PhD Thesis Defense: Topology-Varying Shape Matching and Modelling - Ibraheem Alhashim
The automatic creation of man-made 3D objects is an active area in computer graphics. Mixing and blending of components or sub components from existing example shapes can help users quickly produce interesting and creative designs. A key factor for automating this task is using computer algorithms that can map between objects of different shape and structure. However, due to the coarse correspondence computed by current matching algorithms, automatic shape blending is mainly limited to the substitution of compatible part sets. In this thesis, we address the problem of relating 3D shapes having different geometry and topology with applications in shape synthesis. Our goal is to compute a fine-grained mapping between two shapes differing in the geometry, cardinality, and connectivity of their parts and use this mapping in a continuous shape interpolation process.
First, we propose a framework for shape matching using a joint geometric and topological transformation. The framework follows the assumption that the best mapping for a pair of shapes is one that results from a transformation that minimally distorts the structural properties of a shape. We establish meaningful correspondences for shapes having large topological discrepancy by going beyond shape deformations and incorporating topological operations such as part split, duplication, and merging. We evaluate our correspondence algorithm on a diverse set of shape classes and compare the results to state-of-the-art methods.
Second, we propose an algorithm for synthesizing continuous interpolations of structurally different 3D shapes. Our algorithm produces a continuous and plausible shape transformation that gradually morphs the geometry of the individual parts as well as performs the necessary topological operations. We further demonstrate the utility of our framework by developing intuitive shape creation tools. We show how these tools allow users to synthesize new shapes from continuous blends of topologically different shapes.