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Ausgewählte Kapitel der Mustererkennung 183.111, 195.044, 2011WS

Selected topics of pattern recognition
WS2011: Shape-from-function methods

shape analysis, description, and comparison
based on properties of real functions


Guest: Claudia Landi (Reggio Emilia, I)

This lecture covers a variety of methods for shape analysis and retrieval that are characterized by the use of a real-valued  function defined on the shape to derive its signature. Shape-from-function methods are discussed following a framework that distinguishes among the three main components of this class of methods:
• shape analysis, via the application of the function;
• shape description, via the construction of a signature;
• shape comparison, via the definition of a distance measure.
The lecture will focus on three shape-from-function methods:
Reeb graphs, size functions, persistent homology.

Schedule+Slides, S: Seminarraum 183/2, Z: Zemanek Saal
12.12.2011, Z: 12-14 Lecture 1
13.12.2011, S: 10-12

Lecture 2(ppt)

Lecture 2 (pdf)

14.12.2011, Z: 12-14 Lecture 3
15.12.2011, Z: 9-12 Lecture 4
16.12.2011, Z:14-16

Lecture 5

(Slides 1-8)

09.01.2012, Z:12-14

Lecture 5

(Slides 9-31)

10.01.2012, S: 16-18 Lecture 6
11.01.2012, Z: 12-14

Lecture 7 (ppt)

Lecture 7 (pdf)

12.01.2012, Z: 9-12 Exercise class
13.01.2012, Z: 14-16 Feedback on coursework



















Related reading: a general introduction to the methods:
Biasotti S; De Floriani L; Falcidieno B; Frosini P; Giorgi D; C. Landi;
Papaleo L; Spagnolo M (2008) Describing shapes by geometrical- topological
properties of real functions ACM COMPUTING SURVEYS, Vol 40:1-87

Another related, recent paper can be found here.

Schedule WS 2011/2012 

1st lecture: 11.10.2011 16ct

Part I: 12.-16.12.2011

Part II: 9.-13.1.2012

Details of schedule can be found here.

Further nice papers introducing size functions and Reeb graphs, respectively, are:

Verri, A., Uras, C., Frosini, P., Ferri, M.,On the use of size functions for
shape analysis
, Biological Cybernetics, 70, (1993), 99-107.

Shinagawa, Kunii, Kergosien: Surface Coding Based on Morse Theory, IEEE
Computer Graphics and Applications archive, Volume 11 Issue 5, September 1991
(http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=90568 )

For Persistence I'd suggest section VII.1 of

Herbert Edelsbrunner and John Harer. Computational Topology: An Introduction.
American Mathematical Society, 2010.

Evaluation criteria for Certificate (Zeugnis):

  • Written critical discussion of selected paper
    • Correctness of the exposed concepts.
    • How complet and detailed is the paper.
    • How comprehensible is the paper.
  • Attendance and attitude during lessons.