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## Publications [#287106] of Ingrid Daubechies

Papers Published

1. Al-Aifari, R; Daubechies, I; Lipman, Y, Continuous Procrustes distance between two surfaces, Communications on Pure & Applied Mathematics, vol. 66 no. 6 (2013), pp. 934-964, ISSN 0010-3640 [doi]
(last updated on 2018/03/18)

Abstract:
The Procrustes distance is used to quantify the similarity or dissimilarity of (three-dimensional) 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 $\inf_{R}\sum_{j=1}^N \|Rx_j-x'_j\|^2$, 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 two-dimensional 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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