Publications | Max Planck Institute for Intelligent Systems

Statistical models of non-rigid deformable shape have wide application in many fields, including computer vision, computer graphics, and biometry. We show that shape deformations are well represented through nonlinear manifolds that are also matrix Lie groups. These pattern-theoretic representations lead to several advantages over other alternatives, including a principled measure of shape dissimilarity and a natural way to compose deformations. Moreover, they enable building models using statistics on manifolds. Consequently, such models are superior to those based on Euclidean representations. We demonstrate this by modeling 2D and 3D human body shape. Shape deformations are only one example of manifold-valued data. More generally, in many computer-vision and machine-learning problems, nonlinear manifold representations arise naturally and provide a powerful alternative to Euclidean representations. Statistics is traditionally concerned with data in a Euclidean space, relying on the linear structure and the distances associated with such a space; this renders it inappropriate for nonlinear spaces. Statistics can, however, be generalized to nonlinear manifolds. Moreover, by respecting the underlying geometry, the statistical models result in not only more effective analysis but also consistent synthesis. We go beyond previous work on statistics on manifolds by showing how, even on these curved spaces, problems related to modeling a class from scarce data can be dealt with by leveraging information from related classes residing in different regions of the space. We show the usefulness of our approach with 3D shape deformations. To summarize our main contributions: 1) We define a new 2D articulated model -- more expressive than traditional ones -- of deformable human shape that factors body-shape, pose, and camera variations. Its high realism is obtained from training data generated from a detailed 3D model. 2) We define a new manifold-based representation of 3D shape deformations that yields statistical deformable-template models that are better than the current state-of-the- art. 3) We generalize a transfer learning idea from Euclidean spaces to Riemannian manifolds. This work demonstrates the value of modeling manifold-valued data and their statistics explicitly on the manifold. Specifically, the methods here provide new tools for shape analysis.

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ps Freifeld, O. Statistics on Manifolds with Applications to Modeling Shape Deformations Brown University, August 2013 (phdthesis)

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Dry adhesives and methods of making dry adhesives

Sitti, M., Murphy, M., Aksak, B.

March 2013, US Patent App. 13/845,702 (misc)

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pi Sitti, M., Murphy, M., Aksak, B. Dry adhesives and methods of making dry adhesives March 2013, US Patent App. 13/845,702 (misc)

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Modelling and Learning Approaches to Image Denoising

Burger, HC.

Eberhard Karls Universität Tübingen, Germany, 2013 (phdthesis)

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ei Burger, HC. Modelling and Learning Approaches to Image Denoising Eberhard Karls Universität Tübingen, Germany, 2013 (phdthesis)

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Linear mixed models for genome-wide association studies

Lippert, C.

University of Tübingen, Germany, 2013 (phdthesis)

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ei Lippert, C. Linear mixed models for genome-wide association studies University of Tübingen, Germany, 2013 (phdthesis)

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Leveraging Weak Supervision for Video Understanding

Garcia Cifuentes, C.

University College London, 2013 (phdthesis)

link (url) [BibTex]

Garcia Cifuentes, C. Leveraging Weak Supervision for Video Understanding University College London, 2013 (phdthesis)

link (url) [BibTex]

Modeling and Learning Complex Motor Tasks: A case study on Robot Table Tennis

Mülling, K.

Technical University Darmstadt, Germany, 2013 (phdthesis)

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ei Mülling, K. Modeling and Learning Complex Motor Tasks: A case study on Robot Table Tennis Technical University Darmstadt, Germany, 2013 (phdthesis)

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Intention Inference and Decision Making with Hierarchical Gaussian Process Dynamics Models

Wang, Z.

Technical University Darmstadt, Germany, 2013 (phdthesis)

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ei Wang, Z. Intention Inference and Decision Making with Hierarchical Gaussian Process Dynamics Models Technical University Darmstadt, Germany, 2013 (phdthesis)

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Quantum kinetic theory for demagnetization after femtosecond laser pulses

Teeny, N.

Universität Stuttgart, Stuttgart, 2013 (mastersthesis)

mms

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mms Teeny, N. Quantum kinetic theory for demagnetization after femtosecond laser pulses Universität Stuttgart, Stuttgart, 2013 (mastersthesis)

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Ab-initio modeling of ultrafast demagnetization after laser irradiation in nickel, iron and cobalt

Illg, C.

Universität Stuttgart, Stuttgart, 2013 (phdthesis)

mms

link (url) [BibTex]

mms Illg, C. Ab-initio modeling of ultrafast demagnetization after laser irradiation in nickel, iron and cobalt Universität Stuttgart, Stuttgart, 2013 (phdthesis)

link (url) [BibTex]

2009

Kernel Learning Approaches for Image Classification

Gehler, PV.

