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Hierarchical Modeling of Local Image Features through $L_p$-Nested Symmetric Distributions
Fabian H Sinz · Eero Simoncelli · Matthias Bethge

Wed Dec 09 07:00 PM -- 11:59 PM (PST) @
We introduce a new family of distributions, called $L_p${\em -nested symmetric distributions}, whose densities access the data exclusively through a hierarchical cascade of $L_p$-norms. This class generalizes the family of spherically and $L_p$-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family also includes the Independent Subspace Analysis (ISA) model, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. $L_p$-nested distributions are easy to estimate and allow us to explore the variety of models between ISA and the $L_p$-spherically symmetric models. Our main findings are that, without a preprocessing step of contrast gain control, the independent subspaces of ISA are in fact more dependent than the individual filter coefficients within a subspace and, with contrast gain control, where ISA finds more than one subspace, the filter responses were almost independent anyway.

Author Information

Fabian H Sinz (University Göttingen)
Eero Simoncelli (FlatIron Institute / New York University)

Eero P. Simoncelli received the B.S. degree in Physics in 1984 from Harvard University, studied applied mathematics at Cambridge University for a year and a half, and then received the M.S. degree in 1988 and the Ph.D. degree in 1993, both in Electrical Engineering from the Massachusetts Institute of Technology. He was an Assistant Professor in the Computer and Information Science department at the University of Pennsylvania from 1993 until 1996. He moved to New York University in September of 1996, where he is currently a Professor in Neural Science, Mathematics, and Psychology. In August 2000, he became an Associate Investigator of the Howard Hughes Medical Institute, under their new program in Computational Biology. In Fall 2020, he resigned his HHMI appointment to become the scientific director of the Center for Computational Neuroscience at the Flatiron Institute, of the Simons Foundation. His research interests span a wide range of topics in the representation and analysis of visual images, in both machine and biological systems.

Matthias Bethge (University of Tübingen)

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