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Computer Vision Group
TUM School of Computation, Information and Technology
Technical University of Munich

Technical University of Munich



Analysis of Three-Dimensional Shapes (IN2238) (2h + 1h, 4 ECTS)


Oral exams will take place on July 17th and July 25th!
Location: Room 02.09.058
Organization: Please contact us (windheus@in.tum.de) and tell us your preferred day and time. If both dates collide with other exams, please let us know. We will find a solution.
Content: The exam will cover the contents of the lecture and exercises.


Location: Room 02.09.023
Time and Date: Mondays 10:00 - 12:00, Thursdays 16:00 - 18:00 (check the calendar below)
Lecturer: Dr. Emanuele Rodolà
Start: April 7th
The lecture is held in English.


Location: Room 02.09.023
Time and Date: Tuesday 13:45 - 15:15
Organization: Thomas Windheuser, Matthias Vestner
Start: April 15th

The excercise sheets consist of two parts:

  1. Mathematics
  2. Programming

You can submit your solutions via email to windheus@in.tum.de until monday (23:59) before the corresponding exercise class. Since we are not experts in decryption we ask you to hand in typewritten solutions for the first part and commented source code for the second part.

In the exercise class the solutions to the first part will be discussed.


By handing in reasonable solutions to 60% of the exercises you can obtain a bonus of 0.3 in the final exam. Extra points can be achieved by presenting exercises in class. Note that you can neither improve a 1.0 nor a 4.3.



Name Score Avg. geo. error Matched (first shape) Matched (second shape) Method
-1.0000.00100%100%Ground-truth correspondence.
Thomas Hörmann0.9476.39100%100%Closest points in HKS descriptor space with further post-processing to redistribute matches all over the second shape.
Thomas Hörmann0.6338.81100%36.64%Closest points in GPS/HKS descriptor space.
-0.45053.80100%63.16%Random matching.

All the students are invited and encouraged to participate in The Matching Game. You are given the two shapes depicted above, and your task is to find a correspondence between them (the best you can). You are allowed to use all the techniques explained in the course, you can try new ones from the literature, you can mix them up, you can even invent your own. Be creative!

Download the shapes.

Submission instructions: The matches should be sent via e-mail to rodola@in.tum.de, in .txt format, where each line contains a pair of matching indices from the first shape and the second shape respectively. The solution is not required to be dense nor surjective. The only requirement is that points in the first shape are allowed to match at most one point in the second shape. Symmetric matches are also accepted (i.e. matching the left part of the first shape to the right part of the second shape).

The best solution will receive a prize. In any case, discussing your approach to matching the two shapes will be a good starting point in the final exam.


The exam will be oral.


It is a classical problem in Computer Vision to compare three-dimensional shapes and to find correspondences between them. In the last years this field has known a fast development leading to a number of very powerful algorithms with a solid mathematical foundation. In this course we will present some of these, discussing both, the mathematics involved and the practical issues for the implementation.

Topics we plan to cover include:

  • Foundations of Differential Geometry of surfaces (tangent spaces, shape operator, Riemannian metric, geodesics and their discrete versions)
  • The Gromov-Hausdorff distance and its variants
  • Spectral methods (Laplace-Beltrami operators and their eigenvalues)
  • Conformal geometry applied to shape matching
  • Shape matching based on continuum mechanics
Lecture Material

[BBK] = Numerical geometry of non-rigid shapes. Bronstein, Bronstein, Kimmel. Springer 2008.

[BBI] = A course in metric geometry. Burago, Burago, Ivanov. AMS 2001.

[DC] = Differential geometry of curves and surfaces. Do Carmo. Pearson 1976.

[K] = Differential geometry: curves - surfaces - manifolds. W. Kühnel. AMS 2005.

Date Slides Exercise Reading
Mon. 07.04.2014Introduction Exercise Sheet 1 Matlab Exercise Code [BBK]
Mon. 14.04.2014Shapes as Metric SpacesExercise Sheet 2 Matlab Exercise Code [BBK] [BBI] [M08] [MS04] [M07]
Thur. 24.04.2014The Assignment ProblemExercise Sheet 3Matlab Exercise Code [M07] [LH05] [RB12]
Mon. 05.05.2014Euclidean Embeddings[BBK]
Thur. 08.05.2014Differential Geometry I[DC] [K]
Thur. 15.05.2014Differential Geometry IIExercise Sheet 4 Matlab Exercise Code[DC] [K]
Thur. 22.05.2014Isometries[DC]
Mon. 26.05.2014The LaplacianExercise Sheet 5 Matlab Exercise Code[C] [G]
Thur. 05.06.2014Intrinsic Shape Descriptors[R07] [SOG09]
Thur. 12.06.2014Functional Maps[OBSBG12]
Thur. 26.06.2014Intrinsic Metrics[CL05] [E05]
Thur. 03.07.2014(Very) Recent Advances on Shape Analysisdownload

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