Lecture

Statistical Geometry Processing (Winter Semester 2011/2012)

Contact

Instructor:

• Michael Wand

Teaching Assistants:

• Jens Kerber
• Silke Jansen
• Art Tevs

Statistical Geometry Processing

This lecture gives an introduction to the research field of statistical geometry processing. Informally spoken, the goal in this research area is to develop algorithms that are able to understand geometry. We want to develop algorithms that can analyze and represent the structure of geometric objects, and use this knowledge for analyzing, reconstructing, and modeling 3D geometry. There are a many application domains where such approaches are needed, such as medical data analysis (3D tomography), 3D scanning of cities for virtual maps, or content creation for 3D computer games.

The approach of this lecture will be to look at mathematical tools and then see how these could be applied: Figuratively spoken, we will iterate between searching for hammers (tools) and nails (problems to be solved). We will look at the theory, the applications, and conduct exercises to test the tools in practice.

Many of the techniques introduced in this lecture are actually rather generic and applicable beyond the domain of computer graphics and vision so that the lecture might be useful even for solving problems in other areas of algorithmic data analysis.

This is the first time this lecture is held. Therefore, the information given is so far still subject to change.

Lecture Topics

The topics covered in this lecture will probably include (subject to change):

Mathematical background:

• Differential geometry
• Basic probability theory & statistics (recap)
• Calculus of variation
• Local and global optimization techniques

Machine learning fundamentals

• Introduction to statistical problem modeling

Modeling tools

• Least-squares fitting (regression, total least-squares, moving least-squares)
• Robust statistics
• Linear and non-linear principal component analysis and dimensionality reduction
• Linear and non-linear shape spaces

Surface reconstruction

• Surface reconstruction approaches

Correspondence problems

• Rigid shape matching
• Non-rigid shape matching
• Local and global optimization techniques
• Invariant features (rigid motions / isometries / semantic classes)
• Invariant descriptors
• Intrinsic geometry for non-rigid shape matching
• Robustness issues (noise, incomplete data, outliers)
• Machine learning techniques: semantic matching

Prerequisites

The course is targeting master students and advanced bachelor students (towards the end of their studies). We will introduce most of the necessary background in the course, but some prior knowledge in the following areas might still be required to follow at the intended pace:

• Basic math (calculus, linear algebra, basic probability theory)
• Some prior exposure to computer graphics (basic modeling techniques, 3D geometry)
• Prior experience with computer vision / machine learning is a plus, but not required.

Location

The lecture will be held Tuesdays 16-18h (s.t.) in E1 4 (MPI-Informatik), Room 024 (ground floor).

Excercise course: Wednesday, 12:00-13:30h (s.t.) in E1 4 (MPI-Informatik), Room t.b.a..

Organization

There will be a lecture (2h a week) and exercises (2h a week). The exercises will focus on practical experiments with the techniques discussed in the lecture.

If you are interested in the course, and/or you have any questions or suggestions relating the course, feel invited to contact us via email at any time.

Slides

This is the collection of slides available so far. The schedule for future slides is only approximate. You need a password to access the slides; for external viewers, a public version is provided below as well.

• Lecture #1 (October 18th 2011):
  01 - Formalities (updated Nov. 8th 2011)
  02 - Introduction
• Lecture #2 (October 25th 2011):
  03 - Linear Algebra & Linear Inverse Problems (updated Nov. 8th 2011)
  
• Lecture #3,#4 (November 8th/22nd 2011):
  04 - Differential Geometry (updated Nov. 22nd 2011)
• Lecture #5,#6 (November 23rd/29th 2011)
  05 - Representing Geometry (updated Nov. 8th 2011)
• Lectures #7,#8 (December 6th, 13th, 14th(tutorial))
  06 - Bayesian Statistics (updated Dec. 14th 2011)
  07 - Machine Learning (updated Dec. 21th 2011)
  08 - SignalTheoryPrimer (updated Dec. 14th 2011)
• Lecture #9 (December 20th)
  07b - Shape Spaces and Surface Reconstruction (updated Dec. 21th 2011)
  slide set 07 - Machine Learning updated
• Lecture #10,#11 (January 10th/18th 2012)
  09 - Least-Squares (updaetd January 19th 2012)
  
• Lecture #12,#13 (January 24th/25th 2012)
  10 - Variational Modeling (updaetd January 24th 2012)
• Lecture #14 (January 25th/31st 2012)
  11 - Deformable Shape Matching (updated February 9th 2012)
• Lecture #15 (February 7th 2012)
  12 - Global Shape Matching (updated February 9th 2012)
  13 - Summary (updated February 9th 2012)
  

Public versions of the slides (only minor differences, no password required):

• 02 - Introduction
• 03 - Linear Algebra & Linear Inverse Problems
• 04 - Differential Geometry
• 05 - Representing Geometry
• 06 - Bayesian Statistics
• 07 - Machine Learning
• 07b - ShapeSpaces and SurfaceReconstruction
• 08 - Signal Theory Primer
• 09 - Least-Squares
• 10 - Variational Modeling
• 11 - Deformable Shape Matching
• 12 - Global Shape Matching

Assignments

Here is the collection of assignment sheets handed-out so far.

• Assignment #0 - Installing and Using GeoX (not graded: no due date, this is only an introduction to our software framework)
• Assignment #1 - Inverse Problems (out: Nov 2nd, due: Tutorial course two weeks later, Nov 16th 12:00-13:30h R023)
  A new version of GeoX has been released for this assignment (see also below; please note the platform restrictions; contact us in case of problems).
• Assignment #2 - Classical Multi-Dimensional Scaling (out: Nov 16th, due: Tutorial course two weeks later, Nov 30th 12:00-13:30h R023)
• Assignment #3 - Representing Bunnyfold Objects (out: Nov. 29th, due: Tutorial course two weeks later, Dec 14th 12:00-13:30h in R023)
• Assignment #4 - Bayesian Bunny Denoising (out: Dec. 14th, due: Tutorial course on Jan. 18th (shifted by one week!)).
  Please see your instructor / TA to discuss details of the assignment.
• Assignment #5 - The space of your Handwriting (out: Jan 19th 2012, due: Tutorial course two weeks later, Wednesday, Feb. 1st, 2012)
• Assignment #6 - Fit your Handwriting (out: Jan 31st 2012, due: Tutorial course two weeks later, Wednesday, Feb. 8th, 2012)

Software Framework

Below is the software framework we provide for solving the assignments. Using the framework is optional, but please contact us in advance if you are planning on using different platforms.

Schedule

(Schedule updated: Jan. 30th 2012, 19:07h CET)