Compression for Smooth Shape Analysis
This addresses efficiency issues in 3D shape analysis for applications like computer graphics and 3D scanning, though it is incremental as it builds on existing subdivision methods.
The paper tackles the high computational and memory costs of 3D shape analysis using fine triangular meshes by introducing a compression technique based on subdivision surfaces, achieving comparable accuracy at a fraction of the cost.
Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric operators like normals, curvatures, or Laplace-Beltrami eigenfunctions at large computational and memory costs. We avoid this bottleneck with a compression technique that represents a smooth shape as subdivision surfaces and exploits the subdivision scheme to parametrize smooth functions on that shape with a few control parameters. This compression does not affect the accuracy of the Laplace-Beltrami operator and its eigenfunctions and allow us to compute shape descriptors and shape matchings at an accuracy comparable to triangular meshes but a fraction of the computational cost. Our framework can also compress surfaces represented by point clouds to do shape analysis of 3D scanning data.