A Metric for Distributions with Applications to Image Databases
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Using the Inner-Distance for Classification of Articulated Shapes
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Numerical Geometry of Non-Rigid Shapes
Numerical Geometry of Non-Rigid Shapes
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
International Journal of Computer Vision
Geodesic shape retrieval via optimal mass transport
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Shape Recognition with Spectral Distances
IEEE Transactions on Pattern Analysis and Machine Intelligence
EMD-L1: an efficient and robust algorithm for comparing histogram-based descriptors
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
Photometric heat kernel signatures
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
A general framework for low level vision
IEEE Transactions on Image Processing
PHOG: photometric and geometric functions for textured shape retrieval
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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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.