Towards Fully Automatic Optimal Shape Modeling Karlsson, Johan 2008 Link to publication Citation for published version (APA): Karlsson, J. (2008). Towards Fully Automatic Optimal Shape Modeling. 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LUND UNIVERSITY PO Box 117 221 00 Lund +46 46-222 00 00 TOWARDS FULLY AUTOMATIC OPTIMAL SHAPE MODELING JOHAN KARLSSON Faculty of Engineering Centre for Mathematical Sciences Mathematics Mathematics Centre for Mathematical Sciences Lund University Box 118 SE-221 00 Lund Sweden http://www.maths.lth.se/ Doctoral Theses in Mathematical Sciences 2008:9 ISSN 1404-0034 ISBN 978-91-628-7226-7 LUTFMA-1033-2008 Johan Karlsson, 2008 Printed in SWEDEN by MediaTryck, Lund 2008 Preface When I finished high school (gymnasium), I said I would never again do anything con- cerned with natural sciences or technology, it was just too boring. I kept my word for seven years, during which I worked as a cinema projectionist and got a B.A. (fil.kand.) in philosophy. I loved it. Then I realized I had to get a job, and since philosophers were not in high demand at the time, I sat down and considered the alternatives. I made a list of educations I could get and the jobs they would lead to and I wrote them down in order of priority based on what I thought I would endure best. Then I applied. At the top of the list was M.D. but my grades were only almost good enough so I didn’t get in. In second place I had put down computer engineer and there I got in. I figured I would just barely make it through and then I would get a job. Not a dream job, but it would pay the rent. I didn’t just barely make it through, it went very well. Little by little something happened that surprised me more that anyone. I started to enjoy mathematics. When we got to choose courses I directed my education towards mathematics and when I took my first course in mathematical image analysis for Kalle Åström I felt that this was it, this was what I wanted to do. So I took some more courses and then I decided to do my masters thesis in the field. I was still interested in medicine so I talked to Kalle about it and it turned out that he had a Ph.D.-student working with medical image analysis. That was Anders Ericsson and he and Kalle supervised my masters thesis "Automatic positioning of landmarks for shape analysis". That went very well too and things got even more in- teresting and enjoyable so I started talking to Kalle about doing a Ph.D. and now here I am. Life is funny. The work of this thesis makes contributions to the field of automatic optimal shape modeling. The reason that the title is "Towards fully automatic optimal shape modeling" instead of simply "Fully automatic optimal shape modeling" is that automaticity and optimality are important properties that I think can never be fully reached, because we can always redefine what we mean by automatic and optimal. We develop our tools in this direction, getting better and better tools. This thesis is part of this eternal development of the tools. i The contents of the thesis is based on the following papers, Main papers I J. Karlsson and K. Åström, "Generative Models of Shape and Local Appearance from Unlabeled Images with Occlusions using MDL", Submitted to IJCV (Interna- tional Journal of Computer Vision). II J. Karlsson and K. Åström, "MDL Patch Correspondences on Unlabeled Images", ICPR (International Conference on Pattern Recognition), 2008. III J. Karlsson and K. Åström, "MDL Patch Correspondences on Unlabeled Images with Occlusions", NORDIA - Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, CVPR (IEEE Computer Society Conference on Computer Vision and Pattern Recognition), 2008. IV K. Åström, J. Karlsson, O. Enqvist, A. Ericsson and F. Kahl, "Automatic Feature Point Correspondences and Shape Analysis with Missing Data and Outliers", SCIA (Scandinavian Conference on Image Analysis), 2007. V A. Ericsson and J. Karlsson, “Measures for Benchmarking of algorithms for auto- matic shape modeling”, JMIV (Journal of Mathematical Imaging and Vision), 2007. VI A. Ericsson and J. Karlsson, “Benchmarking of algorithms for automatic corre- spondence localisation”, BMVC (British Machine Vision Conference), 2006. VII J. Karlsson and A. Ericsson, “A Geodesic Ground Truth Correspondence Measure for Benchmarking”, ICPR (International Conference on Pattern Recognition), 2006. VIII A. Ericsson and J. Karlsson, “Aligning Shapes by Minimising the Description Length”, SCIA (Scandinavian Conference on Image Analysis, 2005. IX J. Karlsson, A. Ericsson and K. Åström, “Parameterisation Invariant Statistical Shape Models”, in Proc. ICPR (International Conference on Pattern Recognition), 2004. Subsidiary papers X K.M. Henriksson, K. Wickström, N. Maltesson, A. Ericsson, J. Karlsson, F. Lind- gren, K. Åström, T.F. McNeil and I. Agartz, “A pilot study of facial, cranial, and brain MRI morphometry in men with schizophrenia”, Psychiatry Research: Neu- roimaging, 2006. XI A. Ericsson and J. Karlsson, “A Geodesic Ground Truth Correspondence Measure for Benchmarking”, in Proc. SSBA (Swedish Symposium on Image Analysis), 2006. ii XII A. Ericsson and J. Karlsson, “Aligning Shapes by Minimising the Description Length”, in Proc. SSBA (Swedish Symposium on Image Analysis), 2005. XIII K. Josephson, A. Ericsson and J. Karlsson, “Segmentation of Medical Images Us- ing Three-Dimensional Active Shape Models”, SCIA (Scandinavian Conference on Image Analysis), 2005. XIV J. Karlsson, A. Ericsson and K. Åström, “Parameterisation Invariant Statistical Shape Models”, SSBA (Swedish Symposium on Image Analysis), 2004. XV J. Karlsson "Automatic positioning of landmarks for shape analysis", Master’s the- sis, Centre for mathematical sciences, Lund University, 2003. iii iv Acknowledgments My primary thanks go to Anders Ericsson whom I have worked with during a lot of my research. The value of the discussions and teamwork has been immense. Thanks also go to my supervisors. Primarily to Kalle Åström who’s optimism and knowledge have been a great help. I also thank my other supervisors Gunnar Sparr and Lars Edenbrandt. The colleagues at the department have also been great, I mention none and forget none. Also, great thanks go to my friends and family who are a haven of support and per- spective. Research projects are not possible without money. I am deeply grateful for the finan- cial support of this project by the Swedish Knowledge Foundation through the Industrial PhD programme in Medical Bioinformatics at Karolinska Institutet, Strategy and Devel- opment Office, in cooperation with UMAS and by the Swedish Foundation for Strategic Research (SSF) through the programme Vision in Cognitive Systems (VISCOS). v vi Contents 1 Introduction 1 1.1 Motivation................................ 1 1.2 OrganizationoftheThesis. 1 1.3 MainContributions ........................... 3 I Shape Models 5 2 Shape Model Theory 7 2.1 Introduction............................... 7 2.2 Shape .................................. 11 2.3 AlignmentandMeanoftheTrainingSet . 15 2.4 DimensionalityReduction. 20 2.5 ShapeModel............................... 22 2.6 MeasuringShapeModelQuality . 23 2.7 Segmentation Using an Active Shape Model . .. 26 3 Shape Model Application 31 3.1 Introduction............................... 31 3.2 Shape Reconstruction from Point Clouds . .. 32 3.3 EstablishingCorrespondences . 32 3.4 BuildingtheShapeModel . 33 3.5 Experiments ............................... 34 3.6 SummaryandConclusions . 37 4 SegmentationusingIntegralApproximation 39 4.1 Introduction............................... 39 4.2 Modification of Segmentation Search Algorithm . ..... 41 4.3 Experiments ............................... 43 4.4 Extensions................................ 44 4.5 SummaryandConclusions . 46 vii CONTENTS II Automatic and Optimal Construction of Shape Models 47 5 Establishing Correspondences on Object Outlines Using MDL 49 5.1 Introduction............................... 49 5.2 TheMinimumDescriptionLength . 50 5.3 CorrespondenceOptimization. 55 5.4 The Gradient of the Minimum Description Length . ... 58 6 Aligning Shapes by Optimizing MDL 61 6.1 Introduction............................... 61 6.2 OptimizingMDLusingtheGradient . 62 6.3 ExperimentalValidation . 64 7 Stable Correspondence Optimization using ParameterizationInvariance 73 7.1 Introduction............................... 74 7.2 Preliminaries .............................. 75 7.3 TheProblemwithParameterizationDependence . .... 77 7.4 AParameterizationInvariantMethod . .. 79 7.5 ExperimentalValidation . 84 7.6 SummaryandConclusions . 86 8 Benchmarking of Algorithms for Correspondence