Article

Nonlinear Shape Statistics in Mumford-Shah Based Segmentation

Authors:

Daniel Cremers,

Timo Kohlberger,

Christoph SchnörrAuthors Info & Claims

ECCV '02: Proceedings of the 7th European Conference on Computer Vision-Part II

Pages 93 - 108

Published: 28 May 2002 Publication History

Abstract

We present a variational integration of nonlinear shape statistics into a Mumford-Shah based segmentation process. The non-linear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a stochastic framework.The idea is to assume that the training data forms a Gaussian distribution after a nonlinear mapping to a potentially higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non-Gaussian. It can capture essentially arbitrary data distributions (e.g. multiple clusters, ring- or banana-shaped manifolds).Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real-world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.

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Index Terms

Nonlinear Shape Statistics in Mumford-Shah Based Segmentation
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
  2. Machine learning

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Guide Proceedings

ECCV '02: Proceedings of the 7th European Conference on Computer Vision-Part II

May 2002

895 pages

ISBN:3540437444

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 28 May 2002

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Wang YXiang SPan CWang LMeng G(2013)Level set evolution with locally linear classification for image segmentationPattern Recognition10.1016/j.patcog.2012.12.00646:6(1734-1746)Online publication date: 1-Jun-2013
https://dl.acm.org/doi/10.1016/j.patcog.2012.12.006
Rathi YMalcolm JBouix SMcCarley RSeidman LGoldstein JWestin CShenton M(2010)Disease classificationProceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro10.5555/1855963.1856306(1345-1348)Online publication date: 14-Apr-2010
https://dl.acm.org/doi/10.5555/1855963.1856306
Schmidt FCremers D(2009)A Closed-Form Solution for Image Sequence Segmentation with Dynamical Shape PriorsProceedings of the 31st DAGM Symposium on Pattern Recognition - Volume 574810.5555/3089925.3089930(31-40)Online publication date: 9-Sep-2009
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Chen PSteen RYezzi AKrim H(2009)Joint brain parametric T1-map segmentation and RF inhomogeneity calibrationJournal of Biomedical Imaging10.1155/2009/2695252009(1-14)Online publication date: 1-Jan-2009
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Etyngier PSégonne FKeriven R(2007)Active-contour-based image segmentation using machine learning techniquesProceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I10.5555/1780201.1780322(891-899)Online publication date: 29-Oct-2007
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Etyngier PKeriven RPons J(2007)Towards segmentation based on a shape prior manifoldProceedings of the 1st international conference on Scale space and variational methods in computer vision10.5555/1767926.1768013(895-906)Online publication date: 30-May-2007
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Zoller TBuhmann J(2007)Robust Image Segmentation Using Resampling and Shape ConstraintsIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2007.115029:7(1147-1164)Online publication date: 1-Jul-2007
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Rathi YVaswani NTannenbaum AYezzi A(2007)Tracking Deforming Objects Using Particle Filtering for Geometric Active ContoursIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2007.108129:8(1470-1475)Online publication date: 1-Aug-2007
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Cremers DRousson MDeriche R(2007)A Review of Statistical Approaches to Level Set SegmentationInternational Journal of Computer Vision10.1007/s11263-006-8711-172:2(195-215)Online publication date: 21-Apr-2007
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Yilmaz AJaved OShah M(2006)Object trackingACM Computing Surveys10.1145/1177352.117735538:4(13-es)Online publication date: 25-Dec-2006
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