Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study. The neural activity without explicit stimuli shows highly structured patterns in space and time, known as spontaneous activity. This spontaneous activity plays a key role in the behavior of the response to external stimuli generated by the interplay between the spontaneous activity and external input. Studying this interplay and how it is shaped by learning is an essential step toward understanding the principles of neural processing. To address this, we proposed a novel viewpoint, memories-as-bifurcations, in which the appropriate changes in the activity upon the input are embedded through learning. Based on this viewpoint, we introduce here an associative memory model with sequential learning by a simple Hebbian-type rule. In spite of its simplicity, the model memorizes the input/output mappings successively, as long as the input is sufficiently large and the synaptic change is slow. The spontaneous neural activity shaped after learning is shown to itinerate over the memorized targets in remarkable agreement with the experimental reports. These dynamics may prepare and facilitate to generate the learned response to the input. Our results suggest that this is the possible functional role of the spontaneous neural activity, while the uncovered network structure inspires a design principle for the memories-as-bifurcations. The way in which neural processing of sensory inputs leads to cognitive functions is one of the most important issues in neuroscience. Neural activity in the presence of sensory stimuli The response activity has been the main focus both in modeling studies and experiments, while pre-stimulus, i.e., spontaneous, activity has been dismissed simply as background noise. However, spontaneous activity has recently been garnering more attention since experimental measurements have revealed that the spontaneous activity is not random noise and that it shows characteristic spatiotemporal patterns Spontaneous activity has been analyzed theoretically over the last few decades by using neural network models of rate-coding or spiking neurons with random, designed, or biologically realistic connections To analyze the formation of the spontaneous activity and its response to the memorized input through the learning of I/O mappings, we previously proposed a novel view on memory in Previously, we designed a neural-network connection matrix through correlations among memorized inputs and targets so that an output that matches a target is generated, as a result of bifurcations from the spontaneous activity, by applying the corresponding input In the present study, we introduce a sequential learning model with a simple Hebbian-type learning rule that changes the synaptic strength according to the activities of the pre- and postsynaptic neurons. From extensive numerical simulations, we have confirmed that through this learning the networks memorize In spite of the sequential learning scheme, the neural network does not lose the memory it learned earlier; it has a capacity of up to Remarkably, the network generated through the learning process to obtain a high memory capacity is found to have a similar structure to the network designed in We consider a system composed of For each input pattern We first select two random binary patterns, Here, although the validity of this learning rule is not mathematically proven in contrast to the perceptron, it is expected by the following argument. According to The learning process stops automatically when the neural activity matches the target since in this case During the learning process, double  dynamics run concurrently, and the neural and synaptic states have to be set as initial states: the neural and synaptic states are randomly selected from As our purpose in this study is to analyze the relationship between the spontaneous and evoked dynamics, we analyze the neural dynamical system in the absence and presence of input after learning. After the learning is completed, the synaptic connections are fixed and only the neural activities evolve. Note that there is no need for the input strengths for learning and memory recall to be identical: we can set the input strength As recall and memory for the memories-as-bifurcations viewpoint are defined differently from those for the memories-as-attractors viewpoint, we outline the definitions of recall and then memory here. A network succeeds in recalling a target Memory is defined as the ability of a network to recall a target for most initial states. The condition for whether a network memorizes an I/O (To examine whether a network shaped through the learning process memorizes the I/O mapping(s), we measure the evoked activity. Then we analyze the possible relationship between the spontaneous and evoked activities, and also analyze the characteristic features of the connection matrix Due to the high dimensionality of neural dynamics, it is difficult to directly analyze the time evolution in the entire phase space. Instead, we mainly use the overlaps of the neural activities with some patterns: that with the target During a learning process, the flow structures of the spontaneous and evoked activities change. Hence, the recall process also changes through the learning process. lied  in , but thesee also :The spontaneous activity shows chaotic behavior around the origin, while the evoked activity shows stationary activity, which matches the target pattern shown in , and theOnly fixed-point attractors that match the target and the “reverse” target patterns exist both in the absence and presence of the input shown in . Here, tWe now analyze the spontaneous and evoked neural dynamics in these two regimes. First, to reveal the dependence of the evoked dynamics on the parameters, To analyze the spontaneous dynamics, we note that due to the symmetry, the mean overlap for each target over time is generally zero because the orbit can approach both the target and reverse-target with equal probability. Thus, we measure the standard deviation (SD) of the overlap to quantify the approach to each target. The SD Neural activity responds to multiple inputs so that an attractor that matches each learned pattern is generated respectively upon each input. Thus, multiple mappings are successfully memorized. (ii) The neural activity does not respond to any input. The two attractors that match the latest learned target and its reverse pattern exist in the absence and presence of the input. Recall in response to an input is not observed either. We call these the R and NR regimes, respectively, in the same manner as the analysis for one-learning step.In In the R regime, by applying an input erns see , as longh input  . Thus, tTo examine the memory capacity, we compute the average overlaps with the targets We also analyze the spontaneous neural dynamics that underlie the responses to the learned inputs analyzed above in the R regime. The spontaneous neural activity shows noisy behavior, and no fixed pattern is stable, as shown in Therefore, the spontaneous activity approaches the learned targets from time to time and the closeness to the target In the NR regime, in contrast, the latest target and its reverse pattern exist as attractors in the absence and presence of inputs for  see . This isSo far, we have analyzed the spontaneous neural activity with In the R regime, the overlap with the 1st  target Apart from the change to a fixed-point attractor, the bifurcation sequences involve a large degree of freedom in a high-dimensional Click here for additional data file.Figure S2The neural dynamics after 40 learning steps in the non-response (NR) regime.A. The time series of the neural activities shown by the overlap with the 1st, 5th, and 30th targets B. The time-averaged overlaps with the learned targets as a function of C. The average overlap D. The average overlap (EPS)Click here for additional data file.Figure S3Dependence of evoked neural activity on the number of the elements. The overlap of evoked activity with (EPS)Click here for additional data file.


