Estimation of linear deformations of 2D and 3D fuzzy objects

• n-Dimensional image registration method by shape/object matching.
• The approach is based on generating and solving polynomial systems of equations.
• Detailed discussion of fast and efficient algorithmic solution techniques.
• Efficiency confirmed by a thorough evaluation performed on synthetic and real data.
• Especially suitable, due to time efficiency, for registration of large objects.

Registration is a fundamental task in image processing, it is used to determine geometric correspondences between images taken at different times and/or from different viewpoints. Here we propose a general framework in n-dimensions to solve binary shape/object matching problems without the need of establishing additional point or other type of correspondences. The approach is based on generating and solving polynomial systems of equations. We also propose an extension which, provided that a suitable segmentation method can produce a fuzzy border representation, further increases the registration precision. Via numerous synthetic and real test we examine the different solution techniques of the polynomial systems of equations. We take into account a direct analytical, an iterative least-squares, and a combined method. Iterative and combined approaches produce the most precise results. Comparison is made against competing methods for rigid-body problems. Our method is orders of magnitude faster and is able to recover alignment regardless of the magnitude of the deformation compared to the narrow capture range of others. The applicability of the proposed methods is demonstrated on real X-ray images of hip replacement implants and 3D CT volumes of the pelvic area. Since the images must be parsed through only once, our approach is especially suitable for solving registration problems of large images.