Abstract
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.
Publisher
Cold Spring Harbor Laboratory
Reference36 articles.
1. Understanding the statistics of the natural environment and their implications for vision;Vision Res,2016
2. Pouli, T. , D.W. Cunningham , and E. Reinhard , Image statistics and their applications in computer graphics. Proceedings of Eurographics 2010-State of the Art Reports, 2010: p. 83–112.
3. Lyu, S. and H. Farid , Higher-order wavelet statistics and their application to digital forensics. IEEE Workshop on Statistical Analysis in Computer Vision, 2003: p. 94–101.
4. Steganalysis using higher-order image statistics;Ieee Transactions on Information Forensics and Security,2006
5. Detecting hidden messages using higher-order statistics and support vector machines;Information Hiding,2003