Share Email Print

Optical Engineering

Factorization and structure of natural 4×4 patch densities
Author(s): Kostadin Koroutchev; Jose R. Dorronsoro
Format Member Price Non-Member Price
PDF $20.00 $25.00

Paper Abstract

The objective of this work is to give an approximate statistical model of the distribution of 4×4 pixel natural image patches B. Given the huge size of the sample space, we collect the required statistics not directly over B, but, instead, over a fractal compression inspired representation of B, namely by a triplet (DBBB), with σB being the patch's contrast, μB its brightness, and DB a codebook representation of the mean-variance normalization of B:(B-μB)/σB. While not coinciding exactly with the true natural patch density p(B), the density p^(B)=p(DBB, σB) should give an adequate approximation of p(B), because B~=σBDBB. Our first main result is a factorization of the probability density p(D,μσ,) as p(D,μσ,)~=p(D)p(μ)p(σ)Φ(||ΔB||), with Φ being a high-contrast correction. Here, the brightness term p(μ) is largely irrelevant, and our second main result deals with the structure of the other two factors, showing that p(σ) follows an exponential distribution, and that p(D) is uniformly distributed with respect to volume in image space. These results are largely independent of the codebook used.

Paper Details

Date Published: 1 December 2006
PDF: 10 pages
Opt. Eng. 45(12) 127003 doi: 10.1117/1.2402520
Published in: Optical Engineering Volume 45, Issue 12
Show Author Affiliations
Kostadin Koroutchev, Univ. Autónoma de Madrid (Spain)
Jose R. Dorronsoro, Univ. Autónoma de Madrid (Spain)

© SPIE. Terms of Use
Back to Top