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 nonli...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2009-01.
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| Subjects: | |
| Online Access: | Get fulltext Get fulltext Get fulltext |
| Summary: | 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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