<sod>Axiomatically{{clarify|date=September 2016}} determined functional models of simple cells in V1 have been determined by Lindeberg<ref name=Lin13BICY>[http://dx.doi.org/10.1007/s00422-013-0569-z T. Lindeberg "A computational theory of visual receptive fields", Biological Cybernetics 107(6): 589-635, 2013]</ref><ref name=Lin16-JMIV>[http://www.csc.kth.se/~tony/abstracts/Lin16-JMIV.html T. Lindeberg "Time-causal and time-recursive spatio-temporal receptive fields", Journal of Mathematical Imaging and Vision 55(1): 50-88, 2016.]</ref> in terms of directional derivatives{{clarify|date=September 2016}} of affine Gaussian kernels{{clarify|date=September 2016}} over the spatial domain{{clarify|date=September 2016}} in combination with temporal derivatives{{clarify|date=September 2016}} of either non-causal or time-causal scale-space kernels{{clarify|date=September 2016}} over the temporal domain (see [[axiomatic theory of receptive fields]]). Specifically, it has been shown that this theory both leads to predictions about receptive fields with good qualitative agreement with the biological receptive field measurements performed by DeAngelis et al <ref>G. C. DeAngelis, I. Ohzawa and R. D. Freeman "Receptive field dynamics in the central visual pathways". Trends Neurosci. 18(10), 451–457, 1995.</ref><ref>G. C. DeAngelis and A. Anzai "A modern view of the classical receptive field: linear and non-linear spatio-temporal processing by V1 neurons. In: Chalupa, L.M., Werner, J.S. (eds.) The Visual Neurosciences, vol. 1, pp. 704–719. MIT Press, Cambridge, 2004.</ref> and guarantees good theoretical properties of the mathematical receptive field model, including covariance and invariance properties under natural image transformations.<ref name=Lin13PONE>[http://dx.doi.org/10.1371/journal.pone.0066990 T. Lindeberg "Invariance of visual operations at the level of receptive fields", PLOS ONE 8(7): e66990, pages 1-33, 2013]</ref>{{relevance inline|date=September 2016}}<eod>
<sod>Axiomatically{{clarify|date=September 2016}} determined functional models of simple cells in V1 have been determined by Lindeberg<ref name=Lin13BICY>[http://dx.doi.org/10.1007/s00422-013-0569-z T. Lindeberg "A computational theory of visual receptive fields", Biological Cybernetics 107(6): 589-635, 2013]</ref><ref name=Lin16-JMIV>[http://www.csc.kth.se/~tony/abstracts/Lin16-JMIV.html T. Lindeberg "Time-causal and time-recursive spatio-temporal receptive fields", Journal of Mathematical Imaging and Vision 55(1): 50-88, 2016.]</ref> in terms of directional derivatives{{clarify|date=September 2016}} of affine Gaussian kernels{{clarify|date=September 2016}} over the spatial domain{{clarify|date=September 2016}} in combination with temporal derivatives{{clarify|date=September 2016}} of either non-causal or time-causal scale-space kernels{{clarify|date=September 2016}} over the temporal domain (see [[axiomatic theory of receptive fields]]). Specifically, it has been shown that this theory both leads to predictions about receptive fields with good qualitative agreement with the biological receptive field measurements performed by DeAngelis et al. <ref>G. C. DeAngelis, I. Ohzawa and R. D. Freeman "Receptive field dynamics in the central visual pathways". Trends Neurosci. 18(10), 451–457, 1995.</ref><ref>G. C. DeAngelis and A. Anzai "A modern view of the classical receptive field: linear and non-linear spatio-temporal processing by V1 neurons. In: Chalupa, L.M., Werner, J.S. (eds.) The Visual Neurosciences, vol. 1, pp. 704–719. MIT Press, Cambridge, 2004.</ref> and guarantees good theoretical properties of the mathematical receptive field model, including covariance and invariance properties under natural image transformations.<ref name=Lin13PONE>[http://dx.doi.org/10.1371/journal.pone.0066990 T. Lindeberg "Invariance of visual operations at the level of receptive fields", PLOS ONE 8(7): e66990, pages 1-33, 2013]</ref>{{relevance inline|date=September 2016}}<eod>