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Binary Image Registration Using Covariant Gaussian Densities
"... Abstract. We consider the estimation of 2D affine transformations aligning a known binary shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the two images and then compute the transformation parameters from these landmarks. I ..."
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Abstract. We consider the estimation of 2D affine transformations aligning a known binary shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the two images and then compute the transformation parameters from these landmarks. In this paper, we propose a novel approach where the exact transformation is obtained as a leastsquares solution of a linear system. The basic idea is to fit a Gaussian density to the shapes which preserves the effect of the unknown transformation. It can also be regarded as a consistent coloring of the shapes yielding two rich functions defined over the two shapes to be matched. The advantage of the proposed solution is that it is fast, easy to implement, works without established correspondences and provides a unique and exact solution regardless of the magnitude of transformation. 1
Francos, “Parametric estimation of affine deformations of binary images
 in Proc. of Int. Conf. on Acoustics, Speech, and Signal Processing, Las Vegas
, 2008
"... We consider the problem of planar object registration on binary images where the aligning transformation is restricted to the group of affine transformations. Previous approaches usually require established correspondences or the solution of nonlinear optimization problems. Herein we show that it is ..."
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We consider the problem of planar object registration on binary images where the aligning transformation is restricted to the group of affine transformations. Previous approaches usually require established correspondences or the solution of nonlinear optimization problems. Herein we show that it is possible to formulate the problem as the solution of a system of up to third order polynomial equations. These equations are constructed in a simple way using some basic geometric information of binary images. It does not need established correspondences nor the solution of complex optimization problems. The resulting algorithm is fast and provides a direct solution regardless of the magnitude of transformation. Index Terms — Image registration, affine transformation, binary image.
J Math Imaging Vis DOI 10.1007/s1085100901884 Parametric Estimation of Affine Transformations: An Exact Linear Solution
"... Abstract We consider the problem of estimating the geometric deformation of an object, with respect to some reference observation on it. Existing solutions, set in the standard coordinate system imposed by the measurement system, lead to highdimensional, nonconvex optimization problems. We propose ..."
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Abstract We consider the problem of estimating the geometric deformation of an object, with respect to some reference observation on it. Existing solutions, set in the standard coordinate system imposed by the measurement system, lead to highdimensional, nonconvex optimization problems. We propose a novel framework that employs a set of nonlinear functionals to replace this originally high dimensional problem by an equivalent problem that is linear in the unknown transformation parameters. The proposed solution includes the case where the deformation relating the observed signature of the object and the reference template is composed both of the geometric deformation due to the affine transformation of the coordinate system and a constant amplitude gain. The proposed solution is unique and exact and is applicable to any affine transformation regardless of its magnitude.