Total hip arthroplasty restores lost mobility to patients suffering from osteoarthritis and acute trauma. In recent years, navigated surgery has been used to control prosthetic component placement. Furthermore, there has been increasing research on what constitutes correct placement. This has resulted in the definition of a safe-zone for acetabular cup orientation. However, there is less definition with regard to femoral anteversion and how it should be measured. This study assesses the validity of the femoral anteversion measurement method used in imageless navigation, with particular attention to how the neutral rotation of the femur is defined. CT and gait analysis methodologies are used to validate the reference which defines this neutral rotation, i.e., the ankle epicondyle piriformis (AEP) plane. The findings of this study indicate that the posterior condylar axis is a reliable reference for defining the neutral rotation of the femur. In imageless navigation, when these landmarks are not accessible, the AEP plane provides a useful surrogate to the condylar axis, providing a reliable baseline for femoral anteversion measurement. A successful total hip replacement normalizes the biomechanics of the hip joint, enabling a patient to regain mobility without pain or discomfort . NormaliWhile many articles have been published concerning the validity and reliability of computer-assisted navigation with regard to the orientation of the pelvic acetabular cup, less has been written about femoral stem placement. This study aimed to assess the method used by an imageless navigation system to determine the neutral rotation of the femur from which the measurement of femoral anteversion is determined.Femoral anteversion has been defined by Murphy et al.  as the aIn imageless navigation, the ankle epicondyle piriformis (AEP) plane is used instead of the condylar axis to define the neutral position of the femur. The AEP plane replicates the ‘figure-of-four’ axis used in non-navigated surgery as a reliable reference to the condylar axis . The AEPTo assess whether the condylar axis accurately defines the neutral rotation of the femur, the angle between the pelvic medial-lateral axis and the femoral transepicondylar axis was measured in the transverse plane. Before performing the measurement, the condylar axis was aligned with the coronal plane in which the medial-lateral axis lies. This angle was measured on 10 subjects using a CT-based method. The angle was also measured in a separate cohort of 18 subjects using a gait analysis method, where it was not possible to align the condylar axis. The purpose of this was to assess the agreement between the two measurements: If agreement was found, then it could be inferred that when a subject is stood in the anatomical neutral posture the condylar axis lies in the coronal plane. Therefore, the method of Murphy et al.  can be uThe gait analysis method was then used to assess whether the normal vector to the AEP plane was coincident with the condylar axis. The angle between the pelvic medial-lateral axis and the femoral medial-lateral axis was measured. This angle was measured in the transverse plane, providing a measure of the difference between the pelvic coronal plane and the femoral coronal plane in which the AEP normal vector lies. If minimal deviation was found to exist, then it could be inferred that the normal vector to the AEP plane can reliably define the neutral rotation of the femur. Consequently, the AEP plane can be used reliably in imageless navigation where the posterior aspect of the femoral condyles is not accessible.http://rsbweb.nih.gov/ij/) and segmented so that only matter with the same density as bone remained. Each slice was then cleaned, removing any non-bone material and filling gaps in the pelvic and femoral traces. This ensured maximum fidelity with regard to the bony landmarks of the femur and pelvis. Each cleaned image stack was then imported into the Simpleware ScanIP software package . A morphological smoothing filter set at one-pixel spacing was applied to smooth the inconsistencies between slices, and a 3D model mesh was then generated for the pelvic and femoral masks. These 3D models were then imported into the Rhino 4.0 NURBS modeling package  for measurement.To measure, in the transverse plane, the angle between the pelvic medial-lateral axis and the femoral transepicondylar axis, CT scans were acquired of 10 subjects in the supine position. The subjects were all male and exhibited no evidence of osteoarthritis or abnormal morphology. Table II lists the age of each subject. The scans were acquired on a General Electric lightSpeed CT scanner with a slice thickness of 1.25 mm, encompassing the complete anatomy of the pelvis and femur. Each of the CT scans was segmented to produce three-dimensional (3D) models of the pelvis and femur. Each slice of every patient CT scan was imported into the ImageJ image-processing software  . The medThe coordinate system of the femur was defined according to the standard defined by Murphy et al. . The supThe gait analysis method was used to measure two angles. First, the angle between the pelvic medial-lateral axis and the femoral transepicondylar axis in the transverse plane was measured. Secondly, the angle between the pelvic medial-lateral axis and the femoral medial-lateral axis was measured, again in the transverse plane. Eighteen subjects were recruited to perform three experiments. The subjects were all male and exhibited no evidence of osteoarthritis or abnormal morphology. Table III lists the age of each subject. Measurements were taken using a Vicon MX motion-capture system  housed at the Gait Laboratory within the School of Engineering, University of Warwick. This system consisted of 12 infrared cameras located around the laboratory. The cameras tracked the 3D coordinate locations of passive marker spheres placed on the subject. The marker spheres were placed on the subject in the following locations: the medial and lateral ankle malleoli, the medial and lateral femoral epicondyles, the pelvic right and left ASIS, and the pelvic right and left PSIS. This configuration is shown in The first experiment determined the center of the hip joint. This landmark was estimated based on the motion of the femur relative to the pelvis. It was required to be determined because the landmark of the piriformis fossa was not accessible. Therefore, to form the AEP plane an alternative proximal femoral landmark was used as a surrogate, namely the hip joint center. To begin the experiment, the subject was asked to stand, positioning himself so that the centers of his knees were directly below the centers of his hips, defining the neutral posture , 32. TheIn the second experiment, the angle between the pelvic medial-lateral axis and the transepicondylar axis was measured. Similar to the first experiment, the subject was asked to stand so that the centers of his knees were directly below the centers of his hips, defining the neutral posture , 32. TheIn the final experiment, the angle between the pelvic medial-lateral axis and the femoral medial-lateral axis was measured. Again, to start the experiment the subject was asked to stand in the neutral posture. The subject was then asked to flex his hip to approximately 65° and his knee to 90°, ensuring minimal leg abduction or adduction. Once this was completed, the AEP plane was calculated using the estimated hip joint center, the mid-point of the two femoral epicondyles, and the mid-point of the two ankle malleoli. The AEP plane normal was determined and used to construct the femoral coordinate frame. The angle between the pelvic medial-lateral axis and the femoral medial-lateral axis was then measured. This measurement was taken in the transverse plane where the normal vector to the AEP plane is coincident with the femoral medial-lateral axis. Measurement of the minimum angle between the two axes was recorded, as well as the angular deviation at 25°, 45° and 65° of hip flexion. The mathematical formulae used to construct the AEP plane and calculate this angle are shown in Appendix 3.﹛a = 2.2°). Based on these findings, it was determined that the transepicondylar axis in both the CT and gait analysis experiments should be externally rotated by an average of 5.7° when measured from the pelvic medial-lateral axis. To assess the agreement between the experimental means, two statistical tests were performed. First, a t-test using the a value determined by Yoshioka and Cooke [To assess whether the condylar axis lies in the coronal plane, thus defining the neutral position of the femur, the findings of Yoshioka and Cooke  were usend Cooke  with a snd Cooke . The pernd Cooke .a = 2.5° when measured in the transverse plane. If the results of this experiment met the criteria, then the normal vector to the AEP plane could be considered to lie in the coronal plane and could be used as a basis from which to measure the anteversion of the femoral neck.To assess whether the normal vector to the AEP plane lies in the coronal plane, a mean angle between the medial-lateral axes of the pelvis and femur was defined. This angle should be within 2.5° with a Using the CT-based method, the angle in the transverse plane between the pelvic medial-lateral axis and the femoral transepicondylar axis was measured to be, on average, 6.61° externally rotated (<r = 2.43°). The same angle, using the gait analysis method, was measured to be, on average, 4.12° externally rotated (<x=7.69°). The results for the CT and gait analysis methods are shown in As determined using the gait analysis method, the measurements in the transverse plane between the pelvic medial-lateral axis and the femoral medial-lateral axis are shown in The measurement of femoral anteversion is congruent to the definition of anatomical anteversion presented by Murray , as showThe null hypothesis for this study was that the condylar axis can reliably determine the neutral rotation of the femur when a person is posed in the anatomical neutral posture, upright and erect on both legs with the knee centers located below the hip joint centers , 32. To The second factor to be validated in this study was whether the normal vector to the AEP plane can be used to construct a femoral coordinate frame which accurately defines the neutral rotation of the femur. The results of this study have shown that the medial-lateral axes of the femoral and pelvic coordinate frames align extremely closely with a mean deviation of 0.38°. This validates the concept that when the posterior aspects of the femoral condyles are not available to construct the condylar axis, the AEP plane can be used to construct a coordinate frame which accurately defines the neutral rotation of the femur. Therefore, the AEP plane can be used to construct a reliable medial-lateral axis from which to measure femoral anteversion, similar to the ‘figure-of-four’ axis. There was evidence that the orientation of this axis varied throughout the movement cycle, and this variation had no correlation with hip flexion. It is hypothesized that this variation could be associated with tibial varus/valgus, although this was not measured in the study. Further work needs to be done to establish how to define a consistent AEP plane which can be used in imageless navigation.There were a number of experimental assumptions which could affect the validity of the study findings. The first was associated with the reference frame used to construct the pelvic coordinate frame. Imageless navigation uses the anterior pelvic plane (APP), while this study used the reference points of the transverse pelvic plane (TPP) . HoweverThis study assessed the validity of using the posterior aspects of the femoral condyles as a reliable reference for defining the neutral rotation of the femur. The measurements supported this assessment, although there was some variation. Also, it has been found that in imageless navigation the AEP plane can be used to define the neutral rotation of the femur. This provides a reliable basis from which to measure femoral anteversion.


