/universal_covering_python

Canonical coordinate by universal covering space

Primary LanguagePython

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

Image of mesh along fundamental group Image of mesh along fundamental group Image of mesh along fundamental group

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 Image of mesh along fundamental group

Step 3: Convolution along the canonical coordinates

Apply the convolution Now!

Applications

Surface Classification

Surface Registration

Surface Generation

Surface Transfer Learning