Machine und Deep Learning Seminar

Abstract – Deep Geometric Consistent 3D Shape Matching

In this work, the possibility of combining the advantages of learning-based and combinatorial formalisms for 3D shape matching is discussed. While learning-based solutions for shape matching lead to matching performances that are in line with the state of the art, they do not guarantee geometric consistency, so that the matches obtained are not locally smooth. In contrast, axiomatic methods enable the consideration of geometric consistency by explicitly restricting the space of valid matches. However, existing axiomatic formalisms are impractical because they do not scale to practically relevant problem sizes or require inputs for users to initialize non-convex optimization problems. This gap is to be closed by bringing into play a novel combinatorial solver that combines a unique set of advantageous properties:

Our approach

1. is initialization-free
2. is massively parallelizable by a quasi-Newton method
3. provides optimality gaps 
4. delivers decreased runtime and globally optimal results for many instances.