Wireless capsule endoscopy has been introduced as an innovative, non-invasive diagnostic technique for evaluation of the gastrointestinal tract, reaching places where conventional endoscopy is unable to. However, the output of this technique is an 8 hours video, whose analysis by the expert physician is very time consuming. Thus, a computer assisted diagnosis tool to help the physicians to evaluate CE exams faster and more accurately is an important technical challenge and an excellent economical opportunity.The set of features proposed in this paper to code textural information is based on statistical modeling of second order textural measures extracted from co-occurrence matrices. To cope with both joint and marginal non-Gaussianity of second order textural measures, higher order moments are used. These statistical moments are taken from the two-dimensional color-scale feature space, where two different scales are considered. Second and higher order moments of textural measures are computed from the co-occurrence matrices computed from images synthesized by the inverse wavelet transform of the wavelet transform containing only the selected scales for the three color channels. The dimensionality of the data is reduced by using Principal Component Analysis.The proposed textural features are then used as the input of a classifier based on artificial neural networks. Classification performances of 93.1% specificity and 93.9% sensitivity are achieved on real data. These promising results open the path towards a deeper study regarding the applicability of this algorithm in computer aided diagnosis systems to assist physicians in their clinical practice. Furthermore, and to reduce the dimensionality of the feature set, PCA is applied, being this the third novel point of the paper justified by the high dimensionality of the feature vector when compared with the amount of training data. These features are the input of a Multi-Layer Perceptron classifier, in a classification scheme used to classify real data gathered at the Hospital dos Capuchos. A flowchart with the key processing blocks of the proposed algorithm is illustrated in Figure Although texture can be visually classified as fine, course, grained, smooth, etc., its mathematical definition is not trivial. Nonetheless, it is clear that the textured information in a image corresponds to its medium/high frequency content. Therefore, the texture can be seen as a multi-scale phenomena and thus appropriate computational tools are required to deal with its quantification and analysis. The Discrete Wavelet Transform (DWT) is a mathematical tool that allows a spatial/frequency representation by decomposing the image in different scales with different frequency content. Thus, the DWT is a multi-resolution representation of the information within the image, being therefore well suited to deal with multi-scale phenoma as the texture content of an image. In the present work, we use the DWT to select the appropriate frequency content to further proceed to the analysis of the texture content of a given image. This information is mostly present in the scales corresponding to medium/high frequency content , and thus an image is synthesized from each of these scales. Each synthesized image will thus possess relevant texture information at the selected scale of detail. Nevertheless, one should recall that the sub-band selection is dependent on the image resolution, which imply that a pre-regularization step may be added in order to account for frames with different image resolution.f, which is computed by counting all pairs of pixels at distance d, having pixel intensity of color levels i and j at a given direction θ. The angular displacement used is the set {0, π/4,π/2, 3 π/4}. Several features can be extracted from co-occurrence matrices, corresponding to statistical descriptors containing second order color level information, which are mostly related to the human perception and discrimination of textures [F1), correlation (F2), inverse difference moment (F3), and entropy (F4), representing the homogeneity directional linearity, smoothness and randomness of the co-occurrence matrix, defined respectively as:Once the relevant information is selected by using DWT, several statistical texture descriptors can be extracted. Since texture is a phenomena involving spatial patterns among neighbor pixels, it can be properly exploited using co-occurrence matrices. These are usually built by estimating the second order joint-conditional probability density function textures . In the textures . They arp is the ijth entry of the normalized co-occurrence matrix, Ng the number of gray levels of the synthesized image and μx, μy, σx and σy are the means and standard deviations of the marginal probabilities px(i)/Py(j) obtained by summing up the rows/columns of the matrix p. In the ambit of this paper these features were obtained from pre-processed images, which are synthesized from the inverse wavelet transform of the wavelet transform of source images where information not relevant for texture analysis was discarded in the wavelet domain, as described in the sequel. HOS in the color-scale space was added to cope with joint non-Gaussianity that certainly happens under marginal non-Gaussianity cases. The resulting feature vector will allow to capture enough information in order to identify characteristic texture patterns from normal and abnormal small bowel tissue.where The image pre-processing stage synthesizes two images containing only the most relevant textural information from the source image. The most relevant texture information often appears in the middle frequency channels . TextureThe wavelet transform allows a spatial/frequency representation by decomposing the image in the corresponding scales. When the composition level decreases in the spatial domain it increases in the frequency domain providing zooming capabilities and local characterization of the image . This spI result in three decomposed color channels:Color transformations of the original image i stands for the color channel.where Ii, as shown in Figure A two level discrete wavelet frame transformation is applied to each color channel, l stands for the wavelet band and n is the decomposition level.where Since the textural information is better presented in the middle wavelet detailed channels, then second level detailed coefficients would be considered. However, the relatively low image dimensions (256 × 256) limit the representation of the details, becoming the first level more adequate, than previously expected, for texture representation . NeverthFor the extraction of the second order statistical textural information, co-occurrence matrices would be calculated over the eighteen different sub-images. However, and in order to diminish the dimension of the observation vectors, the image to be processed can be synthesized from inverse discrete wavelet transform (IDWT), with the coefficients of the large scales (lower frequencies) discarded. As the goal is to correlate texture descriptors obtained at different scales and colors, one image must be synthesized from each scale and color channel. The number of scales considered in this paper is 2. Therefore one image must be synthesized from bands {1, 2, 3} and a second image is synthesized from bands {4, 5, 6}, for each color channel. This procedure reduces the dimensionality of the observation vector by a factor of 3, since only six images need to be processed instead of the eighteen obtained in the wavelet domain. Previous results confirmed that the most relevant texture information is maintained with this approach ,29. It iNi,j where j = {1, 2} represents the level of focus, be the reconstructed images for each color channel:Two new images, containing the most important texture information, are then synthesized from the selected wavelet bands, trough the inverse wavelet transform. Each image represents the original image at a different level of focus. Let i stands for color channel, l for wavelet band and IDTW(·) is the inverse wavelet transform. Unfortunately the contribution of the detail information regarding texture characterization can not be visually confirmed since the lack of the coarse scale (low frequency content) retires almost all the visual information. In this regard we perhaps should rely in the well established knowledge that textural information is most present in the higher frequencies (image detail).where Ni,j co-occurrence matrices are calculated. These matrices capture spatial interrelations among the intensities within the synthesized image level. The co-occurrence matrices are estimated in four different directions resulting in 24 matrices:For all the synthesized images α stands for the direction in the co-occurrence computation. Four statistical measures given by equations (1), (2), (3) and (4) are estimated for each matrix resulting in 96 texture descriptors:where m stands for statistical measure.where Since each feature extracted from the co-occurrence matrices represents a different property of the synthesized image, it is expectable that similar textures have close statistical distributions and consequently they present similar features. This similarity between features can be statistically modeled in a two-dimensional space  since features can be simultaneously observed in the three channel colors for both levels of focus.While the texture descriptors can be considered statistically independent , their oTherefore we propose to model the texture descriptors as a multivariate Gaussian distribution in the color-scale space. In this framework 21 correlations must be computed for each texture descriptor as shown in Table Second order statistics is a well established theory that is completely adequate to represent random vectors. Nevertheless, it is limited by the assumptions of Gaussianity, linearity, stationarity, etc. One of the main properties of the multivariate normal distributions is that the marginal distributions are also normal although the converse is not necessarily true. However, it is very common in practical applications to assume Gaussianity in order to obtain mathematical tractability or to alleviate computational load. Many multivariate statistics used in practice converge in distribution to a multivariate normal, which is acceptable regarding the multivariate central limit theorem. For the most of the Engineering applications, in spite of sometimes the distributions tend to be clearly non-Gaussian, modeling non-Gaussianity usually improves the performance only marginally. This is partially due to the fact