This paper presents a novel approach to deformable image registration using a parametric transformation model. The aligning transformation is simply found by solving a system of non-linear equations. Each equation is generated by integrating the product of a set of polynomial functions and the image intensity function over corresponding image domains. The capabilities of the algorithm have been studied on synthetic and real datasets on which it compares favorably to state of the art methods in terms of alignment accuracy.

A novel affine registration technique is proposed which efficiently handles the partial occlusion problem. The proposed method is working without point wise correspondences or radiometric information's. The aligning transformation is found by solving a system of non-linear equations and minimizing the area of occlusions. Each equation is generated by integrating a non-linear function over the foreground domains of the shapes. In order to deal with occlusions, the shapes are approximated by polygons and the occluded areas are determined with simple boolean operators. Based on the tests on a large synthetic dataset, the proposed approach outperforms state of the art algorithms.

A novel correspondence-less approach is proposed to find a thin plate spline map between a pair of deformable 3D objects represented by triangular surface meshes. The proposed method works without landmark extraction and feature correspondences. The aligning transformation is found simply by solving a system of nonlinear equations. Each equation is generated by integrating a nonlinear function over the object's domains. We derive recursive formulas for the efficient computation of these integrals. Based on a series of comparative tests on a large synthetic dataset, our triangular mesh-based algorithm outperforms state of the art methods both in terms of computing time and accuracy. The applicability of the proposed approach has been demonstrated on the registration of 3D lung CT volumes.