Math Research Notes#
Machine Learning Cheatsheet from Scikit:
Geometry Processing#
- Discrete Differential Geometry Course: An Applied Introduction
- Course Videos
- Course Slides
- Course Notes
- Supplemental Material
Techniques#
- SGP 2018 Course: Conformal Geometry Processing
- Course Notes
- Heat Flow Method: Geodesic Distance
- Vector Heat Method: Parallel transport across surface
- Siggraph 2019 Talk
- Can be used for extrapolating level set velocities
- LogMap/Exponential map
- Geometric Medians & Karcher/Frechet means
- Centroidal Voronoi diagrams
- Consistently ordered landmarks (for shape correspondence across near isometric surfaces)
- Variational Surface Cutting: Auto seam mesh
- Siggraph 2018 Talk
- Paper
- Code
- Navigating Intrinsic Triangulations
- Siggraph 2021 Course: Geometry Processing with Intrinsic Triangulations
- A Laplacian for Nonmanifold Triangle Meshes
- Presentation
- Code
- Mobius Registration: Find correspondence between two meshes
- Mesh Unwrapping Techniques
- Boundary First Flattening: minimizes conformal mapping energy but insight is that doesn't matter; where you place the cuts is more important
- ARAP/ARAP++: minimizes a different energy than LSCM
Optimal Transport#
Optimal Transport is a mathematical theory that studies how to transform a shape into another one while minimizing a certain cost.
- SGP2018 Course: Computational Optimal Transport
- Presentation
- Optimal Transport Tutorial in Graphite
- Optimal Transport for Computer Graphics and Temporal Coherence of Image Processing Algorithms Thesis
Dictionary Learning#
- Siggraph 2010 Course: Spectral Mesh Processing
- Course Notes
- Spectral Geometry Processing with Manifold Harmonics
- Geogram implementation
- Siggraph Asia 2011 Course: Elements of Geometry Processing
- Gentle Course Slides on Laplacian:
- Overview
- Mesh Laplacian & Manifold Harmonics
- Sparse Coding & Dictionary Learning
-
Dictionary Learning Using Optimal Transport
- Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning
- Slides
- Alternative approach: Wasserstein principal geodesics
- Fast Dictionary Learning with a Smoothed Wasserstein Loss
- Supplemental Web Material
- Matlab Implementation to perform Wasserstein Dictionary Learning and Non-negative Matrix Factorization
- Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains
Resources#
Learning Resources#
- Symposium on Geometry Processing Courses
- GeoGram Wiki
- Graphite Wiki
- Graphite Wiki
- Polygon Mesh Processing Book
Software#
- Geometry Central: c++ library for geometry processing with a focus on surface meshes
- Geogram
- Graphite: an experimental 3D modeler built around geogram
- Graphite video
- AliceVision
- LibIGL: simple c++ geometry processing library
- CGAL
- Mean Curvature Skeleton
- L1 Medial Skeleton
- Geom Loss Library: geometric loss functions between sampled measures, images and volumes
- Code
- Gradient flows between sampled measures
- WrapX