that usually higher order moments need much more training data to be accurately modeled than second order moments. For the current application, statistical descriptors tend clearly to be non-Gaussian, especially for pathological cases as shown in Figure HOS characterized by higher order moments are adequate to model non-Gaussian distributions under the assumption that all the moments are finite and so their knowledge is in practice equivalent to the knowledge of their probability function . Third agives a measure of assymmetricity of the probability density function around their mean (skewness), while the fourth central moment gives a measure of the peaky structure of the distribution when compared with the Gaussian. Higher than fourth order moments are used seldom in practice, hence not tried in the ambit of this paper. However, and given the authors previous experience  and preli and k refers to the different color channels and j refers to selected wavelet band, and can therefore take the values of 1 and/or 2. This approach results in the computation of 84 coefficients, 21 different correlations computed for each descriptor as shown in Table where From 15) six third order moments are computed for each descriptor, since six color matrices are available, three in each wavelet scale. Equation (16) provides a larger number of possible combinations, all of them required for modeling the joint probability density function of each descriptor when simultaneously observed in the three colors at each scale. However, and since that correlation of the textural information in the same color channel at different detail levels is already implicitly calculated in the second order moments, the third order moments corresponding to combinations that arise from the same color channel at different scales (eg. HhV) were not calculated in order to diminish the observation vector. Preliminary tests have shown that this approximation does not decrease the classification performance. Therefore the third order moments were calculated for the following cases: HSV, hSV, HsV, HSv, hsv, Hsv, hSv and hsV, accordingly with the nomenclature of Table 5 six thiSumming up 56 higher order moments to the 84 second order moments, each frame is characterized by a set of 140 components in the observation vector.As the features in the observation vector are mutually correlated at different color channels it is very likely that some components of the observation vector can have a negligible effect regarding texture characterization. Therefore, these components must be located and discarded in order to save computational resources and consequently accelerating the automatic diagnosis process. Under the assumption of Gaussianity, on the parameters that characterize the joint and marginal distributions of the second order textural descriptors, principal components can be obtained by using Principal Component Analysis, which is a well established theory based on linear algebra concepts.In order to compute the co-occurrence matrix for the new image, synthesized from the wavelet coefficients from the selected bands, a new algorithm was implemented, to avoid computing co-occurrences in the image corners where no image information exists. The co-occurrence computation was done considering d = 1. A similar algorithm was also developed to calculate the histograms of each frame. A 3.2 GHz Pentium Dual Core processor-based with 1 GB of RAM was used with MATLAB to run the proposed algorithm. The average processing time per frame is about 1 minute, which is unacceptable to real world applications. However, as stated in , the redhttp://www.cs.waikato.ac.nz/ml/weka/). A stratified 10-fold cross-validation procedure was chosen to train a standard multilayer perceptron neural network. The default parameters were kept in the classifier options. The choice of a simple classification scheme, with default parameters, was done in order to make the results more representative of the choice of the features. The 10-fold cross-validation method is a standard procedure to validate machine learning classification outputs and has been found to provide an adequate and accurate estimate of the true error rate [The features were imported into the open source machine learning package WEKA  while roughly 80% of this data belong to 5 normal subjects in order to obtain a large degree of generalization. Figure et al., namely the texture descriptors extracted from the histograms/texture spectrums of capsule endoscopic video frames, were extracted for the available dataset [et al. proposed two different schemes to extract features from texture spectra in the chromatic and achromatic domains, namely a structural approach based on the theory of formal languages, which relies on the definition of elementary texture unit TU and texture unit numbers NTU and a statistical approach, where statistical texture descriptors are calculated from the histograms of the RGB and HSV color spaces of capsule endoscopic video frames. A texture unit may be considered as the smallest complete unit which best characterizes the local texture aspect of a given pixel and its neighborhood in all eight directions of a square raster. The texture spectrum histogram is then obtained as the frequency distribution of all the texture units. After the determination of the texture spectrum for each of the RGB and HSV color channels, nine statistical texture descriptors  are extracted from each one, resulting in 54 features. In the statistical approach, the same statistical descriptors are extracted directly from the color histogram of each of the RGB and HSV color channels, with the obvious drawback of not including any kind of information regarding the spatial relationship between the pixels in the image and, therefore, will most probably fail to distinguish between textures with similar distributions of grey levels.A baseline system for comparison purposes was firstly implemented to serve as a reference for the current approach. This system is based on the algorithm proposed by Kodogiannis  dataset . However dataset , since ti.e. using just the DWT coefficients of higher frequency). Thus, the added value of the inclusion of the multi-scale information can be properly evaluated.For the approach proposed in the present work, a preliminary version of the proposed algorithm, where no multi-scale information is used, was also implemented, discarding (10)  improves in this manner the system performance at least for the current database. Additionally the potential for more improvements over larger databases exist since HOS accurate estimates need a large amount of training data. Table Additionally reducing dimensionality by using PCA reduces performance as expected but only moderately which indicates data correlation in the multi-band features. Even a strong reduction from 140 to 40 coefficients, which is the number of coefficients used in the baseline system for the current approach, maintains a performance slight higher  than when the same dimensionality is used without multi-scale analysis . This clearly shows that multi-scale analysis can improve texture discrimination regarding classification of tumoral tissue in the small bowel.An important note should be addressed regarding the specificity of the algorithm. The color of the small bowel tissues may vary between healthy volunteers and patients, which could lead to unbalances in the classification performance of the proposed algorithm in normal tissue in the GI tract of a diseased patient. However, we have not detected a significant difference in the false positive detection rate in our dataset, being this similar in both healthy and diseased subjects. This can be related with the fact that we are not taking first order descriptors associated with the histogram of the image content but rather texture descriptors that are mostly related to the local variation patterns in the image.Regarding the clinical application of the proposed method, we aim indeed to introduce the developed method in a supervised computer-aided diagnostic system, where the clinicians acts as a final reviewer of the selected frames containing potential textural abnormalities. Therefore, the primary aim of the present work is to alleviate the analysis process of a capsule endoscopy video, reducing the time required by the physician to review the acquired data and to detect abnormalities. This will likely reduce the overall costs associated with this modality. Additionally, it may contribute to a smaller dependency on the physician expertise, allowing users with less experience to achieve better diagnosis performance. Nonetheless, and given the size of CE videos (~50.000 frames), the proposed method will return ~3500 false positives for an entire CE exam. However, the time required to review these selected frames will likely be smaller than the total analysis time required to analyze the entire exam. Nonetheless, it should be stressed that the current performance of the proposed algorithm is still unacceptable for clinical applications in routine practice, since each frame classified as abnormal tissue will imply a deeper analysis by the operating physician, which will take longer than the viewing time in the traditional manual CE exam analysis. This may have a canceling effect on the time savings offered by the proposed algorithm. Therefore, additional efforts aiming the improvement of the classification accuracy should be taken. We are aiming to perform this by including the temporal dynamics to improve the detection rate, by taking into account the classification of neighbor frames to discard wrongly classified frames. In fact, this is a limitation present in most of the CE computer-aided diagnosis algorithms, where the CE frames are analyzed independently. This limitation of the proposed method will be tackled in the near future in order to move towards a software solution capable to be used in clinical routine.The results of this paper show that regarding CE video frames classification texture discrimination can be improved by modeling classical texture descriptors in the color-scale plane instead of the color plane as usually assumed by classical approaches. Although a similar approach was proposed in  the currThe authors declare that they have no competing interests.DB implemented the algorithm together with DR, being the last in charge also of its test. The experimental data was provided by JR and he provided the medical feedback that drove our work. The work was done under supervision of CL, auxiliated in this task by AT. All authors read and approved the final manuscript.


