Abstract
We present a novel approach for representing shape knowledge in terms of example views of 3D objects. Typically, such data sets exhibit a highly nonlinear structure with distinct clusters in the shape vector space, preventing the usual encoding by linear principal component analysis (PCA). For this reason, we propose a nonlinear Mercerkernel PCA scheme which takes into account both the projection distance and the within-subspace distance in a high-dimensional feature space. The comparison of our approach with supervised mixture models indicates that the statistics of example views of distinct 3D objects can fairly well be learned and represented in a completely unsupervised way.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
B. E. Boser, I. M. Guyon, and V. N. Vapnik. A training algorithm for optimal margin classifiers. In D. Haussler, editor, Proc. of the 5th Annual ACM Workshop on Computational Learning Theory, pages 144–152, Pittsburgh, PA, 1992. ACM Press.
B. Chalmond and S. C. Girard. Nonlinear modeling of scattered multivariate data and its application to shape change. IEEE Trans. Patt. Anal. Mach. Intell., 21(5):422–432, 1999.
T.F. Cootes and C.J. Taylor. A mixture model for representing shape variation. Image and Vis. Comp., 17(8):567–574, 1999.
T.F. Cootes, C.J. Taylor, D.M. Cooper, and J. Graham. Active shape models-their training and application. Comp. Vision Image Underst., 61(1):38–59, 1995.
V. Cortes, and C. Vapnik. Support vector networks. Machine Learning, 20: 273–297, 1995.
D. Cremers, C. Schnörr, and J. Weickert. Diffusion-snakes: Combining statistical shape knowledge and image information in a variational framework. In IEEE Workshop on Variational and Level Set Methods, Vancouver, Canada, Jul. 13, 2001. To appear.
D. Cremers, C. Schnörr, J. Weickert, and C. Schellewald. Diffusion-snakes using statistical shape knowledge. In G. Sommer and Y.Y. Zeevi, editors, Algebraic Frames for the Perception-Action Cycle, volume 1888 of Lect. Not. Comp. Sci., pages 164–174, Kiel, Germany, Sept. 10-11, 2000. Springer.
T. Heap and D. Hogg. Automated pivot location for the cartesian-polar hybrid point distribution model. In Brit. Machine Vision Conference, pages 97–106, Edinburgh, UK,Sept. 1996.
C. Kervrann and F. Heitz. A hierarchical markov modeling approach for the segmentation and tracking of deformable shapes. Graphical Models and Image Processing, 60:173–195, 5 1998.
M.E. Leventon, W.E.L. Grimson, and O. Faugeras. Statistical shape influence in geodesic active contours. In Proc. Conf. Computer Vis. and Pattern Recog., volume 1, pages 316–323, Hilton Head Island, South Carolina, June 13-15, 2000.
B. Moghaddam and A. Pentland. Probabilistic visual learning for object representation. IEEE Trans. Patt. Anal. Mach. Intell., 19(7):696–710, 1997.
B. Schölkopf, S. Mika, Smola A., G. Rätsch, and Müller K.-R. Kernel PCA pattern reconstruction via approximate pre-images. In L. Niklasson, M. Boden, and T. Ziemke, editors, Internat. Conf. on Art. Neural Networks ICANN, pages 147–152, Berlin, Germany, 1998. Springer.
B. Schölkopf, A. Smola, and K.-R. Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299–1319, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cremers, D., Kohlberger, T., Schnörr, C. (2001). Nonlinear Shape Statistics via Kernel Spaces. In: Radig, B., Florczyk, S. (eds) Pattern Recognition. DAGM 2001. Lecture Notes in Computer Science, vol 2191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45404-7_36
Download citation
DOI: https://doi.org/10.1007/3-540-45404-7_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42596-0
Online ISBN: 978-3-540-45404-5
eBook Packages: Springer Book Archive