@inproceedings{8136a1794f844073ac0b5539710a8012,
title = "Nonlinear shape statistics via kernel spaces",
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 Mercer-kernel PCA scheme which takes into account both the projection distanceand 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 canfairly well be learned and represented in a completely unsupervised way.",
keywords = "Kernel PCA, Mercer kernels, Nonlinear density estimation, Nonlinear shape statistics, Shape learning, Variational methods",
author = "Daniel Cremers and Timo Kohlberger and Christoph Schn{\"o}rr",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2001.; 23rd German Association for Pattern Recognition Symposium, DAGM 2001 ; Conference date: 12-09-2001 Through 14-09-2001",
year = "2001",
doi = "10.1007/3-540-45404-7_36",
language = "English",
isbn = "3540425969",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "269--276",
editor = "Bernd Radig and Stefan Florczyk",
booktitle = "Pattern Recognition - 23rd DAGM Symposium, Proceedings",
}