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Determinant-Constrained Affine Transformations
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PRE
AI
DOI：10.1002/nla.70062.png)
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Abstract
En 中文
We study the problem of estimating an affine transformation with prescribed determinant from point pairs in dimension . The determinant constraint is nonconvex and challenging to handle. We propose a method to reformulate the problem into a system of quadratics and one polynomial of degree in unknowns. We propose a solution method for this system and a procedure to retrieve the single or multiple affine transformation solutions. We show that the related problem of finding the closest -simplex of prescribed volume and orientation to a given arbitrary -simplex is solved as a special case of the proposed method. We report experimental results demonstrating the use of the proposed transformations in three applications.
Keywords:
affine transformation
area
determinant
least-squares
simplex
volume
Journal
N
IF:
2.1
Papers:
47
Citations:
2.1K