Journal ArticleDOI
Least-squares estimation of transformation parameters between two point patterns
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TLDR
The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.Abstract:
In many applications of computer vision, the following problem is encountered. Two point patterns (sets of points) (x/sub i/) and (x/sub i/); i=1, 2, . . ., n are given in m-dimensional space, and the similarity transformation parameters (rotation, translation, and scaling) that give the least mean squared error between these point patterns are needed. Recently, K.S. Arun et al. (1987) and B.K.P. Horn et al. (1987) presented a solution of this problem. Their solution, however, sometimes fails to give a correct rotation matrix and gives a reflection instead when the data is severely corrupted. The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted. >read more
Citations
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Point Set Registration: Coherent Point Drift
Andriy Myronenko,Xubo Song +1 more
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SVO: Fast semi-direct monocular visual odometry
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Book
Markov Random Field Modeling in Image Analysis
TL;DR: This detailed and thoroughly enhanced third edition presents a comprehensive study / reference to theories, methodologies and recent developments in solving computer vision problems based on MRFs, statistics and optimisation.
References
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Closed-form solution of absolute orientation using unit quaternions
TL;DR: A closed-form solution to the least-squares problem for three or more paints is presented, simplified by use of unit quaternions to represent rotation.
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Least-Squares Fitting of Two 3-D Point Sets
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Closed-form solution of absolute orientation using orthonormal matrices
TL;DR: In this paper, a closed-form solution to the least square problem for three or more points is presented, which requires the computation of the square root of a symmetric matrix, and the best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids.
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The matrix minimum principle
TL;DR: The purpose of this paper is to provide an alternate statement of the Pontryagin maximum principle as applied to systems which are most conveniently and naturally described by matrix, rather than vector, differential or difference equations.
Proceedings ArticleDOI
Polyhedral Object Recognition with Sparse Data - Validation of Interpretations.
Derrick Holder,Hilary Buxton +1 more
TL;DR: In this article, a distributed array processor, AMT DAP, is used for the generation of feasible interpretations of scenes with sparse data, in a process that exploits n × n parallelism.