Biologische Kybernetik, Universität des Saarlandes, Saarbrücken, Germany, October 2009 (phdthesis)

Abstract

This thesis extends the use of kernel learning techniques to specific problems of image classification. Kernel learning is a paradigm in the field of machine learning that generalizes the use of inner products to compute similarities between arbitrary objects. In image classification one aims to separate images based on their visual content. We address two important problems that arise in this context: learning with weak label information and combination of heterogeneous data sources. The contributions we report on are not unique to image classification, and apply to a more general class of problems. We study the problem of learning with label ambiguity in the multiple instance learning framework. We discuss several different image classification scenarios that arise in this context and argue that the standard multiple instance learning requires a more detailed disambiguation. Finally we review kernel learning approaches proposed for this problem and derive a more efficient algorithm to solve them. The multiple kernel learning framework is an approach to automatically select kernel parameters. We extend it to its infinite limit and present an algorithm to solve the resulting problem. This result is then applied in two directions. We show how to learn kernels that adapt to the special structure of images. Finally we compare different ways of combining image features for object classification and present significant improvements compared to previous methods.

PDF [BibTex]

2009

ei Gehler, PV. Kernel Learning Approaches for Image Classification Biologische Kybernetik, Universität des Saarlandes, Saarbrücken, Germany, October 2009 (phdthesis)

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Kernel Methods in Computer Vision:Object Localization, Clustering,and Taxonomy Discovery

Blaschko, MB.

Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, March 2009 (phdthesis)

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ei Blaschko, MB. Kernel Methods in Computer Vision:Object Localization, Clustering,and Taxonomy Discovery Biologische Kybernetik, Technische Universität Berlin, Berlin, Germany, March 2009 (phdthesis)

PDF PDF [BibTex]

Motor Control and Learning in Table Tennis

Mülling, K.

Eberhard Karls Universität Tübingen, Gerrmany, 2009 (diplomathesis)

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ei Mülling, K. Motor Control and Learning in Table Tennis Eberhard Karls Universität Tübingen, Gerrmany, 2009 (diplomathesis)

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Hierarchical Clustering and Density Estimation Based on k-nearest-neighbor graphs

Drewe, P.

Eberhard Karls Universität Tübingen, Germany, 2009 (diplomathesis)

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ei Drewe, P. Hierarchical Clustering and Density Estimation Based on k-nearest-neighbor graphs Eberhard Karls Universität Tübingen, Germany, 2009 (diplomathesis)

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Learning with Structured Data: Applications to Computer Vision

Nowozin, S.

Technische Universität Berlin, Germany, 2009 (phdthesis)

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ei Nowozin, S. Learning with Structured Data: Applications to Computer Vision Technische Universität Berlin, Germany, 2009 (phdthesis)

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From Differential Equations to Differential Geometry: Aspects of Regularisation in Machine Learning

Steinke, F.

Universität des Saarlandes, Saarbrücken, Germany, 2009 (phdthesis)

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ei Steinke, F. From Differential Equations to Differential Geometry: Aspects of Regularisation in Machine Learning Universität des Saarlandes, Saarbrücken, Germany, 2009 (phdthesis)

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Magnetische L10-FePt Nanostrukturen für höchste Datenspeicherdichten

Breitling, A.

Universität Stuttgart, Stuttgart, 2009 (phdthesis)

mms

[BibTex]

mms Breitling, A. Magnetische L10-FePt Nanostrukturen für höchste Datenspeicherdichten Universität Stuttgart, Stuttgart, 2009 (phdthesis)

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Ab-initio Elliott-Yafet modeling of ultrafast demagnetization after laser irradiation

Illg, C.

Universität Stuttgart, Stuttgart, 2009 (mastersthesis)

mms

[BibTex]

mms Illg, C. Ab-initio Elliott-Yafet modeling of ultrafast demagnetization after laser irradiation Universität Stuttgart, Stuttgart, 2009 (mastersthesis)

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Element specific investigation of the magnetization profile at the CrO2/RuO2 interface

Zafar, K.

Universität Stuttgart, Stuttgart, 2009 (mastersthesis)

mms

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mms Zafar, K. Element specific investigation of the magnetization profile at the CrO2/RuO2 interface Universität Stuttgart, Stuttgart, 2009 (mastersthesis)

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Bayesian Methods for Autonomous Learning Systems (Phd Thesis)

Ting, J.

Department of Computer Science, University of Southern California, Los Angeles, CA, 2009, clmc (phdthesis)

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am Ting, J. Bayesian Methods for Autonomous Learning Systems (Phd Thesis) Department of Computer Science, University of Southern California, Los Angeles, CA, 2009, clmc (phdthesis)

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