Matching shapes using the current distance

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Publication Type poster
School or College Scientific Computing and Imaging Institute
Department Computing, School of
Creator Joshi, Sarang; Venkatasubramanian, Suresh
Other Author Kommaraju, Raj Varma; Phillips, Jeff M
Title Matching shapes using the current distance
Description Current Distance: It was introduced by Vaillant and Glaunès as a way of comparing shapes (point sets, curves, surfaces). This distance measure is defined by viewing a shape as a linear operator on a k-form field, and constructing a (dual) norm on the space of shapes. Shape Matching: Given two shapes P;Q, a distance measure d on shapes, and a transformation group T , the problem of shape matching is to determine a transformation T that minimizes d(P; T Q). Current Norm: For a point set P, current norm is kPk2 = X i X j K(pi; pj)) (p) (q) Current Distance: Distance between two point sets P and Q is D2(P;Q) = kP + (??1)Qk2 = kPk2 + kQk2 ?? 2 X i X j K(pi; qj)) (p) (q) It takes O(n2) time to compute the current distance between two shapes of size n. Also current distance between 2 surfaces or curves can be reduced to set of distance computations on appropriately weighted point sets.
Type Text; Image
Publisher University of Utah
Language eng
Bibliographic Citation Joshi, S., Kommaraju, R. V., Phillips, J. M., & Venkatasubramanian, S. (2010). Matching shapes using the current distance. University of Utah.
Rights Management (c)Sarang Joshi, Raj Varma Kommaraju, Jeff M. Philips, Suresh Venkatasubramanian
Format Medium application/pdf
Format Extent 204,298 bytes
Identifier ir-main/14960
ARK ark:/87278/s6543693
Setname ir_uspace
Date Created 2012-07-30
Date Modified 2021-05-06
ID 707735
Reference URL