Bending invariant representations for surfaces Export

@inproceedings{elad01bend, abstract = {Isometric surfaces share the same geometric structure also known as the first fundamental form. For example, bending of a given surface, that includes length preserving deformations without tearing or stretching the surface, are considered to be isometric. We present a method to construct a bending invariant canonical form for such surfaces. This invariant representation is an embedding of the intrinsic geodesic structure of the surface in a finite dimensional Euclidean space, in which geodesic distances are approximated by Euclidean ones. The canonical representation is constructed by first measuring the intergeodesic distances between points on the surfaces. Next, multi-dimensional scaling (MDS) techniques are applied to extract a finite dimensional flat space in which geodesic distances are represented as Euclidean ones. The geodesic distances are measured by the efficient fast marching on triangulated domains numerical algorithm. Applying this transform to various objects with similar geodesic structures (similar first fundamental form) maps isometric objects into similar canonical forms. We show a simple surface classification method based on the bending invariant canonical form.}, author = {Elad, A. and Kimmel, R.}, booktitle = {Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on}, citeulike-article-id = {4754444}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/CVPR.2001.990472}, citeulike-linkout-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=990472}, doi = {10.1109/CVPR.2001.990472}, journal = {Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on}, keywords = {elad, image, manifold, onur2009}, pages = {I-168--I-174 vol.1}, posted-at = {2009-06-05 18:24:59}, priority = {2}, title = {Bending invariant representations for surfaces}, url = {http://dx.doi.org/10.1109/CVPR.2001.990472}, volume = {1}, year = {2001} }

TY - CONF ID - elad01bend L3 - citeulike-article-id:4754444 N2 - Isometric surfaces share the same geometric structure also known as the first fundamental form. For example, bending of a given surface, that includes length preserving deformations without tearing or stretching the surface, are considered to be isometric. We present a method to construct a bending invariant canonical form for such surfaces. This invariant representation is an embedding of the intrinsic geodesic structure of the surface in a finite dimensional Euclidean space, in which geodesic distances are approximated by Euclidean ones. The canonical representation is constructed by first measuring the intergeodesic distances between points on the surfaces. Next, multi-dimensional scaling (MDS) techniques are applied to extract a finite dimensional flat space in which geodesic distances are represented as Euclidean ones. The geodesic distances are measured by the efficient fast marching on triangulated domains numerical algorithm. Applying this transform to various objects with similar geodesic structures (similar first fundamental form) maps isometric objects into similar canonical forms. We show a simple surface classification method based on the bending invariant canonical form. JF - Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on EP - I-174 vol.1 TI - Bending invariant representations for surfaces VL - 1 T2 - Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on SP - I-168 KW - elad KW - image KW - manifold KW - onur2009 AU - Elad, A AU - Kimmel, R PY - 2001/// UR - http://dx.doi.org/10.1109/CVPR.2001.990472 ER -