DocumentCode :
3423529
Title :
A Framework for Shape Analysis via Hilbert Space Embedding
Author :
Jayasumana, Sadeep ; Salzmann, Mathieu ; Hongdong Li ; Harandi, Mehrtash
Author_Institution :
Australian Nat. Univ., Canberra, ACT, Australia
fYear :
2013
fDate :
1-8 Dec. 2013
Firstpage :
1249
Lastpage :
1256
Abstract :
We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall´s shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these spaces, most existing shape classification algorithms resort to nearest neighbor methods and to learning distances on shape spaces. Here, we propose to map shapes on Kendall´s shape manifold to a high dimensional Hilbert space where Euclidean geometry applies. To this end, we introduce a kernel on this manifold that permits such a mapping, and prove its positive definiteness. This kernel lets us extend kernel-based algorithms developed for Euclidean spaces, such as SVM, MKL and kernel PCA, to the shape manifold. We demonstrate the benefits of our approach over the state-of-the-art methods on shape classification, clustering and retrieval.
Keywords :
Gaussian processes; Hilbert spaces; image classification; learning (artificial intelligence); 2D shape analysis; Euclidean geometry; Kendall shape manifold; MKL; Procrustes Gaussian kernel; SVM; high dimensional Hilbert space embedding; kernel PCA; kernel k-means; kernel principal component analysis; kernel-based algorithms; learning distances; multiple kernel learning; nearest neighbor methods; nonlinear space generation; positive definite kernels; shape classification algorithms; shape clustering; shape retrieval; shape spaces; support vector machines; Geometry; Hilbert space; Kernel; Manifolds; Shape; Support vector machines; Vectors; Mercer kernels; Positive definite kernels; Shape analysis; Shape manifold;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Computer Vision (ICCV), 2013 IEEE International Conference on
Conference_Location :
Sydney, NSW
ISSN :
1550-5499
Type :
conf
DOI :
10.1109/ICCV.2013.158
Filename :
6751265
Link To Document :
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