Least squares contour alignment
Least squares contour alignment
The contour alignment problem, considered in this paper, is to compute the minimal distance in a least squares sense, between two explicitly represented contours, specified by corresponding points, after arbitrary rotation, scaling, and translation of one of the contours. This is a constrained nonlinear optimization problem with respect to the translation, rotation and scaling parameters, however, it is transformed into an equivalent linear least squares problem by a nonlinear change of variables. Therefore, a global solution of the contour alignment problem can be computed efficiently. It is shown that a normalization of the cost function minimum value is invariant to ordering and affine transformation of the contours and can be used as a measure for the distance between the contours. A solution is also proposed to the problem of finding a point correspondence between the contours.
Contour alignment, image registration, translation, rotation, scaling, affine invariance, least squares.
41-44
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Mahmoodi, Sasan
91ca8da4-95dc-4c1e-ac0e-f2c08d6ac7cf
January 2009
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Mahmoodi, Sasan
91ca8da4-95dc-4c1e-ac0e-f2c08d6ac7cf
Markovsky, Ivan and Mahmoodi, Sasan
(2009)
Least squares contour alignment.
IEEE Signal Processing Letters, 16 (1), .
Abstract
The contour alignment problem, considered in this paper, is to compute the minimal distance in a least squares sense, between two explicitly represented contours, specified by corresponding points, after arbitrary rotation, scaling, and translation of one of the contours. This is a constrained nonlinear optimization problem with respect to the translation, rotation and scaling parameters, however, it is transformed into an equivalent linear least squares problem by a nonlinear change of variables. Therefore, a global solution of the contour alignment problem can be computed efficiently. It is shown that a normalization of the cost function minimum value is invariant to ordering and affine transformation of the contours and can be used as a measure for the distance between the contours. A solution is also proposed to the problem of finding a point correspondence between the contours.
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Published date: January 2009
Keywords:
Contour alignment, image registration, translation, rotation, scaling, affine invariance, least squares.
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 266829
URI: http://eprints.soton.ac.uk/id/eprint/266829
PURE UUID: 5a29aba2-adbe-4608-9f0c-2c1201b8df3f
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Date deposited: 25 Oct 2008 10:46
Last modified: 14 Mar 2024 08:35
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Contributors
Author:
Ivan Markovsky
Author:
Sasan Mahmoodi
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