New methods for anechoic demixing with application to shift invariant feature extraction [Elektronische Ressource] / Lars Omlor

Sujets

• Informatik

Informations

• Publié par: universitat_ulm
• Publié le: 01 janvier 2010
• Nombre de lectures: 45
• Langue: English
• Poids de l'ouvrage: 62 Mo

Extrait

Ulm University
Faculty of Engineering and Computer Science
New methods for anechoic
demixing with application to
shift invariant feature extraction
Lars Omlor
aus St. Wendel
Dissertation
zur Erlangung des Doktorgrades Dr.rer.nat.
der Fakultat fur Ingenieurswissenschaften und Informatik
der Universitat Ulm
supervised by
Prof. Martin A. Giese
Section for Computational Sensomotorics
University Tubingen
and
Prof. Heiko Neumann
Institute of Neural Information Processing
Ulm UniversityAmtierender Dekan: Prof. Dr.-Ing. Michael Weber
Gutachter: Prof. Dr. Heiko Neumannhter: Dr. Martin A. Giese
(Gutachter:) Prof. Dr. Andreas Schilling
Tag der Promotion: 09:03:2010Abstract
Blind source separation problems emerge in many applications, where signals can be
modeled as superpositions of multiple sources. Many popular applications of blind
source separation are based on linear instantaneous mixture models. If speci c invari-
ance properties are known about the sources, e.g. translation or rotation invariance,
the simple linear model can be extended by inclusion of the corresponding transforma-
tions. When the sources are invariant against translations (i.e. spatial displacements
or time shifts) the resulting model is called anechoic mixing model.
The main focus of this thesis is the development of new mathematical framework for
the solution of the anechoic mixing problem and the successive derivation of concrete
algorithms. This framework integrates approaches from many distinct elds of signal
processing like stochastic time-frequency analysis, convex optimization, projection onto
convex set methods, delay estimation and naturally blind source separation.
The developed method is tested on a variety of applications including music recordings,
natural two dimensional images, two-dimensional shapes and optic ow. However the
main application is the analysis and synthesis of human motion trajectories, which is
motivated by the idea in motor control that complex motor behavior can be explained
by a superposition of simple basis components, or spatio-temporal primitives.
The new anechoic demixing algorithm allows to approximate high-dimensional move-
ment trajectories accurately based on a small number of learned primitives or source
signals. It is demonstrated that the new method is signi cantly more accurate than
other common techniques. This allows the modeling of subtle style changes, like the
bodily expression of emotion as well as a su cient synthesis quality for computer ani-
mation with only few mixture components.Contents
1 Introduction 6
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.1 Why motion analysis? . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.2 Why blind source separation ? . . . . . . . . . . . . . . . . . . . 6
1.1.3 Why anechoic demixing ? . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Detailed chapter overview . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Time frequency methods 15
2.1 Bilinear energy distributions . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Wigner-Ville distribution . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Basic examples for the WVS . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Properties of the WVS and the Wigner distribution . . . . . . . 18
2.2.3 WV spectrum estimation for non-stationary signals . . . . . . . . 20
2.2.4 The Wigner-Ville spectrum of linear signal spaces . . . . . . . . 20
2.3 The linear canonical transform (LCT) . . . . . . . . . . . . . . . . . . . 21
2.3.1 Main properties of the linear canonical transform . . . . . . . . . 22
2.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Non-negative least squares 24
3.1 NNLS as projection problem . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The Halpern{Lions{Wittmann{Bauschke algorithm . . . . . . . . . . . . 25
3.2.1 Application to the non-negative least squares problem . . . . . . 26
3.2.2 Improvement of the basic HLWB algorithm . . . . . . . . . . . . 30
3.2.3 Numerical simulations . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Blind source separation and nonnegative matrix factorization 38
4.1 General form of blind source separation problems . . . . . . . . . . . . . 38
4.2 Instantaneous mixtures and ICA . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Nonnegative matrix factorization (NMF) . . . . . . . . . . . . . . . . . . 40
4.3.1 Convolutive non-negative matrix factorization . . . . . . . . . . . 42
4.3.2 Continuous time non-negative matrix factorization . . . . . . . . 45
4.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2Lars Omlor CONTENTS
5 Time delay estimation 53
5.1 Single source methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.1 Single path propagation . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.2 Multi path . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Multiple source methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2.1 Maximum likelihood estimator . . . . . . . . . . . . . . . . . . . 58
5.2.2 Distinct independent signals . . . . . . . . . . . . . . . . . . . . . 59
5.2.3 Improving the independent signals estimator . . . . . . . . . . . 60
5.2.4 Nonlinear Gauss-Jacobi Method for the multiple signals TDE
problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6 Anechoic demixing 65
6.1 The anechoic mixing model . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.1.1 Existing work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 New algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.2.1 Modi ed alternating least squares . . . . . . . . . . . . . . . . . 66
6.2.2 Anechoic demixing using Wigner marginals . . . . . . . . . . . . 67
6.2.3 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.3 Computational complexity and limitations . . . . . . . . . . . . . . . . . 75
6.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7 Miscellaneous applications 76
7.1 Sound mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.2 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.3 Scale and rotation invariant shape analysis . . . . . . . . . . . . . . . . 78
7.4 Optic ow analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.4.1 Independent component analysis of optic ow . . . . . . . . . . . 80
7.4.2 Optic ow data set . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8 Human motion data: representation and analysis 84
8.1 Motion analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.1.1 Trajectory data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.1.2 Independent component analysis of single joint angle trajectories 85
8.1.3 Approximation quality . . . . . . . . . . . . . . . . . . . . . . . . 86
8.1.4 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2 Example applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.2.1 Asymmetry of emotional body expression [152] . . . . . . . . . . 89
8.2.2 Real time synthesis of body movements [72] . . . . . . . . . . . . 90
8.3 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9 Summary 93
3CONTENTS Lars Omlor
A Representation of motion data 96
A.1 Motion capture and movement recording . . . . . . . . . . . . . . . . . . 96
A.1.1 Joint Center computation . . . . . . . . . . . . . . . . . . . . . . 96
A.2 Movement representations . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.2.1 Joint angle computation . . . . . . . . . . . . . . . . . . . . . . . 100
A.2.2 Reconstruction of 3D positions from angles . . . . . . . . . . . . 102
A.2.3 Retargeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
A.3 Avatar model and Animation . . . . . . . . . . . . . . . . . . . . . . . . 105
B Implementation 106
4Lars Omlor CONTENTS
Acknowledgements
Many thanks to my advisors Prof. Martin A. Giese and Prof. Heiko Neumann. Addi-
tional thanks to Prof. Guenther Palm, Prof. Wolfgang Minker, Prof. Susanne Biundo-
Stephan, Prof. Tamar Flash and Prof. Jean-Jacques E. Slotine. Also I have to thank
my colleagues: Claire Roether, Andrea Christensen, Hubertus Becker, Avi Barliya, Falk
Fleischer, Phillip Diesinger, Aee-Ni Park, Albert Mukovskiy, Winfried Ilg and Dominik
Endres for their many:
5Lars Omlor
Chapter 1
Introduction
1.1 Motivation
1.1.1 Why motion analysis?
Flexion is a chan