Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases

Area of Science:

• Computer Vision and Graphics
• Computational Geometry
• Shape Analysis

Background:

• Non-rigid shape matching is crucial for many computer graphics and vision tasks.
• Existing methods often struggle with non-isometric shapes or exact landmark preservation.
• The functional map framework provides a powerful representation for shape correspondence.

Purpose of the Study:

• To develop a principled approach for non-isometric landmark-preserving non-rigid shape matching.
• To introduce a descriptor-free and efficient method robust to mesh variability.
• To achieve state-of-the-art performance on challenging shape matching benchmarks.

Main Methods:

• Utilizes the functional map framework, focusing on near-conformal maps instead of isometries.
• Introduces a novel landmark-adapted basis derived from an intrinsic Dirichlet-Steklov eigenproblem.
• Formulates a conformally-invariant energy optimized using an extended ZoomOut method.

Main Results:

• The proposed method achieves exact landmark preservation.
• Demonstrates state-of-the-art performance on non-isometric shape matching benchmarks.
• Shows near state-of-the-art performance on isometric benchmarks.

Conclusions:

• The novel approach effectively addresses landmark-preserving non-rigid shape matching.
• The method is efficient, robust, and performs competitively across various datasets.
• This work advances the capabilities of the functional map framework for complex shape analysis.