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Open AccessArticle

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

by Qin Hu 1 and Jonathan D. Victor 2,*
1
Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
2
Feil Family Brain and Mind Research Institute, Weill Cornell Medical College, 1300 York Ave, New York, NY 10065, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Marco Bertamini
Symmetry 2016, 8(9), 98; https://doi.org/10.3390/sym8090098
Received: 27 June 2016 / Revised: 12 September 2016 / Accepted: 18 September 2016 / Published: 21 September 2016
(This article belongs to the Special Issue Symmetry in Vision)
Natural 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 one-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. View Full-Text
Keywords: image statistics; skewness; kurtosis; orthogonal functions; steerable filters image statistics; skewness; kurtosis; orthogonal functions; steerable filters
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Hu, Q.; Victor, J.D. Two-Dimensional Hermite Filters Simplify the Description of High-Order Statistics of Natural Images. Symmetry 2016, 8, 98.

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