To solve the color image registration problem where similarity transformations may exist between two images both in spatial and color spaces, a new bispectrum slices formulation suitable for hypercomplex domain was presented. The formulation could be derived by applying the hypercomplex Fourier transform to the time domain form of the complex bispectrum slices. The resulting hypercomplex bispectrum slices was translation invariant and could be used to solve rotation and scale changes between two color images. The simulation results show that compared with the method of complex bispectrum slices, the proposed method has better robustness against disturbances. Its error is generally only half that of the former method.

For the existing point matching algorithms adopting the l1 norm regularization terms, the corresponding l1 norm optimization problems are equivalent to linear programs. But the constraints do not satisfy the total unimodularity property, which causes the point correspondence solutions to be non-integers and post-processing is needed to convert the solutions to integers. Such processing brings error and complicates the algorithms. To resolve the above problem, based on the latest result with the robust point matching algorithm, a new regularization term was proposed. The new regularization term is concave and it can be proved that the objective function has integral optimal solutions. Therefore, no post-processing is needed and it is simpler to implement. The experimental results show that, compared with the algorithms adopting the l1 norm regularization terms, the proposed algorithm is more robust to various types of disturbances, particularly outliers, while its error is only half of the compared algorithms.

This paper proposed a linear programming based point matching method with similarity regularization in order to resolve the problems of non-rigid deformation, positional noise and outliers. Point matching was modeled as an energy minimization problem. Shape context was used to reduce the ambiguity of point correspondence, and similarity transform was used to preserve the continuity of spatial mapping. The continuously relaxed optimization problem is reduced to a linear program where optimality can be guaranteed. The simulation results verified the effectiveness of the method.

To address the rotation-invariant non-rigid point matching problem, a graph matching based algorithm was proposed in this paper. Two sets of edges were constructed from two point sets respectively. Then oriented Shape Context (SC) distances and length differences were both used to measure the similarities of edges between two point sets. Based on edge similarities, point correspondence was recovered via graph matching. The experimental results show the method is capable of achieving good matching results and also robust and efficient.