SPEAKER: Federico Iuricich

TITLE: Shape Analysis in three and higher dimensions based on Morse Theory

ABSTRACT: Represent and efficiently manage morphological information extracted from a scalar fields is a fundamental issue in several applications such as terrain modelling, volumetric data analysis (i.e. for medical or engineering purpose), rather then time-varying 3D scalar fields. Such type of data are usually huge and noise affected and needs ad hoc methods able to reduce their complexity. For these aim Morse theory offers natural and intuitive tools to analyze the structure of a discrete scalar field as well as representing it in a compact way through decompositions of its domain. The goals of our research are mainly three. First of all we are interested in study and develop a multi-resolution framework to represent a 3D scalar field at different level of detail. Such framework would let us to investigate and analyze the morphological structure of a scalar field in an efficient way working out problems linked to the size of the data sets and noise as well as provide the possibility to vary the resolution on the domain at will. Moreover we want combine such multi-resolution framework with an efficient diamond based representation. Most common data sets in fact, are made as clusters of points on a regularly sampled domain from which is easy to obtain hierarchical structure. Second field of interest could be investigate algorithms for Morse and Morse-Smale complexes computation. We have already studied some of such algorithms in previous work. We are planning to go on with such study in order to deeply examine all the known algorithms and to make a comparative evaluation of each approach, in particular considering their applicability in an higher dimension context. Last point would be investigate the analysis of data sets in dimensions higher than three. Having a completely dimension-independent framework in fact, we could be able to manage more complex data sets. In particular starting from a 4D shape, isosurfaces of scalar fields in 4D usually used to modelling time varying 3D scalar fields, we want to investigate the possibility to segment and use our framework basing the computation on a new scalar field defined on the mesh itself. For these purpose the 3D curvature could be an excellent tool. First of all we will investigate the way to compute curvature in the 3D confronting some of the operators proposed in the literature. Next, we will try to gain meaningful result using our framework to investigate the new field computed.