Math @ Duke

Publications [#287106] of Ingrid Daubechies
Papers Published
 AlAifari, R; Daubechies, I; Lipman, Y, Continuous Procrustes distance between two surfaces,
Communications on Pure and Applied Mathematics, vol. 66 no. 6
(2013),
pp. 934964, ISSN 00103640 [doi]
(last updated on 2018/10/19)
Abstract: The Procrustes distance is used to quantify the similarity or dissimilarity of (threedimensional) shapes and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous, as far as possible, and the Procrustes distance is then computed as $\inf_{R}\sum_{j=1}^N \Rx_jx'_j\^2$, where the minimization is over all euclidean transformations, and the correspondences $x_j \leftrightarrow x'_j$ are picked in an optimal way. The discrete Procrustes distance has the drawback that each shape is represented by only a finite number of points, which may not capture all the geometric aspects of interest; a need has been expressed for alternatives that are still easy to compute. We propose in this paper the concept of continuous Procrustes distance and prove that it provides a true metric for twodimensional surfaces embedded in three dimensions. We also propose an efficient algorithm to calculate approximations to this new distance. © 2013 Wiley Periodicals, Inc.


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