An important goal of micronutrient biofortification is to enhance the amount of bioavailable zinc in the edible seed of cereals and more specifically in the endosperm. The picture is starting to emerge for how zinc is translocated from the soil through the mother plant to the developing seed. On this journey, zinc is transported from symplast to symplast via multiple apoplastic spaces. During each step, zinc is imported into a symplast before it is exported again. Cellular import and export of zinc requires passage through biological membranes, which makes membrane-bound transporters of zinc especially interesting as potential transport bottlenecks. Inside the cell, zinc can be imported into or exported out of organelles by other transporters. The function of several membrane proteins involved in the transport of zinc across the tonoplast, chloroplast or plasma membranes are currently known. These include members of the ZIP (ZRT-IRT-like Protein), and MTP  and heavy metal ATPase (HMA) families. An important player in the transport process is the ligand nicotianamine that binds zinc to increase its solubility in living cells and in this way buffers the intracellular zinc concentration. It is estimated that one-third of the world’s population suffers from zinc deficiency with serious consequences . Zinc deArabidopsis thaliana . This transport into and out of the apoplast seems to be the major bottleneck in the process of nutrient translocation within the plant , zinc (Zn2+), manganese (Mn2+), cobalt (Co2+) and cadmium (Cd2+) (ZRT-IRT-like Protein) family of metal transporters, to which IRT1 and IRT2 belong, have been proposed to import zinc into roots   and is sm (Cd2+) . This trm (Cd2+)  and is tm (Cd2+) , 2013. Am (Cd2+)  but in im (Cd2+) , which eto roots  but thisransport . The barransport . In riceransport .A. halleri is the metabolite nicotianamine  AtMTP1 and AtMTP3 have been implicated in this process , which are primary active zinc pumps, are involved in such loading of the root xylem  is associated in the xylem sap with its predominant organic acid, citric acid , zinc can be transported as a free cation. In the zinc hyperaccumulator ric acid . In A. horm only . In riceorm only , but it Zinc is not transported directly to the developing seed by the xylem. Typically, in order to reach the seed, zinc first makes a detour to the leaves. Here it is taken up from the xylem into living xylem parenchyma cells of the leaf symplast. This process is mediated by transport proteins yet to be characterized. Subsequently, zinc is exported from mesophyll cells into the leaf apoplast from where it is loaded into the phloem, which provides the vascular route to the developing seeds. Because of their expression in the vasculature, AtIRT3  and OsZIArabidopsis HMA1 is localized to the chloroplast envelope and involved in the export of zinc  family, which appear to transport complexes of zinc and nicotianamine across membranes, are highly expressed in senescing leaves , and migThe pH of the phloem is slightly alkaline , and theArabidopsis seed. Theseed consists of three genetically distinct tissues: the maternal seed coat, the zygotic embryo and the triploid zygotic endosperm. It is anticipated that such diverse tissues do not contain any symplastic connections and apoplastic barriers are likely to be separating these three tissues in Arabidopsis (Arabidopsis seed where active transport system(s) yet to be identified must be present for translocation of zinc to the embryo: (1) between the outer and inner integuments in the seed coat, (2) between the seed coat and the endosperm, and (3) between the endosperm and the embryo. As active transport is required for zinc in order to escape living cells having a membrane potential highly negative on the inside, zinc efflux from symplasts in the seeds resemble the situation of xylem loading in the root.The mechanisms involved in phloem unloading and post-phloem movement of zinc in the developing seed are not well understood, but a model has been proposed based on the findings of several apoplastic barriers in the bidopsis . Phloem bidopsis . Anotherbidopsis . This giArabidopsis seed. In barley nutrients are also unloaded symplastically from the phloem, but they do not end up in the seed coat as in Arabidopsis. Instead the nutrients flow to highly specialized nucellar projection transfer cells. In the developing barley grain, apparently a single apoplastic barrier is present between the maternal transfer cells and the filial endosperm  is highly expressed and nicotianamine has been shown to be involved in root-to-shoot translocation of zinc with a five-fold decrease in NAS2-RNAi lines. This has been ascribed to a role for nicotianamine in the symplastic mobility of zinc in the root toward the pericycle cells (A. halleri NAS2-RNAi lines (HMA4-RNAi lines (In the zinc hyperaccumulator le cells . The pheAi lines  and the Ai lines  are someNAS genes in rice is able to increase the zinc concentration in the rice grain by in average twofold, also in the polished grain (NAS in combination with ferritin affects Fe accumulation in the rice endosperm (OsNAS do not show an increase in cadmium (Nicotianamine seems to be highly important for the intercellular mobility of zinc but might also be involved in enhancing the mobility of zinc in the phloem essential for getting zinc to the developing seed. Several reports have shown that the constitutive overexpression of ed grain . This prndosperm . Nicotiandosperm  and one ndosperm . Also, indosperm . A signi cadmium , 2011.NAS genes makes nicotianamine an interesting target for zinc biofortification.Taken together, the transport of zinc from the root to the shoot and further to the developing seed results from an interplay not only between different membrane transporters but also between the mobility of zinc both intercellularly and between organs by binding to ligands. The presence of multigenic factors that control the amount of zinc ending up in the edible parts of the seed makes it a challenging future to increase bioavailable zinc in the edible parts of cereal grains. The substantial increase in the grain zinc concentration found in plants overexpressing 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.


The unsymmetrical-cross multihexagon-grid search (UMHexagonS) is one of the best fast Motion Estimation (ME) algorithms in video encoding software. It achieves an excellent coding performance by using hybrid block matching search pattern and multiple initial search point predictors at the cost of the computational complexity of ME increased. Reducing time consuming of ME is one of the key factors to improve video coding efficiency. In this paper, we propose an adaptive motion estimation scheme to further reduce the calculation redundancy of UMHexagonS. Firstly, new motion estimation search patterns have been designed according to the statistical results of motion vector (MV) distribution information. Then, design a MV distribution prediction method, including prediction of the size of MV and the direction of MV. At last, according to the MV distribution prediction results, achieve self-adaptive subregional searching by the new estimation search patterns. Experimental results show that more than 50% of total search points are dramatically reduced compared to the UMHexagonS algorithm in JM 18.4 of H.264/AVC. As a result, the proposed algorithm scheme can save the ME time up to 20.86% while the rate-distortion performance is not compromised. Advances in the mobile communication technologies have enabled portable devices to run complex multimedia applications involving video processing. Due to the rapid growth of the multimedia service, the video compression becomes essential for reducing the required bandwidth for transmission and storage in many applications. In video compression, motion estimation (ME) is the most crucial part since it can reduce the total video data efficiently by exploiting the temporal correlation among successive frames of a video sequence to achieve a high data compression ratio.The block-matching algorithm (BMA) based ME has been widely used in many video compression standards, such as the H.26x and the MPEG-x families because of its simplicity and effectiveness. The previous video coding standards  adopt the fixed block size motion estimation, which uses the same block size for both static and moving objects. The latest H.264/AVC  is the actual value; r is the predicted value which is depend on ref and m; ref is the value of the reference frame; m =  is the coordinate of the current MV; mx and my are the motion components in horizontal and vertical, respectively.In integer prediction for most of the motion estimation search algorithms, the criterion to obtain MV is the sum of absolute differences (SAD). SAD is defined as follows:During motion estimation search, the minimum SAD is chosen and the corresponding MV is regarded as a candidate MV. Because of the large computational working, motion estimation search costs the main time of the whole encoding process.Compared to full search algorithm, UMHexagonS algorithm claims that it can reduce 90% of motion estimation time, drop less than 0.05 dB PSNR, and maintain a low bit rate. In order to make the initial search point close to the best prediction point, UMHexagonS algorithm provides several different initial search point predictions. UMHexagonS algorithm searching strategy begins with cursory search pattern, then turns to elaborate search patterns. With multipatterns, UMHexagonS algorithm gets rid of the disadvantage that the traditional fast algorithms are easy to trap in local minima. In addition, the self-adaptive early termination threshold makes UMHexagonS algorithm more efficient by cutting out the searching process. To sum up, UMHexagonS algorithm improves the effectiveness and robustness of the prediction greatly.based on the feature that layers of search points are progressively decreasing by search radius decreasing designs a new uneven multihexagon-grid search pattern;based on the macroblock motion intensity adaptively selects the layers of the uneven multihexagon-grid search pattern;based on the macroblock motion intensity adaptively selects whether perform the 5 × 5 full search pattern.Apart from the initial search point prediction, it causes a lot of unnecessary search points during the search process that UMHexagonS algorithm does not combine pattern search with MV characteristics. Because of the nonuniform distributed MVs in each search step, there is no need to traverse all search points