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

128 pages
Ulm UniversityFaculty of Engineering and Computer ScienceNew methods for anechoicdemixing with application toshift invariant feature extractionLars Omloraus St. WendelDissertationzur Erlangung des Doktorgrades Dr.rer.nat.der Fakultat fur Ingenieurswissenschaften und Informatikder Universitat Ulmsupervised byProf. Martin A. GieseSection for Computational SensomotoricsUniversity TubingenandProf. Heiko NeumannInstitute of Neural Information ProcessingUlm UniversityAmtierender Dekan: Prof. Dr.-Ing. Michael WeberGutachter: Prof. Dr. Heiko Neumannhter: Dr. Martin A. Giese(Gutachter:) Prof. Dr. Andreas SchillingTag der Promotion: 09:03:2010AbstractBlind source separation problems emerge in many applications, where signals can bemodeled as superpositions of multiple sources. Many popular applications of blindsource 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 displacementsor time shifts) the resulting model is called anechoic mixing model.The main focus of this thesis is the development of new mathematical framework forthe solution of the anechoic mixing problem and the successive derivation of concretealgorithms.
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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 change from a right line to an arc or an angle, straightening a change from
either of these to a right line. Now in all such changes the exion or the straightening must
be relative to one point. Moreover, without exion there could not be walking or swimming
or ying.
On The Gait Of Animals, Aristotle
Now we see that the living creature is moved by intellect, imagination, purpose, wish, and
appetite. And all these are reducible to mind and desire. ::: Therefore the object of desire
or of intellect rst initiates movement, :::
On The Motion Of Animals, Aristotle
As the citations above indicate the understanding of human motion has been a eld of
research since the introduction of systematic sciences. However the issue in the rst of
Aristotle books about the topic, the kinetic and bio-mechanic of animal motion, is far
better understood than the neural mechanism underlying the planning and execution
of voluntary movements. A key problem is how the central nervous system deals with
motor redundancy, namely that a continuum of di erent possible ways to achieve the
same motor task exist. Since the early work of Bernstein [21], who studied the kine-
matics of hitting movements of highly trained blacksmiths striking the chisel with a
hammer, it is known that individual joints do not act independently but are somehow
linked either to correct their errors or to follow stereotypical motion templates. This
has lead to the assumption that animal movements are composed of a relatively small
set of basic motion ’atoms’ or primitives, which simplify the computational problem
involved in motor planning. Evidence for the existence of such motor primitives has
been found on many di erent levels of the motor hierarchy [66]. For example electrical
stimulations of the spinal cord of frogs [129] generate location dependent force elds,
which are superimposed if multiple areas are stimulated. Similar, micro-stimulation in
motor and pre-motor cortex of monkeys caused the animals to make coordinated, com-
plex movements [77]. Reviews of the literature about motor primitives can be found
in [66] and [105].
1.1.2 Why blind source separation ?
Unlike in animals, it is not possible to observe the basic movement patterns in humans
by stimulation of neural structures. Here only the result of neural activity, like muscle
6Lars Omlor 1.1. Motivation
activation (via electromyography (EMG) recordings) or joint angle trajectories (via
motion capturing) can be observed. But this indirect examination only allows the
observation of regular motor behavior which is in general the combinatory product
of many motion primitives. Therefore the task in analyzing the movement data is
to separate the unknown original basis patterns from the mixed observations, which
is by de

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