other physical systems are also important topics that would be exploited in future work. For example, the validation experiments in this paper had been preliminarily conducted for noncontact opto-electronic sensors. For other types of sensors such as contact-type displacement sensors, additional influential factors, such as the geometry of the sensor tip and the characteristics of the target for nonlinearity measurements, are not addressed in this paper but are essential for determining the measurement nonlinearity.After being linearized via the proposed method, the remaining residual errors are mainly composed of random errors such as electronic noise and thermal drift. In-depth work on controlling and reducing such random errors to further promote the accuracy of sensors is of equal importance and will be investigated in the following research. Building on the idea of compensating for systematic errors and eliminating random errors, further research could be conducted on compressing measurement noise and drift via digital filtering approaches. Additionally, the primary focus of this paper has remained on improving the linearization accuracy in practical conditions with noise. Further studies could evaluate and improve its computational efficiency to facilitate on-chip implementations.


Introduction: Various activities in biological cells are affected by three-dimensional genome structure. The insulators play an important role in the organization of higher-order structure. CTCF is a representative of mammalian insulators, which can produce barriers to prevent the continuous extrusion of chromatin loop. As a multifunctional protein, CTCF has tens of thousands of binding sites in the genome, but only a portion of them can be used as anchors of chromatin loops. It is still unclear how cells select the anchor in the process of chromatin looping.Methods: In this paper, a comparative analysis is performed to investigate the sequence preference and binding strength of anchor and non-anchor CTCF binding sites. Furthermore, a machine learning model based on the CTCF binding intensity and DNA sequence is proposed to predict which CTCF sites can form chromatin loop anchors.Results: The accuracy of the machine learning model that we constructed for predicting the anchor of the chromatin loop mediated by CTCF reached 0.8646. And we find that the formation of loop anchor is mainly influenced by the CTCF binding strength and binding pattern (which can be interpreted as the binding of different zinc fingers).Discussion: In conclusion, our results suggest that The CTCF core motif and it’s flanking sequence may be responsible for the binding specificity. This work contributes to understanding the mechanism of loop anchor selection and provides a reference for the prediction of CTCF-mediated chromatin loops. High-order chromatin structure influences a variety of biological processes in the nucleus, including gene transcription, gene regulation and DNA replication. The structure of interphase chromatin has been extensively researched with the development of various chromatin conformation capture techniques , unveiliIn the process of gene expression, the gene regulatory elements work in order. These regulatory elements can be classified as promoters, enhancers, insulators, and other regulatory sequences . Insulatde novo prediction task. We notice that only a portion of CTCF binding sites are used as loop anchors. Can we first distinguish the loop anchor and non-anchor to reduce the search space for loop identification? Motivated by this idea, we intend to determine if a single CTCF binding site may serve as the anchor of loop by using sequence and binding intensity features. We find the binding intensity of CTCF, the core motif and the flanking sequence of the motif all have an important influence. Previous models ignore the flanking sequence features of the CTCF motif. In this paper, we developed support vector machine (SVM) (CTCF was later found to play an important role in chromatin organization. Paired CTCFs binding act as loop anchors to limit the interaction between remote regulatory elements . As a rene (SVM) , convolune (SVM) , random ne (SVM) , linear ne (SVM)  and stocWe download the public ChIP-seq data of CTCF from the ENCODE database . The detThe positive and negative set was constructed as follows: First, ChIA-PET data of CTCF were preprocessed by using ChIA-PET2 . ChIA-PEThe context sequence of CTCF, in addition to its core motif, is crucial for controlling gene expression. The binding intensity of CTCF can affect the movement of cohesin, thereby affecting the formation of the loops. The narrowPeak ChIP-seq data gives the CTCF binding intensity at the corresponding position. There is a large variation among the CTCF binding intensity values. It will greatly affect the training of the model. Due to the unique characteristics of each assessment index, a multi-index evaluation system typically has different dimensions and orders of magnitude. If the original indicator values are used for analysis when there is significant variation between the indicators, the importance of the indicators with higher values will be accentuated, while the significance of the indicators with lower values will be substantially diminished. Therefore, data normalization is required for the CTCF binding intensity to reduce the impact of the large variation