### Announcements

01/07/2020:Welcome to the course!

### General Information

**Times & Places**

TuTh 3:30PM - 4:50PM, EBU3B 4140

**Course Staff**

Name | Office Hours | Location | ||
---|---|---|---|---|

Instructor | Hao Su | haosu@ucsd.edu | 5:00PM-6:00PM, Tu | CSE Building 4109 |

Course Assistant | Meng Song | mes050@ucsd.edu | 5:15PM-6:15PM, Th | CSE Building 4109 |

#### Objectives

This is a graduate level course to cover core concepts and algorithms of geometry that are being used in computer graphics, computer vision and machine learning. I will cover key concepts of differential geometry, the usage of geometry in computer graphics, vision, and machine learning. Students are required to do a course project in pairs.#### Prerequisites

Background assumed includes basic material in linear algebra, optimization, and machine learning.#### Grading (tentative)

- Quizzes 20%
- Course project presentation 40%
- Course project writeup 40%
- There will not be a final exam.

#### Syllabus

The planned syllabus is as below. Certain contents may be added or removed based upon the interactions in class and other situations.- Geometry Basics (3 weeks)
- Curves
- Surfaces
- First Fundamental Form
- Second Fundamental Form
- Geodesics
- Gauss' Remarkable Theorem
- Gauss-Bonnet Theorem
- Vector Field, Flow, Parallel Transportation
- Levi-Civita Connection
- Surface Representation in Computer
- Delaunay Triangulation
- Discrete Differential Geometry

- Laplacian Operator and Spectral Graph Theory (2 weeks)
- Laplacian-Bertrami Operator
- Spectral Graph Theory
- Laplacian Shape Editing
- Functional Map

- Data Embedding and Deep Learning (2 weeks)
- Major Embedding Theorems
- PCA, CCA
- Isomap, LLE, MDS
- Variational Auto-Encoder
- Generative Adversarial Networks
- Optimal Transport
- Characterization of Local Optimas of Deep Networks

- Map Networks (2 weeks)
- The Rigid and Non-rigid Shape Registration Problem
- Cycle Consistency by Semi-Definite Programming
- Functional Map Network, Deep Functional Map Network
- Unsupervised Learning by Map Networks, Cycle GAN

- Deep Learning on 3D Data (2 weeks)
- Multi-view Representation
- Volumetric Representation
- Implicit Function Representation
- Point Cloud Representation
- Embedded-Graph Representation (Graph CNN)
- Structural Representation
- Scene Understanding

- Topological Data Analysis (Optional)
- Topology Review, Complexes
- Homology Groups, Persistent Homology