breast lesion segmentation in mr images is one of the most important parts of clinical diagnostic tools. pixel classification methods have been frequently used in image segmentation with two supervised and unsupervised approaches up to now. supervised segmentation methods lead to high accuracy, but they need a large amount of labeled data, which is hard, expensive, and slow to be obtained. on t...

Generalized semi-infinite optimization problems (GSIP) are considered. The difference between GSIP and standard semi-infinite problems (SIP) is illustrated by examples. By applying the ’Reduction Ansatz’, optimality conditions for GSIP are derived. Numerical methods for solving GSIP are considered in comparison with methods for SIP. From a theoretical and a practical point of view it is investi...

This paper tackles the problem of semi-supervised video object segmentation, that is, segmenting an object in a sequence given its mask in the first frame. One of the main challenges in this scenario is the change of appearance of the objects of interest. Their semantics, on the other hand, do not vary. This paper investigates how to take advantage of such invariance via the introduction of a s...

We point out how capacities (non-additive measures) can be used to provide explanations about the concept of bivariate ageing function. The latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi-copula.

This paper extends the theory of the core, the uncovered set, and the related undominated set to a general set of alternatives and an arbitrary measure space of voters. We investigate the properties of social preferences generated by simple games, we extend results on generic emptiness of the core, we prove the general nonemptiness of the uncovered and undominated sets, and we prove the upper h...

5 PREFACE 7 LIST OF ORIGINAL PUBLICATIONS 8 RESEARCH INPUT AND AUTHORSHIP OF ARTICLES (I-IV) 9

We establish some basic lower semicontinuity properties for a class of weigthed metrics in BV. These Riemann-type metrics, uniformly equivalent to the L 1 distance, are deened in terms of the Glimm interaction potential. They are relevant in the study of nonlinear hyperbolic systems of conservation laws, being contractive w.r.t. the corresponding ow of solutions.