to determine the best matched point. The large search pattern does not take motion characteristics into consideration and point-by-point blind searching contributes little to improving the accuracy of motion estimation, while consuming lots of encoding time. On the basis of the above features, in previous work, we did some researches and proposed NUMHexagonS algorithm. NUMHexagonS algorithm improves the following ways to optimize:NUMHexagonS algorithm search process is shown in Although NUMHexagonS algorithm makes a good progress in reducing motion estimation time, it is still rough that NUMHexagonS algorithm combines MV characteristics with search strategy. It is not precise to predict the MV that NUMHexagonS algorithm only carries out the macroblock motion intensity. Intensity is one of the MV characteristics, but it lacks direction information. This paper will make better use of MV characteristics based on NUMHexagonS algorithm. The statistic of MVs distribution will be figured out and depend on that we develop a more precise search strategy. Next section will mainly analyse MV distribution characteristics.The uneven multihexagon-grid search used in UMHexagonS algorithm has a wide search range and costs lots of search points; hence, it takes too much time. Therefore, it is very necessary to research the feature of MV distribution.In order to obtain the statistic of MV distribution, the search window is divided into multilayer octagon as shown in Central region indicates no motion, and it means that the MV is similar to 0. Other regions indicate the positions where the best matched points appear. Thus, all regions are defined as follows:In  each RanAccording to Motion vectors located in horizontal and vertical are more than that in other directions and the distribution probability in horizontal is higher than that in vertical.A large number of MV's intensity is close to zero.Near the center or the boundary of search window appears higher probability of MVs.In order to further investigate the characteristics of MV distribution, figure out the average numbers which are every sequence in the same region in Characteristic (1) complies with the phenomena that most of video sequence motions exist in horizontal more than in vertical, like human walking, boating, car running, and so forth. Characteristic (2) indicates that the video sequence with low-motion macroblocks shows a high probability of MV distribution in the origin or near the origin, like broadcasting, rotating shoot, and so forth, and also including most of static backgrounds. Characteristic (3) indicates that the video sequence with high motion macroblock appears a high probability of MV distribution at the boundary, like the object moving out of the search window. According to the above characteristics, the search strategy cannot achieve the purpose of accurate search which only distinguishes video sequences simply by low motion or high motion. Therefore, it is necessary to refine those search patterns based on MV distribution, so that it can make motion estimation process more accurately and reduce search points further to raise search efficiency.Based on MV distribution characteristics, the proposed algorithm makes NUMHexagonS algorithm further optimized. The patterns of NUMHexagonS algorithm are divided into different areas which are selected adaptively by MV distribution prediction, thereby the proposed algorithm achieves reducing the motion estimation search points.Unsymmetrical cross search and uneven multihexagon-grid search belong to cursory search processes with wide search ranges. The MV distribution prediction can pinpoint the search position without large search range, so it is necessary to divide the original patterns into different areas and draw up new search strategies.The unsymmetrical cross search pattern of NUMHexagonS algorithm is divided into four Groups as shown in The uneven multihexagon-grid search pattern of NUMHexagonS algorithm is divided into 32 regions as shown in Moreover, in order to speed up the motion estimation, during the search process, the search patterns will be skipped as soon as the MV distribution prediction is equal to 0. In this case the MV is regarded as in center. This search strategy complies with the requirement of characteristic (2) mentioned in To predict MV distribution, it is essential to calculate the size and the direction of the MV.γ)  predmincost represents the upper limit threshold of the MV prediction; (1 + δ)  predmincost represents the lower limit threshold of the MV prediction; in addition predmincost represents the minimum RDmincost of the predicted MV. RDmincost represents the rate-distortion value calculated during the motion estimation and it is defined as follows:Jmotion is the RDmincost; pred is the predicted MV; R is the bit number of MV difference cost; λmotion is the Lagrange parameter; s, m, ref, and SAD are mentioned in , and then the direction of MV can be described by Direction Vector, namely, k which is used to represent the direction of MV as in . The small size macroblock can be predicted by the big size macroblock, because the small size macroblock can be regarded as segment of the big size macroblock. The equation of the Up-Layer Prediction is described as follows:t is predicted by MVt−1 with the same position in the previous frame. The equation of the Corresponding-block Prediction is described as follows:Corresponding-block Prediction belongs to temporal prediction. It makes use of the correlation of the corresponding frame. The different macroblocks with the same position in the current frame and the previous frame are likely to be part of a complete action, so the current predicted MVpred_ref is predicted by MVref. The equation of the Neighboring Reference frame Prediction is described as follows:Neighboring Reference frame Prediction belongs to temporal prediction as well. It makes use of the reference frames. Neighboring Reference frame Prediction is as the same as the Corresponding-block Prediction, but the former will take a quantity of neighbor frames to make the prediction more accurate. The current predicted MVRegard the initial search point as the search center and perform the first time MV distribution prediction in Step 2. In this step the size and the direction of MV will be predicted. If the size of MV distribution prediction is 0, the Step 3 and Step 4 should be skipped, or the searching goes into next step.In Step 3 choose the search Group in the modified unsymmetrical cross search pattern according to the direction of MV distribution prediction.After finishing the modified unsymmetrical cross search, the second time MV distribution prediction is going to perform. In Step 4, the size of MV is predicted. When the MV is low motion, the 5 × 5 full search has to be performed. In this situation the MV is distributed in a low range around the center and the elaborate full search must be selected to ensure finding the most accurate matched point. The optional 5 × 5 full search in Step 5 not only devotes to searching the best matched point accurately but also avoids wasting search points effectively.Then perform the third time MV distribution prediction in Step 6. In this step, the size and the direction of MV will be predicted. If the size of MV distribution prediction is 0, the Step 7 should be skipped, or choose the specific Layer and Range in modified uneven multihexagon-grid search.In Steps 8 and 9 the extended hexagon search and the extend diamond search are performed. The extended hexagon search uses the hexagon pattern to search repeatedly until it obtains the best matched point. The extended diamond search uses the small diamond pattern to search repeatedly until it obtains the final MV. Then, the motion estimation is finished.To further test the effectiveness of the proposed algorithm, simulations have been performed over different intensity QCIF format (176 × 144) standard video sequences: CREW, HARBOUR, ICE, MOBILE, CITY, and COASTGUARD. Simulations present the results of comparing the proposed algorithm with UMHexagonS algorithm and NUMHexagonS algorithm by Y-PSNR, Bit-rate, ME-time, and average ME search points. Y-PSNR is the peak signal to noise ratio of luminance which is defined as follows:s is the current original image and c is the compensated prediction image.In addiction, In order to compare the difference between the proposed algorithm, UMHexagonS algorithm, and NUMHexagonS algorithm, ME time Gain, Y PSNR Gain and Bits rate Gain are defined as follows:The reference software version is JM 18.4. The experimental conditions are shown in To make sure the experimental results meaningful, all the standard sequences are generated in the same configuration. The experimental results are shown in In To compare the efficiency between UMHexagonS algorithm, NUMHexagonS algorithm, and the proposed algorithm accurately, the search points are counted during ME process and drawn in Because each of the 7 macroblock mode should be performed the motion estimation to get the MV for mode decision, the proposed algorithm can save several-fold encoding time by reducing the search points in each time motion estimation. The MV distribution prediction is performed three times to locate the MV before patterns search which is the key point to speed up the motion estimation meanwhile maintaining the search accuracy.In this paper, a flexible and fast ME scheme is proposed. It makes full use of the motion continuity and motion integrity of the video coding objects and combined MV distribution prediction with the new search patterns to make the search position more accurate. The proposed MV distribution prediction algorithm chooses search direction by predicting the MV direction and selects search level by predicting the MV size. Then, the proposed adaptive ME scheme further narrowed the search range of ME and reduces the unnecessary search points. The experimental results show that the proposed algorithm decreased by 20.86% of ME time and 54.62% of ME search points, respectively, compared to UMHexagonS algorithm (JM18.4), while maintaining the quality of the original structure and reconstruction bit streams. The proposed algorithm improves the performance of H.264/AVC real-time encoding effectively, and it can be combined with other fast video coding techniques such as fast mode prediction algorithm and reference frame selection algorithm to improve the encoding speed. The proposed prediction concept for ME estimation in this paper can be further used in HEVC which is the next phase of research direction.


