TY - GEN
T1 - Schrödinger diffusion for shape analysis with texture
AU - Iglesias, Jose A.
AU - Kimmel, Ron
PY - 2012
Y1 - 2012
N2 - In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including near-isometries, topological noise and partialities. Here, we propose to exploit the semigroup of a Schrödinger operator in order to deal with texture data, while maintaining the desirable properties of the heat kernel. We define a family of Schrödinger diffusion distances analogous to the ones associated to the heat kernels, and show that they are continuous under perturbations of the data. As an application, we introduce a method for retrieval of textured shapes through comparison of Schrödinger diffusion distance histograms with the earth's mover distance, and present some numerical experiments showing superior performance compared to an analogous method that ignores the texture.
AB - In recent years, quantities derived from the heat equation have become popular in shape processing and analysis of triangulated surfaces. Such measures are often robust with respect to different kinds of perturbations, including near-isometries, topological noise and partialities. Here, we propose to exploit the semigroup of a Schrödinger operator in order to deal with texture data, while maintaining the desirable properties of the heat kernel. We define a family of Schrödinger diffusion distances analogous to the ones associated to the heat kernels, and show that they are continuous under perturbations of the data. As an application, we introduce a method for retrieval of textured shapes through comparison of Schrödinger diffusion distance histograms with the earth's mover distance, and present some numerical experiments showing superior performance compared to an analogous method that ignores the texture.
KW - Laplace-Beltrami operator
KW - Schrödinger operators
KW - diffusion distance
KW - earth mover's distance
KW - textured shape retrieval
UR - http://www.scopus.com/inward/record.url?scp=84867709715&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-642-33863-2_13
DO - https://doi.org/10.1007/978-3-642-33863-2_13
M3 - منشور من مؤتمر
SN - 9783642338625
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 123
EP - 132
BT - Computer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings
T2 - Computer Vision, ECCV 2012 - Workshops and Demonstrations, Proceedings
Y2 - 7 October 2012 through 13 October 2012
ER -