Multimodal genetic algorithms-based algorithm for automatic point correspondence

In this paper, the problem of automatic determination of point correspondence between two images is formulated as a multimodal function optimization and the usefulness of genetic algorithms (GAs) as a multimodal optimizer is explored. Initially, a number of variations of GAs, capable of simultaneously discovering multiple extremes of an objective function are evaluated on a mathematical benchmark objective function with multiple unequal maxima. The variation of the GAs that performs best on the benchmark function, in terms of the number of maxima discovered, is selected for the determination of automatic point correspondence between two images. The selected variation of the GAs involves an iterative procedure for the formation of a genetic population of individuals (or chromosomes). Each individual encodes the position of a point of interest on one of the available images as well as parameters of a local transformation that generates the position of the corresponding point on the other image. The proposed algorithm aims to discover individuals that corresponds to local maxima of an objective function that measures the similarity between patches of the two images. When the GAs-based multimodal optimization algorithm terminates, pairs of corresponding points between the two images are obtained that can be used for the generation of a dense deformation field by means of the thin plate splines model.The proposed algorithm is applied to 2D medical images (dental and retinal images) under known transformations (similarity and elastic transformation) and is also assessed on medical images with unknown transformations (computer tomography transverse slices). The proposed algorithm is compared against the iterative closest point (ICP) algorithm, and a well-known non-rigid registration algorithm, based on free-form deformations (FFD) using various quantitative criteria. The obtained results indicate that in case of known similarity transformations, the proposed multimodal GAs-based algorithm and the ICP algorithm present equivalent performance, whereas the FFD algorithm is clearly outperformed. In the case of known sinousoidal deformations, the proposed multimodal GAs-based and the FFD algorithm achieve equivalent performance and clearly outperform the ICP algorithm. Finally, in the case of unknown elastic deformations, the proposed GAs-based algorithm appears to perform marginally better than the FFD algorithm, whereas it clearly outperforms the ICP algorithm.