in the training model. Here, we took the logarithm base two of the CTCF binding intensity value to narrow the gap between the value of CTCF binding intensity with the sequence data. Finally, the normalized value of the CTCF binding intensity and one-hot matrix were merged to construct the feature matrix .The basic motivation of the support vector machine (SVM) is to find a decision hyper plane to maximize the interval between the two types of data, construct an objective function according to the maximum interval, and then transform it into its dual problem for solution. For non-linear problems, first use a transformation z = φ (x) to map x to a new feature space z, then transform it into the dual problem of support vector machine, and we use radial basis functions as kernel functions.The random forest (RF) algorithm is an ensemble algorithm composed of multiple decision tree classifiers, with each subclassifier being a CART classification regression tree. Therefore, random forest can perform both classification and regression. The risk of overfitting can be reduced by averaging the decision trees.Convolutional Neural Network (CNN) is a specialized type of artificial neural network commonly used in deep learning for analyzing visual imagery. It is designed to automatically and adaptively learn spatial hierarchies of features from input images or other two-dimensional data, such as audio spectrograms. CNNs are composed of multiple convolutional layers that apply mathematical operations called convolution to the input data, followed by pooling layers that reduce the dimensionality of the output from the convolutional layers. The output of the pooling layers is then fed into fully connected layers, which perform the final classification or regression of the input data.We also use other machine learning models to train on the same dataset, including the linear discriminant analysis (LDA), Naive Bayes (NB): The Naive Bayes method is a classification technique that is based on Bayes’ theorem and the assumption of independently occurring features, logistic regression (LR): logistic regression is a generalized linear regression that utilizes logistic functions, and stochastic gradient descent (SGD): stochastic gradient descent is an iterative optimization algorithm used to update a model’s parameters based on the steepest descent direction of the loss function.We have employed several machine learning models to train on the same dataset, including linear discriminant analysis (LDA), support vector machines, Random Forest (RF)), logistic regression (LR), stochastic gradient descent (SGD), Naive Bayes (NB) models, convolutional neural networks (CNN), support vector machine models (SVM). We then compared the results of each model.To evaluate the prediction performance of the model, Accuracy (Acc), Precision (Pre), F1-score (F1), Area Under ROC Curve (AUROC), Area Under PRC Curve (AUPRC), Specificity (Sp), Sensitivity (Sn) and Matthews correlation coefficient (MCC) are used as evaluation indicators . TP . It alludes to the process of choosing N characteristics from the already-existing M features to optimize the system’s particular indicators. To decrease the dimension of the dataset and enhance the efficiency of the learning algorithm, it is necessary to choose some of the most useful characteristics from the original features. The generating process, evaluation function, stop criteria, and verification procedure are the four main components of the feature selection process. We selected the top 20 features in order of importance, and the most important feature was the value of the CTCF binding intensity corresponding to the sequence. We ranked the significance of the features and find that the flanking sequence sites 12, 45, 46 and 47 significantly contribute to classification. The sites 45 to 47 correspond to CTCF zinc fingers 1 to 3. Based on the analysis combined with From the research results, it can be concluded that the most important factor affecting the formation of loop anchor is the CTCF binding intensity. The sequence preference of flanking sequence and the motif matching score are consistent with the different distributions of CTCF binding strength in the positive and negative sets. A more suitable sequence context is favorable to the stable binding of CTCF and makes it simpler to prevent the sliding of cohesin and thus form a loop anchor. The statistical analysis of these three characteristics revealed that CTCF binding strength, core motif, and flanking sequence are the most important factors in predicting loop anchor.As an important transcriptional regulation mechanism in organisms, the process of chromatin looping has been widely studied. Previous studies have shown that this process can be interpreted by the loop extrusion model . The det


