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In this paper, we propose a novel framework to estimate the parameters of a diffeomorphism that aligns a known shape and its distorted observation. Classical registration methods first establish correspondences between the shapes and then compute the transformation parameters from these landmarks. Herein, we trace back the problem to the solution of a system of nonlinear equations which directly gives the parameters of the aligning transformation. The proposed method provides a generic framework to recover any diffeomorphic deformation without established correspondences. It is easy to implement, not sensitive to the strength of the deformation, and robust against segmentation errors. The method has been applied to several commonly used transformation models. The performance of the proposed framework has been demonstrated on large synthetic data sets as well as in the context of various applications.

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We consider the estimation of affine transformations aligning a known 2D shape and its distorted observation. The classical way to solve this registration problem is to find correspondences between the shapes and then compute the transformation parameters from these landmarks. Here we propose a novel approach where the exact transformation is obtained as the solution of a polynomial system of equations. The method has been tested on synthetic as well as on real images and its robustness in the presence of segmentation errors and additive geometric noise has also been demonstrated. We have successfully applied the method for the registration of hip prosthesis X-ray images. The advantage of the proposed solution is that it is fast, easy to implement, has linear time complexity, works without established correspondences and provides an exact solution regardless of the magnitude of transformation.

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