Conventional quasi-static ultrasound elastography is easily applied to obtain axial strain components along the compression direction, with the results inverted to represent the distribution of tissue hardness under the assumption of constant internal stresses. However, previous works of quasi-static ultrasound elastography have found it difficult to obtain the lateral and shear strain components, due to the poor lateral resolution of conventional ultrasound probes. The physical nature of the strain field is a continuous vector field, which should be fully described by the axial, lateral, and shear strain components, and the clinical value of lateral and shear strain components of deformed tissue is gradually being recognized by both engineers and clinicians. Therefore, a biomechanical-model-constrained filtering framework is proposed here for recovering a full displacement field at a high spatial resolution from the noisy ultrasound data. In our implementation, after the biomechanical model constraint is integrated into the state-space equation, both the axial and lateral displacement components can be recovered at a high spatial resolution from the noisy displacement measurements using a robust  The routine clinical practice of palpation represents a qualitative assessment of tissue stiffness based on the significant difference in elastic properties between normal and diseased tissues Ultrasound elastography, which was originally proposed by Ophir et al. in 1991 Elastography can be broadly classified into two groups based on the mechanisms underlying the generation of the elastograms. In the first group, the relative mechanical attributes are calculated directly from experimental observations , and axial, lateral, and/or shear strains are calculated from the tissue displacement field and then inverted to produce elastograms x-, y-, and z- axes) simultaneously and continuously. However, early methods only focus ed on axial displacement estimation because traditional ultrasound probes provide high spatial resolution along the axial direction, but poor spatial resolution along the lateral direction. A widely used displacement estimation technique is time delay estimation (TDE) For both the calculation of strain images and the reconstruction of elastic parameters, accurate estimation of tissue displacements is the first important step that will critically affect the image quality. This has prompted the development of different motion-tracking techniques for recovering tissue displacements during the past 2 decades However, axial displacements estimated from single ultrasound RF lines are insufficient for reconstruct ing modulus elastograms In this paper we present a biomechanical-model-based filtering framework for improving the quality of the full displacement field obtained from noisy and sparse ultrasound data. A modified PSE method that we proposed previous ly The whole framework includes two parts, motion tracking and motion recovery, as shown in We previously developed a PSE method to calculate the axial displacement of soft tissue under quasi-static compression. The ultrasound RF signals before and after deformation can be modeled in complex expressions:The complex cross-correlation function of a prior i knowledge of the displacement  in thisOne initialization issue of In previous studies of biomechanics and ultrasound elastography, the deterministic FEM has provided an efficient representation of complex tissue geometry and a convenient and effective computational framework a priori statistics, and the observations and loads are corrupted by noise. In this way the stochastic differential or difference equations are combined with the FEM to study dynamic structures for which there is uncertainty in their structural parameters and/or measurements. In the analysis of ultrasound elastography, this framework based on Ito calculus from a Bayesian point of view a priori mechanical model and a posteriori ultrasound imaging pairs.The stochastic FEM (SFEM) has been used for structural dynamics analysis in probabilistic frameworks In our 2D implementation, a Delaunay triangulated finite element mesh is constructed at interested area segmented manually in the first frame of ultrasound elastography. An isoparametric formulation defined in a natural coordinate system is used, where the basis functions for a trinodal linear element are linear functions of the nodal coordinates From Equation (16) to (18), With sampling interval a priori estimates of The popular Kalman filter calculates the estimation error using the The denominator of Many strategies can be used to implement the 1. Compute the FEM matrices; that is 2. Initialize the 3. Start the following iterative procedure:It is obvious that the above This section uses three groups of data–synthetic data, phantom data, and clinical data–to evaluate the performance of our filtering strategy. First, a finite -element model was constructed in ABAQUS  with a hard circular inclusion embedded in a soft background to generate the synthetic data: the displacement map was obtained by applying axial loading to the sample surface as the ground truth, and various levels and types of white noises were added to the simulated axial and lateral displacements in order to construct measurements for the 1. Using the same boundary condition as described above, six sets of displacements were obtained for Poisson's ratio of A x-axis of y-axis is the average nodal position error. The x-axis of y-axis is the average nodal position error. 2. The second experiment evaluated the effect of modeling mismatch or external disturbances on the performance of our method. Unlike the earlier experiment, in this experiment only the axial displacement (with SNR = 30 dB) was used as the measurement, and the average nodal position error  was calculated to evaluate the accuracy of the estimation. The process noise  comprising a transducer having a center frequency of 5 MHz. All of the ultrasound data were collected using freehand elastography on an Elasticity QA Phantom (CIRS Technology). The axial displacements were first obtained using our PSE method from the RF signals as measurements to our method, and the full displacement field  was then recovered at a high spatial resolution from these axial-displacement measurements through our model-based filtering framework. The process noise  in a priori error bounds of disturbances/noises for the iterative recovery process, whereas most previous model-based approaches have require d more information about the disturbances/noise, such as the statistical properties a priori information, our filtering framework recursively assimilate sparse measurements and the biomechanical-model-based constraint, and eventually generate physically meaningful optimal estimates, thereby obtaining a full and smoother displacement field. Noise is compressed in our filtering framework via the efficient determination of optimal results using the The kernel of our proposed approach is the The first of our experiments on synthetic data test ed the tolerance s of the TIAM and our method to variation of Poisson's ratio of the object under investigation. The TIAM gives a poor TIAM see . Our expThe second experiment on synthetic data investigated the tolerance of our method to modeling mismatch and external noises. The model-data mismatch was defined as be the difference between the ground truth and the model used in our filtering strategy, such as in the boundary conditions, Young's modulus, or Poisson's ratio. Since material properties play a key role in the biomechanical modeling framework, we first examine d the effect of material-properties mismatch. Because the adopted biomechanical model is linear elasticity, the effect of the mismatch of Young's modulus and Poisson's ratio was examined in our experiments. Furthermore, since the measurements of lateral displacement provided by elastography are always sparse due to the poor spatial resolution of the ultrasound probe, the ability to recover high-quality lateral displacements was adopted as an important performance indicator in our experiments. The impact of the mismatch of Poisson's ratio on the recovery of the lateral displacement was found to be acceptable over a considerable range of modeling mismatch es  = 2–8; , while tFor the first group of phantom data, a 2D displacement field was recovered at a high spatial resolution only from these axial-displacement measurements through our model-based filtering framework. The strain tensors were calculated based on the recovered axial and lateral displacements. The effectiveness of our filtering strategy with biomechanical strategy in estimating lateral displacements was also extensively examined in the third groups of data. The obtained images indicate that the quality of the displacement field and strain maps was greatly improved using our model-based method. Lateral-strain images, which are usually severely degraded by the noise of lateral displacements, can be recovered with higher quality and have shown some prospective clinical implications. The recovered axial and lateral displacements can be used to reconstruct all components of the strain tensor, as shown in The measurements, the number of iterations and the initialization of the external noise, Young's modulus, and Poisson's ratio are all important in our filtering strategy. The measurements represent information about the examined object, but our method does not explicitly require the type of measurements. Our filtering strategy can recover the full displacement field under the biomechanical modeling constraint. As evident from the experiments involving synthetic data , however, the images of shear strain did not provide any useful clinical information. This issue that should be carefully studied in the near future. Furthermore, the displacement quantification is heavily dependent on the number of elements in and quality of the finite element mesh. If the input data are reasonably accurate, increasing the number of mesh element s will definitely improve the solution accuracy; however, the current experiments indicate that this could make the computational cost unacceptable. Analysis on the computational consumption of our filtering strategy will be studied in the near future, and methods for reducing the computation cost will need to be applied before it could be implemented in a real-time ultrasound system.Several other key issues also remain to be addressed. Since most soft tissues are nonlinear viscoelastic materials, the linear isotropic constructive equations do not properly describe their mechanical behaviors. Further research based on nonlinear material model would be useful for estimating the displacement field from ultrasound measurements. Of equal importance, we should also point out that the distribution of tissue elastic properties in the region of interest is generally not unique, and the performance of our current framework still depends on the appropriate initialization of the parameters of the biomechanical model. The chosen values must be as realistic as possible in order to acquire accurate results. As a continuation of this work, a future study will focus on an extended filtering framework that can estimate tissue displacement and elastic parameters simultaneously. Such a simultaneous-estimation framework is expected to further reduce the dependency on the choice of initial parameters. More work on the clinical application of shear-strain imaging is also expected. Further experiments should also be undertaken to more deeply evaluate the displacement values recovered by our framework. In these experiments the recovered displacements will be used to reconstruct the tissue elasticity modulus, which is likely to be more affected by the quality of the displacement field. Thus, our framework is predicted to be useful in the reconstruction of tissue elasticity.Overall, our model-based framework can accomplish a high-quality tissue motion recovery  from the sparse and noisy measurements. Furthermore, our proposed filtering framework has shown potential in recover ing meaningful strain maps from available ultrasound RF data.