Hands represent an important aspect of pictorial narration but have rarely been addressed as an object of study in art history and digital humanities. Although hand gestures play a significant role in conveying emotions, narratives, and cultural symbolism in the context of visual art, a comprehensive terminology for the classification of depicted hand poses is still lacking. In this article, we present the process of creating a new annotated dataset of pictorial hand poses. The dataset is based on a collection of European early modern paintings, from which hands are extracted using human pose estimation (HPE) methods. The hand images are then manually annotated based on art historical categorization schemes. From this categorization, we introduce a new classification task and perform a series of experiments using different types of features, including our newly introduced 2D hand keypoint features, as well as existing neural network-based features. This classification task represents a new and complex challenge due to the subtle and contextually dependent differences between depicted hands. The presented computational approach to hand pose recognition in paintings represents an initial attempt to tackle this challenge, which could potentially advance the use of HPE methods on paintings, as well as foster new research on the understanding of hand gestures in art. Hands represent an important aspect of our mode of communication, and paintings are no exception. Indeed, from medieval representations of symbolic gestures  to theirIn the last decade, there has been increased interest in exploring computer vision and machine learning methods for analyzing and categorizing digitized collections of paintings. Most of the work in this field is focused on classification ,6,7,8, pstatic or dynamic categories. Static hand gestures are commonly called hand poses, and their understanding relies on their orientation, the positions of the fingers, the angles shaped by their articulations, and their relative positions toward the body [More specifically, computer-vision-based approaches, such as hand gesture recognition (HGR) and classification, have been extensively addressed and defined within the domain of human–computer interaction (HCI) ,36,37,38the body . Ultimatthe body ,37.The field of sign language recognition (SLR) also includes notable research on the development of the live detection and attribution of hand poses ,48. MethNevertheless, most of the deep learning models used in this context are trained on large annotated datasets of photographic images and achieve lower accuracy on artworks, which presents new challenges for the field of computer vision.The first annotated dataset of painted hands (Painted Hand Pose dataset), introducing a new standard for hand pose annotation in the context of digital art history;New hand pose features based on 2D keypoint information produced by HPE methods;The introduction of a novel classification task and a proposed solution method based on keypoint feature extraction.In this work, we propose the exploitation of methods and body characterization proposed in previous research on digital art history and apply it to the hands. Using HPE methods, we explain the process of the creation of a dataset of painted hands. It includes multiple curatorial steps, which reveals gaps between art historical and computational understanding of digitized artistic material. From the dataset produced, we define different features and propose a classification task based on art historical chirograms. In particular, our main contributions are:Our newly introduced Painted Hand Pose dataset and the proposed keypoints feature represent a first attempt to establish a computational framework for the analysis of hand gestures in paintings. This approach can serve as a basis for future research work or different applications, such as browsing data collections of painting through gestures, as presented in . In the The data source consists of digital images and their corresponding metadata from the photographic collection of the Bibliotheca Hertziana—Max Planck Institute for Art History in Rome. Because early modern paintings offer a figurative content and an interesting shift between symbolic and more natural hand gestures, we focused on Western European artworks produced between the 15th and the 17th centuries, thus harvesting a total of 5234 images.These images are photographs of paintings taken over the past century. Many of them are in black and white, and early acquisitions correspond to documents holding both an image and written information on the bottom, as shown in The images are associated with their corresponding metadata, which include the title of the paintings, the author, the estimated year of creation, and the identification number. As the digital photographic collection was created by different art historians and the metadata were produced at different time stages, they often include information in different languages as well as date formats following different art historical conventions. Therefore the first step in the preparation of our dataset included processing, cleaning, and standardizing the available metadata.c: The second step in the creation of the dataset was extracting hands from the collection of paintings. For this purpose, we compared several different approaches based on pretrained convolutional neural network models, such as the DensePose-RCNN , handCNNIf no hand was detected for an image, then the coordinates and score value x and y coordinate values of the different hand keypoints. From the minimum and maximum values, the height H of the hand was calculated in order to define a proportional margin m surrounding the hand. This margin was defined by the height value multiplied by a predefined ratio which was set to a fixed value of 0.3 after visually inspecting the results of different values in several experimental setups.After excluding images without detected