Viterbi Faculty of Electrical Engineering, Technion
Mappings of Deformable Geometric Data and Their Applications in Two and Three Dimensions
This study addresses the problem of how to map two and three-dimensional objects to satisfy a list of geometric constraints while incurring minimal shape distortion. We refer to this problem as to the optimal mapping problem. Our goal is to analyze the optimal mapping problem, find efficient approaches to this problem for scenarios in which previously available methods fail, and to present new practical applications of our algorithms.
We present a new algorithm for optimizing geometric energies and computing orientation-preserving simplicial mappings of triangular and tetrahedral meshes.
Our major improvements over the state-of-the-art are: the introduction of new energies for repairing inverted and collapsed simplices, adaptive partitioning of vertices into coordinate blocks with the blended local-global strategy for more efficient optimization, and the introduction of an improved convergence criterion. Our algorithm achieves state-of-the-art results in distortion minimization, even under hard positional constraints and highly distorted invalid initializations that contain thousands of collapsed and inverted elements. We show that over a wide range of 2D and 3D problems our algorithm is more robust than existing techniques for locally injective mapping.
Furthermore, we present a multi-resolution approach to optimal mapping and a novel conformal initialization scheme for accelerating surface parameterization.
* Ph.D. under the supervision of Yehoshua Y. Zeevi.
Tue 22 Sep 2020
Start Time: 14:30
End Time: 15:30
ZOOM Meeting | Electrical Eng. Building