Continuous Procrustes Distance Between Two Surfaces
نویسندگان
چکیده
منابع مشابه
The Continuous Procrustes Distance between Two Surfaces
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous (i.e. corresponding to each other), as much as possible, and the Procrustes distance is then computed as infR ∑N j=1 ‖Rxj − xj‖, where the minimizati...
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Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the st...
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Computing the Fréchet distance for surfaces is a surprisingly hard problem. It has been shown that it is NP-hard to compute the Fréchet distance between many nice classes of surfaces [God98], [Buc10]. On the other hand, a polynomial time algorithm exists for computing the Fréchet distance between simple polygons [Buc06]. This was the first paper to give an algorithm for computing the Fréchet di...
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We describe two (1 + ε)-approximation algorithms for computing the Fréchet distance between two homeomorphic piecewise linear surfaces R and S of genus zero and total complexity n, with Fréchet distance δ. 1. A 2 (( n+ Area(R)+Area(S) (εδ)2 )2) time algorithm if R and S are composed of fat triangles (triangles with angles larger than a constant). 2. An O(D/(εδ)2) · n + 2O(D/(εδ)) time algorithm...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2013
ISSN: 0010-3640
DOI: 10.1002/cpa.21444