Erick Klassen

Former Visitor, FSU

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Last publications in Ariana Research Group :

Shape Analysis of Elastic Curves in Euclidean Spaces. S. Joshi and E. Klassen and W. Liu and I. H. Jermyn and A. Srivastava. IEEE Trans. Pattern Analysis and Machine Intelligence, 33(7): pages 1415-1428, 2010. Note : to appear Keywords : shape analysis, elastic deformations, Riemannian elastic metric. @ARTICLE{Joshi2010, author = {Joshi, S. and Klassen, E. and Liu, W. and Jermyn, I. H. and Srivastava, A.}, title = {Shape Analysis of Elastic Curves in Euclidean Spaces}, year = {2010}, journal = {IEEE Trans. Pattern Analysis and Machine Intelligence}, volume = {33}, number = {7}, pages = {1415-1428}, note = {to appear}, pdf = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5601739}, keyword = {shape analysis, elastic deformations, Riemannian elastic metric} } Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves. S. Joshi and E. Klassen and A. Srivastava and I. H. Jermyn. In Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Ezhou, China, August 2007. Keywords : Shape, Reparameterization, Metric, Geodesic. Copyright : The original publication is available at www.springerlink.com. @INPROCEEDINGS{Joshi07b, author = {Joshi, S. and Klassen, E. and Srivastava, A. and Jermyn, I. H.}, title = {Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves}, year = {2007}, month = {August}, booktitle = {Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)}, address = {Ezhou, China}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Joshi07b.pdf}, keyword = {Shape, Reparameterization, Metric, Geodesic} } Abstract : This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves. A Novel Representation for Riemannian Analysis of Elastic Curves in R^n. S. Joshi and E. Klassen and A. Srivastava and I. H. Jermyn. In Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Minneapolis, USA, June 2007. Keywords : Shape, Metric, Geodesic, Prior. @INPROCEEDINGS{Joshi07a, author = {Joshi, S. and Klassen, E. and Srivastava, A. and Jermyn, I. H.}, title = {A Novel Representation for Riemannian Analysis of Elastic Curves in R^n}, year = {2007}, month = {June}, booktitle = {Proc. IEEE Computer Vision and Pattern Recognition (CVPR)}, address = {Minneapolis, USA}, url = {http://dx.doi.org/10.1109/CVPR.2007.383185}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Joshi07a.pdf}, keyword = {Shape, Metric, Geodesic, Prior} } Abstract : We propose an efficient representation for studying shapes of closed curves in R^n. This paper combines the strengths of two important ideas---elastic shape metric and path-straightening methods---and results in a very fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features between the two curves while path-straightening ensures that the algorithm results in geodesic paths. For the novel representation proposed here, the elastic metric becomes the simple L^2 metric, in contrast to the past usage where more complex forms were used. We present the step-by-step algorithms for computing geodesics and demonstrate them with 2-D as well as 3-D examples.

All publications in Ariana Research Group