23:T45e,

The two major Markov Random Fields (MRF) based algorithms for image segmentation are the Simulated Annealing (SA) and Iterated Conditional Modes (ICM). In practice, compared to the SA, the ICM provides reasonable segmentation and shows robust behavior in most of the cases. However, the ICM strongly depends on the initialization phase.

In this paper, we combine Bak–Sneppen model and Markov Random Fields to define a new image segmentation approach. We introduce a multiresolution technique in order to speed up the segmentation process and to improve the restoration process. Image pixels are viewed as lattice species of Bak–Sneppen model. The a-posteriori probability corresponds to a local fitness. At each cycle, some objectionable species are chosen for a random change in their fitness values. Furthermore, the change in the fitness of each species engenders fitness changes for its neighboring species. After a certain number of iteration, the system converges to a Maximum A Posteriori estimate. In this multireolution approach, we use a wavelet transform to reduce the size of the system.

24:T4fa,

Borda with None (BwN) adds the binding option of “None of these candidates,” N, to the Borda Count (BC), differing from a method of Dodgson in the scoring of ties. The method incorporates the benefits of approval voting, which allows a simple yes/no vote on each candidate and avoids the disadvantages of adding N as a binding outcome to plurality voting. We prove that BwN uniquely satisfies five rational properties which can be viewed as potential axioms that provide a theoretical basis for the method. It allows individual voters to express a personal veto over all or part of the slate which could, with sufficient numbers, become a veto by the electorate. The power of none, then, is offering a voice to otherwise disaffected voters. We introduce a metric similar to one used in the Bak–Sneppen Evolutionary model, candidate fitness, a number between 0 and 1, which measures a candidate’s ranking relative to N. We illustrate its evolution with a hypothetical example. We examine courses of action if N is ranked in the first place. Using BwN to accommodate partial voting is proposed. We explore the general applicability of BwN. Finally, we address the practical considerations for introducing BwN.

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A Multiresolution Approach Based on MRF and Bak–Sneppen Models for Image Segmentation

The Power of None