A methodology for hierarchical image segmentation evaluation

This paper proposes a method to evaluate hierarchical image segmentation procedures, in order to enable comparisons between different hierarchical algorithms and of these with other (non-hierarchical) segmentation techniques (as well as with edge detectors) to be made. The proposed method builds up on the edge-based segmentation evaluation approach by considering a set of reference human segmentations as a sample drawn from the population of different levels of detail that may be used in segmenting an image. Our main point is that, since a hierarchical sequence of segmentations approximates such population, those segmentations in the sequence that best capture each human segmentation level of detail should provide the basis for the evaluation of the hierarchical sequence as a whole. A small computational experiment is carried out to show the feasibility of our approach.

Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.