Labeling problem, due to its versatile modeling ability, is widely used in various image analysis tasks. In practice, certain prior information is often available to be embedded in the model to increase accuracy and robustness. However, it is not always straightforward to formulate the problem so that the prior information is correctly incorporated. It is even more challenging that the proposed model admits efficient algorithms to find globally optimal solution. In this dissertation, a series of natural and medical image segmentation tasks are modeled as labeling problems. Each proposed model incorporates different useful prior information. These prior information includes ordering constraints between certain labels, soft user input enforcement, multi-scale context between over-segmented regions and original voxel, multi-modality context prior, location context between multiple modalities, star-shape prior, and gradient vector flow shape prior. With judicious exploitation of each problem's intricate structure, efficient and exact algorithms are designed for all proposed models. The efficient computation allow the proposed models to be applied on large natural and medical image datasets using small memory footprint and reasonable time assumption. The global optimality guarantee makes the methods robust to local noise and easy to debug. The proposed models and algorithms are validated on multiple experiments, using both natural and medical images. Promising and competitive results are shown when compared to state-of-art.

A sorted array is a fundamental algorithmic concept. Its on-line variant gives rise to the online labeling problem. In the online labeling problem we are given an array of size m and a stream of n integers from the universe {1, ..., r} coming in an arbitrary order. Our task is to maintain all received items in the array in sorted order. The inserted items do not have to be stored consecutively in the array. Since the final order of the items is not known until we see all the items, moves of already inserted items are allowed but should be minimized. We present two algorithms which together provide an optimal solution for almost all values of m as a function of n. We provide tight lower bounds for almost all ranges of m. We introduce a notion of the limited universe and prove lower bounds also in that setting. Some of our lower bounds also apply to randomized algorithms. Powered by TCPDF (www.tcpdf.org)

Le raisonnement spatial et temporel qualitatif est un domaine principal d’études de l’intelligence artificielle et, en particulier, du domaine de la représentation des connaissances, qui traite des concepts cognitifs fondamentaux de l’espace et du temps de manière abstraite. Dans notre thèse, nous nous focalisons sur les formalismes du domaine du raisonnement spatial et temporel qualitatif représentant les informations par des contraintes et apportons des contributions sur plusieurs aspects. En particulier, étant donnée des bases de connaissances d’informations qualitatives sur l’espace ou le temps, nous définissons des nouvelles conditions de consistance locale et des techniques associées afin de résoudre efficacement les problèmes fondamentaux se posant. Nous traitons notamment du problème de la satisfiabilité qui est le problème de décider s’il existe une interprétation quantitative de toutes les entités satisfaisant l’ensemble des contraintes qualitatives. Nous considérons également le problème de l’étiquetage minimal qui consiste à déterminer pour toutes les contraintes qualitatives les relations de base participant à au moins une solution ainsi que le problème de redondance consistant à déterminer les contraintes qualitatives non redondantes. En outre, nous enrichissons le domaine des formalismes spatio-temporels par des contributions concernant une logique spatio-temporelle combinant la logique temporelle propositionnelle (PTL) avec un langage de contraintes qualitatives spatiales et une étude de la problématique consistant à gérer une séquence temporelle de configurations spatiales qualitatives devant satisfaire des contraintes de transition. / Qualitative Spatial and Temporal Reasoning is a major field of study in Artificial Intelligence and, particularly, in Knowledge Representation, which deals with the fundamental cognitive concepts of space and time in an abstract manner. In our thesis, we focus on qualitative constraint-based spatial and temporal formalisms and make contributions to several aspects. In particular, given a knowledge base of qualitative spatial or temporal information, we define novel local consistency conditions and related techniques to efficiently solve the fundamental reasoning problems that are associated with such knowledge bases. These reasoning problems consist of the satisfiability problem, which is the problem of deciding whether there exists a quantitative interpretation of all the entities of a knowledge base such that all of its qualitative relations are satisfied by that interpretation, the minimal labeling problem, which is the problem of determining all the atoms for each of the qualitative relations of a knowledge base that participate in at least one of its solutions, and the redundancy problem, which is the problem of obtaining all the non-redundant qualitative relations of a knowledge base. Further, we enrich the field of spatio-temporal formalisms that combine space and time in an interrelated manner by making contributions with respect to a qualitative spatio-temporal logic that results by combining the propositional temporal logic (PTL) with a qualitative spatial constraint language, and by investigating the task of ordering a temporal sequence of qualitative spatial configurations to meet certain transition constraints.