scholarly journals The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images

2017 ◽  
Vol 29 (10) ◽  
pp. 2769-2799 ◽  
Author(s):  
P. N. Loxley
Keyword(s):  
Receptive Field ◽  
Spatial Frequency ◽  
Generative Model ◽  
Natural Image ◽  
Two Dimensional ◽  
Natural Image Statistics ◽  
Image Statistics ◽  
Gabor Function ◽  
Gabor Functions ◽  
Probabilistic Generative Model

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Different spatial frequency bands selectively signal for natural image statistics in the early visual system

2012 ◽  
Vol 108 (8) ◽  
pp. 2160-2172 ◽  
Author(s):  
Bruce C. Hansen ◽  
Aaron P. Johnson ◽  
Dave Ellemberg
Keyword(s):  
Spatial Frequency ◽  
Broad Band ◽  
Amplitude Spectrum ◽  
Structural Complexity ◽  
Luminance Contrast ◽  
Natural Image ◽  
Natural Image Statistics ◽  
Natural Scene ◽  
Image Statistics ◽  
Neural Processes

Early visual evoked potentials (VEPs) measured in humans have recently been observed to be modulated by the image statistics of natural scene imagery. Specifically, the early VEP is dominated by a strong positivity when participants view minimally complex natural scene imagery, with the magnitude of that component being modulated by luminance contrast differences across spatial frequency (i.e., the slope of the amplitude spectrum). For scenes high in structural complexity, the early VEP is dominated by a prominent negativity that exhibits little dependency on luminance contrast. However, since natural scene imagery is broad band in terms of spatial frequency, it is not known whether the above-mentioned modulation results from a complex interaction within or between the early neural processes tuned to different bands of spatial frequency. Here, we sought to address this question by measuring early VEPs (specifically, the C1, P1, and N1 components) while human participants viewed natural scene imagery that was filtered to contain specific bands of spatial frequency information. The results show that the C1 component is largely unmodulated by the luminance statistics of natural scene imagery (being only measurable when such stimuli were made to contain high spatial frequencies). The P1 and N1, on the other hand, were observed to exhibit strong spatial frequency-dependent modulation to the luminance statistics of natural scene imagery. The results therefore suggest that the dependency of early VEPs on natural image statistics results from an interaction between the early neural processes tuned to different bands of spatial frequency.

scholarly journals Reconstruction of natural images from responses of primate retinal ganglion cells

2020 ◽  
Author(s):  
Nora Brackbill ◽  
Colleen Rhoades ◽  
Alexandra Kling ◽  
Nishal P. Shah ◽  
Alexander Sher ◽  
...  
Keyword(s):  
Receptive Field ◽  
Ganglion Cells ◽  
Natural Images ◽  
Natural Image ◽  
Retinal Ganglion ◽  
Natural Image Statistics ◽  
Image Statistics ◽  
Visual Message ◽  
Spatial Properties ◽  
Reconstruction Filter

AbstractThe visual message conveyed by a retinal ganglion cell (RGC) is often summarized by its spatial receptive field, but in principle also depends on the responses of other RGCs and natural image statistics. This possibility was explored by linear reconstruction of natural images from responses of the four numerically-dominant macaque RGC types. Reconstructions were highly consistent across retinas. The optimal reconstruction filter for each RGC – its visual message – reflected natural image statistics, and resembled the receptive field only when nearby, same-type cells were included. ON and OFF cells conveyed largely independent, complementary representations, and parasol and midget cells conveyed distinct and expected features. Correlated activity and nonlinearities had statistically significant but minor effects on reconstruction. Simulated reconstructions, using linear-nonlinear cascade models of RGC light responses that incorporated measured spatial properties and nonlinearities, produced similar results. Spatiotemporal reconstructions exhibited similar spatial properties, suggesting that the results are relevant for natural vision.

scholarly journals Two-Dimensional Hermite Filters Simplify the Description of High-Order Statistics of Natural Images

2016 ◽  
Author(s):  
Qin Hu ◽  
Jonathan Victor
Keyword(s):  
Order Statistics ◽  
Dimensional Subspace ◽  
High Order ◽  
Natural Images ◽  
Natural Image ◽  
Two Dimensional ◽  
Natural Image Statistics ◽  
Image Statistics ◽  
High Order Statistics ◽  
Orthogonal Set

AbstractNatural image statistics play a crucial role in shaping biological visual systems, understanding their function and design principles, and designing effective computer-vision algorithms. High-order statistics are critical for conveying local features, but they are challenging to study – largely because their number and variety is large. Here, via the use of two-dimensional Hermite (TDH) functions, we identify a covert symmetry in high-order statistics of natural images that simplifies this task. This emerges from the structure of TDH functions, which are an orthogonal set of functions that are organized into a hierarchy of ranks. Specifically, we find that the shape (skewness and kurtosis) of the distribution of filter coefficients depends only on the projection of the function onto a 1-dimensional subspace specific to each rank. The characterization of natural image statistics provided by TDH filter coefficients reflects both their phase and amplitude structure, and we suggest an intuitive interpretation for the special subspace within each rank.

scholarly journals Reconstruction of natural images from responses of primate retinal ganglion cells

eLife ◽  
2020 ◽  
Vol 9 ◽  
Author(s):  
Nora Brackbill ◽  
Colleen Rhoades ◽  
Alexandra Kling ◽  
Nishal P Shah ◽  
Alexander Sher ◽  
...  
Keyword(s):  
Receptive Field ◽  
Ganglion Cells ◽  
Natural Images ◽  
Natural Image ◽  
Retinal Ganglion ◽  
Natural Image Statistics ◽  
Image Statistics ◽  
Visual Message ◽  
Spatial Properties ◽  
Reconstruction Filter

The visual message conveyed by a retinal ganglion cell (RGC) is often summarized by its spatial receptive field, but in principle also depends on the responses of other RGCs and natural image statistics. This possibility was explored by linear reconstruction of natural images from responses of the four numerically-dominant macaque RGC types. Reconstructions were highly consistent across retinas. The optimal reconstruction filter for each RGC – its visual message – reflected natural image statistics, and resembled the receptive field only when nearby, same-type cells were included. ON and OFF cells conveyed largely independent, complementary representations, and parasol and midget cells conveyed distinct features. Correlated activity and nonlinearities had statistically significant but minor effects on reconstruction. Simulated reconstructions, using linear-nonlinear cascade models of RGC light responses that incorporated measured spatial properties and nonlinearities, produced similar results. Spatiotemporal reconstructions exhibited similar spatial properties, suggesting that the results are relevant for natural vision.

scholarly journals Visualizing Natural Image Statistics

2013 ◽  
Vol 19 (7) ◽  
pp. 1228-1241 ◽  
Author(s):  
Hui Fang ◽  
G. K-L Tam ◽  
R. Borgo ◽  
A. J. Aubrey ◽  
P. W. Grant ◽  
...  
Keyword(s):  
Natural Image ◽  
Natural Image Statistics ◽  
Image Statistics
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