Hoel Le Capitaine

A fast fuzzy c-means algorithm for color image segmentation

Color image segmentation is a fundamental task in many computer vision problems. A common approach is to use fuzzy iterative clustering algorithms that provide a partition of the pixels into a given number of clusters. However, most of these algorithms present several drawbacks: they are time consuming, and sensitive to initialization and noise. In this paper, we propose a new fuzzy c-means algorithm aiming at correcting such drawbacks. It relies on a new efficient cluster centers initialization and color quantization allowing faster and more accurate convergence such that it is suitable to segment very large color images. Thanks to color quantization and a new spatial regularization, the proposed algorithm is also more robust. Experiments on real images show the efficiency in terms of both accuracy and computation time of the proposed algorithm as compared to recent methods of the literature.

A family of measures for best top-n class-selective decision rules

When classes strongly overlap in the feature space, or when some classes are not known in advance, the performance of a classifier heavily decreases. To overcome this problem, the reject option has been introduced. It simply consists in withdrawing the decision, and let another classifier, or an expert, take the decision whenever exclusively classifying is not reliable enough. The classification problem is then a matter of class-selection, from none to all classes. In this paper, we propose a family of measures suitable to define such decision rules. It is based on a new family of operators that are able to detect blocks of similar values within a set of numbers in the unit interval, the soft labels of an incoming pattern to be classified, using a single threshold. Experiments on synthetic and real datasets available in the public domain show the efficiency of our approach.

An Optimum Class-Rejective Decision Rule and Its Evaluation

Decision-making systems intend to copy human reasoning which often consists in eliminating highly non probable situations (e.g. diseases, suspects) rather than selecting the most reliable ones. In this paper, we present the concept of class-rejective rules for pattern recognition. Contrary to usual reject option schemes where classes are selected when they may correspond to the true class of the input pattern, it allows to discard classes that can not be the true one. Optimality of the rule is proven and an upper-bound for the error probability is given. We also propose a criterion to evaluate such class-rejective rules. Classification results on artificial and real datasets are provided.

A Family of Cluster Validity Indexes Based on a l-Order Fuzzy OR Operator

Clustering is one of the most important task in pattern recognition. For most of partitional clustering algorithms, a partition that represents as much as possible the structure of the data is generated. In this paper, we adress the problem of finding the optimal number of clusters from data. This can be done by introducing an index which evaluates the validity of the generated fuzzy c -partition. We propose to use a criterion based on the fuzzy combination of membership values which quantifies the l -order overlap and the intercluster separation of a given pattern.

On Selecting an Optimal Number of Clusters for Color Image Segmentation

This paper addresses the problem of region-based color image segmentation using a fuzzy clustering algorithm, e.g. a spatial version of fuzzy c-means, in order to partition the image into clusters corresponding to homogeneous regions. We propose to determine the optimal number of clusters, and so the number of regions, by using a new cluster validity index computed on fuzzy partitions. Experimental results and comparison with other existing methods show the validity and the efficiency of the proposed method.

On (weighted) k-order fuzzy connectives

In this paper, we present new fuzzy connectives that allow to specify an order to the considered operation. These operators are generalization of usual fuzzy connectives, i.e. triangular norms and triangular conorms. A potential use of the proposed operators consists in assessing to what extent several values are high or low in unconstrained fuzzy sets is given. We also present weighted k-order fuzzy connectives, where weights are associated to different subsets of criteria. Finally, we show that these fuzzy connectives can be used from a set-theoretic point of view, enabling to define new kinds of fuzzy intersection and union.

Class-Selective Rejection Rules Based on the Aggregation of Pattern Soft Labels

Let Ω = {ω1, · · · , ωc} be a set of c classes and let x be a pattern described by p features, namely a vector x = (x1 · · · xp) in a p-dimensional real space R p. Classifier design aims at defining rules that allow to associate an incoming pattern x with one class of Ω. Let Lhc be the set of c-dimensional binary vectors whose components sum up to one. Then, such a rule, defined as a mapping D: Rp → Lhc, x → h(x), is called a crisp classifier. In most theoretical approaches to pattern classification, it is convenient to define a classifier as a couple (L, H) where: L is a labeling function: Rp → L•c, x → u(x), L•c depending on the mathematical framework the classifier relies on, Lpc = [0, 1]c for degrees of typicality or L f c =