Geometric Data Processing Group

Description:

Introduces mathematical, algorithmic, and statistical tools needed to analyze geometric data, with applications to computer graphics, computer vision, medical imaging, machine learning, architecture, and other fields. Potential topics include: applied introduction to differential geometry; discrete notions of curvature; PDE on geometric domains via the finite element method (FEM) and discrete exterior calculus (DEC); computational spectral geometry; correspondence and mapping; metric geometry; level set methods; descriptors; shape collections; and vector field design. (EECS departmental listing, catalog listing)

Logistics:

Time: Tuesday/Thursday, 1pm-2:30pm
Location: 32-124

Staff:

Instructor: Justin Solomon, office hours Wednesdays 1pm-3pm (32-D460)
TA: Abhishek Bajpayee, office hours Thursday 3pm-5pm (1-225)

Policies:

• There will be four homework assignments, worth 40% of your grade as well as a course project worth 50%; you must complete all parts of the project to pass the course. The remaining 10% will be devoted to nanoquizzes every other Thursday; the lowest nanoquiz score will be dropped. There will be no final exam.
• Our goal is to present this exciting set of highly-technical tools in an approachable and intuitive fashion. But the course is in its first year, so feedback is needed to calibrate. For this reason, ±5% can be rewarded for course participation, through engagement in lecture, discussion in office hours, and/or contribution to discussion online.
• Assignments must be submitted by 8pm on the listed due date. You will be permitted a total of three late days over the course of the quarter, measured in periods of 24 hours. Beyond this, late assignments will lose 25% credit per day (additively).
• Students are encouraged to ask questions and discuss the lecture content on Piazza (sign up here).
• Collaboration on homework is permitted, but final writeups/implementations must be individual students' work. The final project can be completed in groups.

Assignments:

• Final project: instructions; final paper template
• Homework 1: iPython notebook (due 2/24/17 2/27/17)
• Homework 2: iPython notebook and data (due 3/17/17 3/20/17)
• Homework 3: iPython notebook and data (due 4/14/17)
• Homework 4: iPython notebook and data (due 5/5/17 5/8/17)

Slides:

• Topic 1: Introduction
• Topic 2: Numerical tools
• Topic 3: Curves: Continuous and Discrete
• Topic 4: Representing surfaces
• Topic 5: Surface curvature
• Topic 6: Computing geodesic distance
• Topic 7: Inverse distance problems
• Topic 8: The Laplacian operator (recommended reading)
• Topic 9: Discrete Laplacians
• Topic 10: Applications of the Laplacian
• Topic 11: Vector field processing (recommended reading; recommended reading 2)
• Topic 12: Discrete exterior calculus (recommended reading; exterior algebra on Wikipedia)
• Topic 13: Optimal transport
• Topic 14: Clustering and segmentation
• Topic 15: Registration and alignment
• Topic 16: Surface correspondence
• Topic 17: Consistent correspondence

Schedule:

The following is a highly tentative lecture schedule for 6.838. It will be updated dynamically as the course proceeds. The list of topics is ambitious and likely to be shortened; if there are topics you feel strongly should be included/emphasized/added, feel free to contact Justin with this information.

Links to slides, Youtube videos of lectures, and homeworks will be posted on this spreadsheet as the course proceeds.