Morse Decomposition of Geometric Meshes with Applications

Large datasets describing geometric shapes are nowadays available in a variety of applications, including Geographical Information System. Handling such shapes require extensive computing resources. One of the most computer-intensive task is the analysis of their morphological structure. Morse Theory is a powerful theory, that is used to address the problem of describing topology, i.e., the shape features of an object and their relations. Morse theory is defined for a subset of C∞ functions, that are called Morse functions. We have focused on morphological analysis of 2D scalar fields based on Morse Theory, in particular we have developed techniques for decomposing models according to their semantic structure. Thanks to mesh-based multi-resolution techniques, we can handle large models and dynamically extract smaller-size representations of the an object, that can be efficiently visualized and manipulated. This thesis combines a decomposition of the shape, that takes into account the semantic of each of its components, with a multi-resolution approach. State-ofthe-art multi-resolution techniques do not take into account the morphological structure of a geometric shape, but simply rely on error measures like the distance between the model at full resolution or one of its approximations. A multi-resolution approach, that is aware of the morphological structure of a shape, can result in a more expressive representation, that may capture and describe the structure of an object, at different resolution levels. To Alessandro and Benedetta: pride and joy of these years