Active shape models and the shape approximation problem
A. Hill,Timothy F. Cootes,Christopher J. Taylor +2 more
- 01 Jul 1995
- Vol. 14, Iss: 8, pp 157-166
TL;DR: A new method of shape approximation which uses directional constraints is presented, and it is shown how the error term for the shape approximation problem can be extended to cope with directional constraints, and iterative solutions to the 2D and 3D problems are presented.
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Abstract: Active Shape Models (ASM) use an iterative algorithm to match statistically defined models of known but variable objects to instances in images. Each iteration of ASM search involves two steps: image data interrogation and shape approximation. Here we consider the shape approximation step in detail. We present a new method of shape approximation which uses directional constraints. We show how the error term for the shape approximation problem can be extended to cope with directional constraints, and present iterative solutions to the 2D and 3D problems. We also present an efficient algorithm for the 2D problem in which a modification of the error term permits a closed-form approximate solution which can be used to produce starting estimates for the iterative solution.
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Citations
Statistical shape models for 3D medical image segmentation: a review.
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Statistical Shape Models for 3D Medical Image Segmentation
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References
Active shape models—their training and application
TL;DR: This work describes a method for building models by learning patterns of variability from a training set of correctly annotated images that can be used for image search in an iterative refinement algorithm analogous to that employed by Active Contour Models (Snakes).
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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.
Least-Squares Fitting of Two 3-D Point Sets
TL;DR: An algorithm for finding the least-squares solution of R and T, which is based on the singular value decomposition (SVD) of a 3 × 3 matrix, is presented.
Least-squares estimation of transformation parameters between two point patterns
TL;DR: The proposed theorem is a strict solution of the problem, and it always gives the correct transformation parameters even when the data is corrupted.
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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.