hand keypoints, we proceeded to extract the hand images from those artwork images on which the OpenPose model detected hand keypoints for one or more hands. Based on the coordinates used for the keypoint descriptions, a bounding box was generated around the hand in order to crop the image, as illustrated in After performing this process on all of the available images, a total of 18,641 cropped images were produced. However, as not all the resulting images actually included hands, manual cleaning of the dataset of cropped images was performed.During the first visual inspection, cropped images that did not represent a hand were removed from the dataset, which resulted in 15,124 samples. The following step then consisted of checking the quality of the keypoint estimation: the keypoint information was superimposed on each remaining image. This second visual inspection allowed us to remove hands where the keypoints were visibly outside the limits of the depicted hand, as well as left and right hand duplicates, thus resulting in a total of 5993 images of painted hands. Besides the false positives and inaccurate detections, some poses were also more complex to detect and were not recognized by the OpenPose model, which is an issue that has already been documented in related studies ,30.Le langage des mains dans l’art, she described a total of 30 hand poses [The categorization of hands in our dataset was based on an interpretation of the work of the art historian Dimova . In her In this work , the difthumb up, index and auricular up, or hand under the chin. Additionally, the variations between different chirograms can be very subtle. In particular, we noticed the case of the pointing finger, which most often indicates a discursive situation, but which can also refer to a higher authority when pointing up [pointing index. Finally, after excluding all under-represented and ambiguous categories from the chirograms, we restricted our final data annotation task to nine different categories of hand poses, shown in Another challenge for our data labeling process based on Dimova’s categorization is the scarce representativity of specific categories, such as, for example, nting up  (p. 320)benedictio and the intertwined fingers, are associated with less than 100 samples, whereas the pointing index has almost 250 samples. However, although this represents a challenge for computational classification, it is a property that is inherent to both the dataset and the categorization task itself, as not all hand poses appear equally frequently in paintings from the early modern times.The images were then manually annotated by the first author of this paper. The final annotated dataset, named the Painted Hand Pose (PHP) dataset, represents 23.3% of the entire dataset of the 5993 initially extracted hand images. The distribution of the number of images into each category can be seen in https://doi.org/10.5281/zenodo.8069651 (accessed on 24 April 2023)). In order to analyze the potential of this dataset in the context of computational analysis of artwork images, we further explored feature extraction methods and several approaches to the automated classification of the defined hand gestures.The resulting PHP dataset has been made publicly available for future research .The hand keypoint features were exclusively based on the hand keypoint information obtained using the OpenPose model. In order to understand the descriptive potential of those features for the task of hand gesture recognition, we compared them to other image-based features. In particular, we extracted feature representations of the hand images from two different pretrained neural network models.In the first case, we used a ResNet50 model pretrained on the well-known ImageNet dataset , which hspace and delete signs, and a nonhand class, which includes images without hands. The training dataset contains 87,000 images, where each sample is a 200 × 200 pixels image. The fine-tuned model requires a 64 × 64 input shape and the addition of sequential layers with a final softmax activation layer to output a prediction on the 29 possible classes. We fine-tuned the model using the categorical cross entropy loss function and the Adam optimizer for 50 epochs, with a 128 batch size and a learning rate of 0.0001. The model reached 84% accuracy on the American Sign Language (ASL) dataset. After fine-tuning this model, we utilized it to extract features from our Painted Hand Pose dataset. We used the outputs of the last sequential layer, which form a 512-dimensional vector, to refer to this descriptor as the ASL ResNet50FT (fine-tuned) features.Additionally, in order to test whether we can leverage the availability of larger sign language datasets for our task, we fine-tuned the same ImageNet pretrained Resnet50 model on a dataset for sign language recognition, called the American Sign Language (ASL) dataset . The datThe classification of the hands was performed on each type of feature and with different machine learning methods. In total, we compared the results of three different classifiers: a Multilayer Perceptron (MLP), a Support Vector Machine (SVM), and a K-Nearest Neighbor (KNN) classifier. For the SVM, a Radial Basis Function (RBF) kernel was used. The parameters of the MLP setup included a 200 batch size, with a maximum of 10,000 iterations, and a 0.001 learning rate. A ReLu activation layer