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By Ho P.-G.P. (ed.)

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Theoretically speaking, the probability of occurrence of the gray-level value, within a uniform region is always one. In practice, when one works with real images the entropy value does not reach, in general, the zero value. This is due to the existent noise in the image. Therefore, if we consider entropy as a measure of the disorder within a system, it can be used as a good stopping criterion, by the use of the mean shift filtering, for an iterative process. Entropy within each region diminishes in measure in that the regions become more homogeneous, and at the same time in the whole image, until reaching a stable value.

Block). Then, we generate a sub-image from each local fitted model, preserving intensities on the boundary to smooth the edges between blocks. The final fitted image is yielded by putting together all generated sub-images. LetZ = Z m,n ,0 ≤ m ≤ M − 1 ,0 ≤ n ≤ N − 1 , be the original image, and letX = Xm,n , ¯ , and Z ¯ is the 0 ≤ m ≤ M − 1, 0 ≤ n ≤ N − 1, where for all0 ≤ m ≤ M − 1,0 ≤ n ≤ N − 1 ,X m,n = Z m,n − Z mean ofZ. Let 4 ≤ k ≤ min(M , N )and consider the rearrange images Z = Zm,n , X = X m,n , where0 ≤ m ≤ M ′ − 1,0 ≤ n ≤ N ′ − 1 ib = 1, ⋯ , M −1 k −1 fined as BX (ib, jb) = X r ,s , , and for all jb = 1, ⋯ , M ′= N −1 k −1 M −1 k −1 (k − 1) + 1,N ′ = N −1 k −1 (k − 1) + 1.

A new approach to perform image segmentation based on the estimation of AR-2D process‐ es has been recently suggested (Ojeda 2010). First an image is locally modeled using a spatial autoregressive model for the image intensity. Then the residual autoregressive image is computed. This resulting image possesses interesting texture features. The borders and edges 26 Advances in Image Segmentation are highlighted, suggesting that the algorithm can be used for border detection. Experimen‐ tal results with real images clarify how the algorithm works in practice.

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