Directional Variance Adjustment (DVA) algorithm, which diminishes the systematic error. In a thorough empirical study for the US, European, and Hong Kong stock market we show that our proposed method leads to improved portfolio allocation.Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices derived from the statistical Factor Analysis model exhibit a systematic error, which is similar to the well-known systematic error of the spectrum of the sample covariance matrix. Moreover, we introduce the  The advent of modern finance began with Markowitz and his seminal paper on portfolio optimization Covariance estimation and coping with its uncertainties have occupied both researchers and practitioners since then. One of the major difficulties with robust covariance matrix estimation arises from nonstationarity of financial time series high dimensional and small sample size are rather vague and interdependent, the difficulty of the task of covariance estimation is commonly characterized by the ratio of sample size to dimensionality, As the terms Directional Variance Adjustment (DVA) algorithm, which estimates the magnitude of the imposed bias in specific directions by means of a Monte Carlo sampling approach and hence enables for its correction.In this paper, we will analyse a purely statistical factor model called (Maximum Likelihood) Factor Analysis In the portfolio optimization literature Monte Carlo sampling is known from Resampling Efficiency At this point we would like to emphasize that in this paper we will solely focus on the structure of risk in the stock market. A discussion of the structure of expected returns . Here, “best” model refers to the model that maximizes the data likelihood. The application of Factor Analysis to financial data was first introduced in order to test the Arbitrage Pricing Theory Factor Analysis models the asset returns as a mixture of unobserved source signals with additive noise. The signals and the noise are assumed to be i.i.d., zero-mean normally distributed. Independence of the noise  for independent and standard normal factors. For Factor Analysis the number of parameters is reduced from Alternative approaches to solving the optimization problem are proposed in the literature, the best known is the quasi-newton method by Jöreskog Unlike for the sample covariance, there are no analytical results for the spectrum of the Factor Analysis covariance matrix. Therefore, we run a simulation to study systematic errors in Factor Analysis. To this end, we generate In Factor Subspace) and another orthonormal basis In the following we will study systematic errors in terms of misspecification of directional variances. More precisely, we will investigate systematic errors in the factor subspace and its complementary orthogonal space separately. To this end we first calculate an orthonormal basis For each subspace, we obtain a new basis , about 600 European stocks (3.1.2001–20.4.2009) and a set of 200 stocks from the Hong Kong stock exchange (3.1.2001–26.9.2008). Removing stocks which do not have data for the whole time horizon covered by the data set, the Hong Kong data set reduces to 100 assets.There are different applications of covariance matrices in portfolio optimization. Covariance matrices are needed for index tracking, hedging and the search for minimum variance portfolios. In the following, we will focus on minimum variance portfolios,Depending on the particular application, additional constraints are incorporated into the optimization. Commonly applied constraints include:Note that the application of constraints tremendously prunes the set of feasible portfolios and hence diminishes the influence of the covariance estimate In the case of small sample sizes, this approach will tend to overfit the directions of smallest variance and is hence expected to favour the restricted covariance estimators. Therefore, we will also investigate the performances of portfolios obtained from a regularized optimization problem of eq. (10), where the additional regularization enforces diversified portfolios.In order to evaluate the performance of the different covariance estimator we use the realized (out-of-sample) variance of the estimated portfolios:In order to reduce the variance of the performance evaluation and to thoroughly explore the estimated covariance structure, In this section we will provide portfolio simulation results for different covariance estimation approaches, namely the sample covariance matrix, Resampling Efficiency, the Fama-French three-factor model, shrinkage to a one-factor Model, a Factor Analysis model with seven factors, and a directional variance adjusted Factor Analysis (DVA FA). The results for the different markets are summarized in First note that the equal weights portfolio has very high risk, a result which is also reported by Kourtis et al. As expected, the sample covariance matrix is not the most suitable tool for portfolio optimization. Across all data sets, the portfolios derived from the different factor based models and Shrinkage clearly outperform the sample covariance matrix based portfolios in terms of realized risk. A direct comparison of these models reveals that the DVA method always significantly outperforms Fama-French, standard Factor Analysis and Shrinkage with respect to realized variance and realized absolute deviation. On our data sets, Resampling Efficiency does not give an advantage over the sample covariance matrix.The Sharpe-Ratios do not give a clear picture: Fama-French, Statistical Factor Modelling and Shrinkage each perform best in one market. This is not suprising, as we did not optimize for high returns.The turnovers on the other hand show an additional advantage of DVA Factor Analysis over standard Factor Analysis: covariance estimates are more stable.Without knowledge of the covariance structure of the assets, the best portfolio allocation would have weights inverse to the variance of the assets and hence be highly diversified. Minimization of eq. (10), on the other hand, gives the optimal portfolio only for the true covariance matrix. Therefore, for a given covariance matrix estimate, it should in principle be possible to additionally reduce the realized risk of a portfolio by increasing its diversification, e.g., by regularization of eq. (10).Consequently, the aim of the following analysis is twofold. First of all and from a theoretical perspective, we want to investigate if the superior performance of the DVA method can be simply explained away by a higher degree of diversification or if the true covariance structure is indeed better captured. Secondly, with respect to practical considerations, we are interested in the best achievable performance.In order to analyze these aspects, for each of the covariance matrix estimates In particular, we set the metric ios cmp.  and 2. AShrinkage to the one-factor model profits as well from additional shrinkage to Surprisingly, the Fama-French Three-Factor model benefits less from regularization than Shrinkage, although the unregularized performance is similar. This implies that the performance gain of the unregularized Fama-French model over the sample covariance matrix is mainly due to a strong imposed prior towards highly diversified portfolios. Compared to the statistical factor models FA and DVA FA, the performance difference remains on the same level as without additional regularization. This means that the covariance structure is better captured by the statistical Factor models than by the Fama-French model. These effects are strongest for the US and EU markets.The risk of the portfolios obtained from the Factor Analysis model as well as from its DVA version also improve considerably. At the optimal degree of regularization, the DVA FA model significantly outperforms the optimally regularized sample covariance matrix based model for all markets. Regarding eq. (13) as being a shrinkage towards At the optimal degree of regularization the difference in performance between the standard Factor Analysis and the DVA Factor Analysis is reduced. In general, this was to be expected as regularization can equivalently be achieved either by adding a penalty term to the objective function or by additionally constraining the feasible set. In this respect, it was shown that the actual influence of the covariance matrix estimate on the minimum variance portfolio diminishes when additionally constraining the set of feasible portfolios Nevertheless, in the US and EU market, the peformance gain in MAD of DVA over standard Factor Analysis remains significant at the 5% level. In Hong Kong the difference is -for optimal regularization- not significant.Comparing the different markets, it turns out that the Hong Kong market shows a slightly different behavior than the American and European. At the Hong Kong market, all methods likewise benefit from additional diversification. One possible explanation is that the HK data set contains quite a few outliers and missing data as opposed to the US and EU data. Thus covariance estimates as well as least square estimates of factor exposures are hampered in general. Hence and in contrast to the other markets, the Fama-French model also clearly profits from the additional regularization, although its overall performance remains inferior to DVA Factor Analysis.The fundamental issue in portfolio allocation is the accurate and precise estimation of the covariance matrix of asset returns from historical data. Among many challenges, the data is typically high dimensional, noisy, contaminated with outliers and nonstationarity interferes with the use of long estimation windows. Thus, reliable statistical parameter estimation is impeded. Our work has contributed to alleviate this problem in theoretical and practical aspects: we (1) demonstrated that the data driven statistical Factor Analysis model has a systematic estimation error (2) proposed the algorithmic Directional Variance Adjustment (DVA) framework, which alleviates this bias, and finally (3) provided extensive simulations of minimum variance portfolios of EU, US and Hong Kong markets, underpinning the usefulness of the DVA approach in terms of significant gains in realized variance and realized mean absolute deviation. Compared to standard Factor Analysis, covariance estimates are more stable and turnover is reduced. or each covariance estimator, we additionally studied the effect of regularizing the minimum variance portfolios towards a higher degree of diversification. As expected, diversification improved portfolio performance across the different estimators. Our empirical study showed that while regularization slightly decreases the overall advantage gained by DVA, the remaining difference in the minimum stayed significant for the US and EU data sets, here the DVA Factor Analysis method is superior to standard Factor Analysis.A second interesting finding of the regularization experiments was that the advantage of the Fama-French model over the sample covariance matrix estimator appears rather due to an imposed strong diversification prior than to an improved estimation of the underlying covariance structure. Here, clearly the combination of regularization and statistical factor models like standard FA and in particular DVA FA led to better model performance.Note, however, that down-weighting/regularizing away the estimated correlations may not always be a valid option. In an application where the covariance structure is of higher importance - e.g. because an index needs to be tracked with a reduced number of assets - increased diversification would clearly be no option.Therefore, both scenarios, the one with and the one without regularization, yield interesting insight and provide clear evidence for the superiority of DVA FA.Whilst we have studied and modeled daily returns, the DVA method is of course equally capable of being employed to derive covariances for intraday returns. Intraday covariance matrices are particularly relevant when dealing with portfolios with significant (intraday) churn. Examples of such portfolios include internalization portfolios at most major brokerages, and those used for market making. Using DVA FA, a covariance matrix may be tuned for the typical period a position remains in a portfolio, allowing, potentially, better risk management and asset allocation.We do not consider serial correlation, as it is common for covariance estimation methods like Shrinkage