and a limited-memory BFGS (lbfgs) solver for weight optimization were used. In order to train the different classification models and due to the small size of the dataset, a five-fold cross-validation method was used with an 80% and 20% split between the training and testing datasets over each fold. The reported accuracy of the selected models corresponds to the mean of the five scores obtained for each fold.In order to gain a better understanding of the dataset and the defined class categories, we performed an exploratory analysis which included visualizing the separability of different classes within the dataset. We employed the well-known dimensionality reduction method t-distributed Stochastic Neighbor Embedding (t-SNE) to the KP features extracted from each image in our dataset. The visualization presented in the pointing index and the fist, as well as the joint palms praying, the hand on chest, and the opened hand up.The overlapping clusters in the t-SNE visualization indicate that certain classes possess similarities, such as As well as gaining insight about the underlying data structure in regard to the historically defined art categories, our exploratory analysis also focused on general hand categorization aspects, such the relation of the left and right hands. Based on the indication of the left or right hand keypoints, we found that 58% of the hand images in our dataset were labeled as right hands. A more detailed analysis of the distribution of left and right hands within each class category is shown in benedictio, the pointing index, and the hand on chest, tended to be mostly performed by the right hand. This tendency for right-handedness in conventional gestures found in early modern paintings correlates with contemporary research on the perception of the right hand as being the dominant hand [benedictio was only performed by the right hand, and our findings align with historical art observations on the long-standing gestural convention and the liturgical practices from which it derives [As we can see from the results, all gestures, especially the ant hand ,55. Furt derives ,57. HoweThe comparison of different feature descriptors based on three different classification methods is shown in The 50% accuracy achieved using the MLP classifier on the ImageNet ResNet50 features also indicates a promising result, particularly considering that the model was trained to classify images from very diverse object categories. These features also significantly outperform features extracted from the ResNet50 model fine-tuned on the sign language datasets, with which we achieved an accuracy of only 37% using the MLP classifier. Our initial intuition that we might achieve better results if we fine-tuned a general object recognition model on a sign language recognition task using a specific dataset of hands was therefore proven wrong. As well as the fact that the dataset of photographic sign language hand images is very different to our dataset of painted hands, we also assume that the model trained for the very specific task of sign language classification cannot generalize well to different types of hand poses of early modern paintings because those are, in the end, fundamentally different tasks. This outcome also indicates, once again, the very intricate nature of the computational approach towards painted hand gesture classification and demonstrates the limits of leveraging existing pretrained models and available large datasets of real hand images.In order to better understand the challenges of painted hand gesture classification, we analyzed the per-class classification performance. The detailed per-class classification results of the MLP are presented with the confusion matrix shown in fist, the opened hand forward, the joint palms praying, and the pointing index classes. The confusion matrix demonstrates that classes with the largest available number of images in the training set also achieved the highest per-class accuracy scores. This observation was additionally confirmed by the comparison of the F1 score of each set of features with the number of test set images available in each class, as expressed in fist class. The high F1 score for the fist class reflects the obvious distinctiveness of this hand gesture in comparison to other gestures, mainly as it usually includes a hand with all fingers folded towards the palm.The presented results indicate that the best overall results were achieved for the Additionally, the comparison of the F1 scores of all the different feature types indicates the strength of each feature type on the different classes. For example, the simplified KP features, which included only the angle value information, successfully described the fist and pointing index, but generated low results for all other categories. The ImageNet ResNet50 embeddings also showed good descriptive features for the opened hand up, and the ASL fine-tuned version offered a slightly better representation for intertwined fingers. Overall, it seems that the KP features performed the best for the majority of hand pose classes.benedictio gesture was often misclassified as pointing index and opened palm forward, while the hand on chest was most commonly misclassified as the praying gesture and vice versa. As well as indicating the well-known problem that occurs when classifying datasets with imbalanced numbers of images per