Inférence quantitative des relations spatiales directionnelles

Abstract

Nowadays, the knowledge of spatial relations between objects is a key point in Image Processing and commonly used in pattern recognition, computer vision, scene interpretation and more specifically in Geographical Information Systems (GIS), scene descriptions in natural language and autonomous navigation of mobile robots. Human beings are skilled in estimating spatial relationships and can make very precise deductions despite the ambiguous definition of these relations. This thesis propose quantitative inference methods of directional spatial relations. We address the following problem: deduce the spatial relationships between two objects A and C knowing relationships which connect them to a third object B. Everybody has already tried to deduce a path from his position and visible reference buildings. First, we present and discuss the basic quantitative models, essentially based on fuzzy logic theory. Then we develop a new model which can represent at the same time angular information, necessary to quantify spatial relationships, and metric knowledge, useful for the deduction step. In the case of unknown distance information, we have used a fuzzy aggregation network to deduce directional spatial relationships. The network parameters (structure, type and parameters of operators) are learned from examples. In order to explain the fuzzy aggregation network results, we have developed an evaluation of the position probability of a point C which is known to be in a direction β with respect to a point B, itself in the direction α with respect to another point A. We solve the problem for different distributions of points in the plane. These distributions represent prior knowledge about spatial localisation of points B and C. We generalized our formulas to the case of continuous distributions. These results constitute an important basis of probabilistic spatial reasoning.