Canonical Coordinate System for Geometry Learning

Introduction

• It is not handy to apply CNN on graph convolution because no grid system
• This project provide such grid system on the parametrization

Steps

Step 1: Cut the surface and map to Poincare disk

Step 2: Set canonical coordinate and generate geometry image

There is a X-Y coordinate for the poincare disk, so that the poincare disk can be one to one map to the euclidean coordinate The illustrative figure is

Step 3: Convolution along the canonical coordinates

Apply the convolution Now!

Applications

Surface Classification

Surface Registration

Surface Generation

Surface Transfer Learning