CS395T: Numerical Optimization for Graphics and AI

The University of Texas at Austin
Computer Science Department

Computer Science 395T
Numerical Optimization for Graphics and AI (3D Vision)

Fall 2019

General Information:

Time: Mondays and Wednesdays 3:30PM-5:00PM
Place: GDC 1406
Instructor: Qixing Huang
Office hour: Fridays 5pm-7pm at GDC 5422 (or By Appointment).

This course will cover a broad range of topics in the general area of 3D Vision and 3D Geometry Processing, ranging from 1) reconstructing 3D models from images and depth scans, 2) 3D representations (e.g., for neural networks), and 3) analysis and processing of 3D models. An unique characteristics of this course is that we will install the basic theory of numerical optimization throughout. The course is a graduate-level course that combines instruction of basic material, written homeworks , and a final project. The course targets for students who will conduct research in Graphics, Vision, Robotics, and Computational Biology. Grading is based on homeworks (50%), the Midterm (20%), and the final project (30%). Several final projects are expected to become conference/journal publications.

Prereqs: The course assumes a good knowledge of linear algebra and probability. Please talk to me or email me if you are unsure if the course is a good match for your background.

Textbooks (Not Required but Recommended):

[NW]: Numerical Optimization

[MKSS]: An Invitation to 3D Vision

[BKPAL]:Polygon Mesh Processing

[GP]: Point-Based Graphics

Schedule (A: Application, T: Theory):

Date	Topics	Reading	Notes
August 28th (W)	(A): Introduction
September 4th (W)	(T):Math Review (Linear Algebra, Rotation, Quaternion)	Rotation Quaternion	Homework 1
September 9th (M)	(T): Fundamentals of Unconstrained Optimization	Chapter 2 of [NW]
September 11th (W)	(T): Fundamentals of Constrained Optimization	Chapter 12 of [NW]
September 16th (M)	(A): Image Formation	Chapter 3 of [MKSS]
September 18th (W)	(A): Image Primitives and Correspondence	Chapter 4 of [MKSS]
September 23th (M)	(A): Reconstruction from Two Calibrated Views	Chapter 5 of [MKSS]
September 25th (W)	(A): Camera Calibration and Self-Calibration	Chapter 6 of [MKSS]
September 30th (M)	(A): Introduction to Multiple View Reconstruction	Chapter 7 of [MKSS]	Homework 1 due. Homework 2 out.
October 2th (W)	(T): Line Search Techniques	Chapter 3 of [NW]
October 7th (M)	(T): Trust Region Methods	Chapter 4 of [NW]
October 9th (W)	(A): Image Matching and Bundle Adjustment	Chapter 14.3-14.4 of [MKSS]
October 14th (M)	(A): Optimization for SLAM
October 16th (W)	(A): Multi-View Stereo	Chapter 14.5 of [MKSS]	Homework 2 due. Homework 3 out.
October 21th (M)	(T): Large-Scale Optimization (Proximal Gradient)	Proximal Gradient Method	Sample Midterm is out.
October 23th (W)	(T): Large-Scale Optimization (ADMM)
October 28th (M)	3D Representation I (PointCloud)
October 30th (W)	Midterm		Homework 3 due. Homework 4 out.
November 4th (M)	(A): 3D Representation II (Implicit)
November 6th (W)	(A): 3D Representation III (Parametric)
November 11th (M)	(A): 3D Representation IV (Triangular Mesh)
November 13th (W)	(A): 3D Representation V (Part-Based and Scene-Graph)
November 18th (M)	(A): Hybrid 3D Representation		Homework 4 due. Homework 5 out.
November 20th (W)	(A): 3D Deep Learning I (Understanding)
November 25th (M)	(A): 3D Deep Learning II (Understanding)
December 2th (M)	(T): 3D Deep Learning III (Synthesis)
December 4th (W)	(T): 3D Deep Learning IV (Synthesis)		Homework 5 due.
December 9th (M)	Final Project Presentations		Final project report due.

Final Project:

The final project is done in groups of 2-3 students. Each project should have an initial proposal, a final report, and a final poster presentation. The project proposal shall describe four key components of a research project (namely Motivation, Technical Merit, Broader Impact, and Project Plan). The final report should be written as an academic research article. A more detailed instruction will be given later.