2018/04/16 by Jesús Malo, Jesus Malo, Malo, Jesus +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · #FOS: Biological sciences #Image and Signal Denoising Methods #Neural Networks and Applications #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Visual perception and processing mechanisms #q-bio.NC
paper · pdf · doi:10.48550/arxiv.1804.05964
MODVIS-18 and Celebration of Cowan's 50th anniv. at Univ. Chicago
arxiv created 2018/04/16 · openalex publication_date 2018/04/16 · arxiv updated 2018/04/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The interaction between wavelet-like sensors in Divisive Normalization is classically described through Gaussian kernels that decay with spatial distance, angular distance and frequency distance. However, simultaneous explanation of (a) distortion perception in natural image databases and (b) contrast perception of artificial stimuli requires very specific modifications in classical Divisive Normalization. First, the wavelet response has to be high-pass filtered before the Gaussian interaction is applied. Then, distinct weights per subband are also required after the Gaussian interaction. In summary, the classical Gaussian kernel has to be left- and right-multiplied by two extra diagonal matrices. In this paper we provide a lower-level justification for this specific empirical modification required in the Gaussian kernel of Divisive Normalization. Here we assume that the psychophysical behavior described by Divisive Normalization comes from neural interactions following the Wilson-Cowan equations. In particular, we identify the Divisive Normalization response with the stationary regime of a Wilson-Cowan model. From this identification we derive an expression for the Divisive Normalization kernel in terms of the interaction kernel of the Wilson-Cowan equations. It turns out that the Wilson-Cowan kernel is left- and-right multiplied by diagonal matrices with high-pass structure. In conclusion, symmetric Gaussian inhibitory relations between wavelet-like sensors wired in the lower-level Wilson-Cowan model lead to the appropriate non-symmetric kernel that has to be empirically included in Divisive Normalization to explain a wider range of phenomena.