class, the results also demonstrate the impact of a low interclass visual variation. For example, the https://github.com/VBernasconi/GAB_project (accessed on 22 March 2022)).Finally, it is important to indicate that our dataset and the defined hand keypoint features can be utilized beyond the scope of the presented classification task. More specifically, the defined hand keypoint features serve as a basis for the gesture-based image search engine Gestures for Artworks Browsing (GAB), which is presented and described in more detail in . This apLa main baladeuse [As shown in aladeuse  presenteAn application such as the Gesture-Based Browsing Interface can be used in a research context to easily access specific painted hands, but it can also be used as a novel and unconventional way of exploring art collections in museum spaces, offering a new experience of the artworks. Combined with a classification model trained for the recognition of pictorial early modern hand gestures, the tool could potentially become a didactic instrument, employed to better understand the diversity of depicted hands and their various connotations in early modern paintings.To summarize, in this paper, we introduced a new dataset of hand images extracted from paintings from the European early modern period, named the Painted Hand Pose dataset. We presented, in detail, the various challenging steps in the dataset creation process, which highlight the complexity of working with digitized collections of artworks. The dataset creation process included significant manual cleaning effort as well as laborious categorization and annotation work that required historical art expertise.As well as introducing a novel dataset, we proposed a new feature extraction method based on the use of deep learning methods for human pose estimation. More specifically, we focused on the hand keypoint coordinates obtained using the OpenPose model. These keypoints were used as the basis for our hand keypoint feature descriptor which integrates information about the absolute and relative positions of the palm and fingers by combining the angle values between the different joints in the hand and unites vector values of the different bones of the hand.Those features serve as the basis for additional computational exploration. For this purpose, in the context of our paper, we introduced a new challenging and interdisciplinary classification task. The work of the art historian Dimova on the categorization of hand gestures in paintings served as a basis for defining our classification task and identifying the different hand pose classes. In this paper, we propose a classification setting in order to better understand the complexity of hand pose classification in the context of artworks as well as to compare our keypoint features with other neural-network-based image features. The features created from the HPE 2D keypoint information showed promising results for this classification task and demonstrated the importance of the angles shaped by the articulation of the fingers and the orientation of the hand as descriptors.The presented classification results primarily serve to illustrate the complexity of adopting a computational approach towards hand pose recognition in early modern paintings. There are various possibilities for improving the classification results that might be explored in the future, such as exploring different feature ensemble techniques or including features extracted from deep neural network models fine-tuned on different tasks. However, the goal of this work was not to find the best possible classification method but to introduce a novel and challenging interdisciplinary task. The subtle differences between hand poses belonging to different historical art gestural categories outline the importance of integrating additional contextual information. Therefore, another possible future extension of this work includes combining hand pose image features with other global image scene features or existing metadata information  in a multimodal setting.Possible future improvements of the classification results also include the augmentation of the dataset, although this would require manual human effort and expert-level knowledge on hand gestures in the early modern times. There is, however, the possibility of augmenting the existing dataset with synthetically generated images by using generative models such as variational autoencoders, generative adversarial networks, or diffusion models. As well as the issue of homogenization, where not enough diverse data are produced, it seems that hands also represent a great challenge for contemporary text-to-image generative diffusion models, as reported in various media ,60. ThesFinally, our newly introduced classification task represents an interesting challenge in the context of the emerging discipline of digital art history. It also contributes to existing challenges in the field of computer vision and hand gesture recognition. Our research represents the first step in the direction of computational understanding of hand poses in paintings. It will, therefore, hopefully foster not only new methods in the context of computer vision, but also new research work on art history that will led to a better understanding of the language of hands in art, the comprehension of various gestural patterns, and their evolution in early modern times.