Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. Three different codebook sources have been used, the Lena image and the prior two images from van Hateren’s database. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. Large sample (left) and small sample (right) behavior of the mutual information I(σ ∥ μ) estimates; they are basically independent of the image used as a domain source. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. Total entropy (left) and mutual information estimates (right) computed over Lena and the first van Hateren image codebooks. Neither estimate seems to converge to a saturation point. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. (a) Deviations from the first order factorization in Eq. arise over the edges of the codebook source image. (b) Values of E ∥∇ B ∥ in logarithmic scale (y axis) and second-order epitaxy-inspired approximation. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. The μ distribution is essentially uniform, except for drops at the left and right extremes. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. (a) Projection over Lena of the −logp[σ(i,j)] distribution. (b) Relative frequencies (y axis, logarithmic scale) of σ. The linear central behavior suggests an exponential distribution. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. (a) The number of ranges each (i,j) domain gets for the Lena image in gray scale. (b) The y axis show values of −logp(m), with p(m) the relative number of Lena domains getting m blocks (m is depicted on the x axis). The near-parabolic behavior hints to a uniform distribution. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. Values (y axis) of logN(m), with N(m) the relative number of domains getting a volume-corrected number m (x axis) of natural blocks for the Lena (left) and van Hateren (right) codebooks. The left image also shows the average patch σ as a growing function of m. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. Volume-corrected bin counts (y axis) for all high σ>12 natural patches (top) and for natural patches B, such that σDB>σB>12 (bottom), for which noise effects are smaller. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /

Date of download: 6/26/2016 Copyright © 2016 SPIE. All rights reserved. (a) Domains with a higher count of high contrast patches. They clearly correspond to edges. (b) The proportion of high contrast patches is clearly bigger among high count domains. Figure Legend: From: Factorization and structure of natural 4×4 patch densities Opt. Eng. 2006;45(12): doi: /