Topological Modeling and Stochastic Analysis of Images

摘要

In this report, we include the dissertation thesis the grant has funded together with a list of publications, and invitations the funded research has generated. Concepts in classification and recognition problems. 1. We have explored the potential of combining geometrical as well as topological information in capturing the essence of an object for classification and recognition purposes. The geometrical information within a topologically homogeneous part of an object is captured through a set of level curves, while the topology is extracted from the singular points. 2. Defining probability models on manifolds as would be required by the surface of an object remains a challenging topic. The approach here exploits a triangulated approximation on which a geodesic is defined to capture the nonlinear intrinsic structure of an object surface. 3. Obtaining distribution for objects in turn allows us to compare them by IT measures.