Registration Of The Non-rigid Biological Tissues Deformation From MR Images In Riemannian Space

Deformation field measurements of nonuniform and nonrigid biological tissues from magnetic resonance(MR) images are often needed in clinical diagnosis, simulation and planning of surgery, and evaluation of the physical characteristics of biological tissues. Due to the nonlinear and non-uniform deformation of non-rigid tissues, it is difficult to match a number of feature points distributed somewhat uniform in the tissues from MR images for deformation measurement. Deformation measurement aims to obtain the displacements of a number of feature points, which are usually distributed on the inner parts, boundaries and separatrixes of layers in the tissues. Considering the spatial structures of several feature points in a small region, although the absolute distance between two points may change significantly under nonrigid deformation, the topological structure of a point neighborhood is generally well preserved due to the physical constraints. Due to the local of the Riemannian manifold is homeomorphism to the European space, so the Riemann manifold can measure the degree of the deformation of the biological tissue.In this paper, we propose the descripting feature point on Riemannian manifold and preserving topology structures of local neighborhood based method of feature point matching. Firstly, from the template and deformed images, the DoG and Harris detector are used to extract the feature point. In order to build the descriptor, 2D image patches are initially treated as 3D surfaces. Patches are then embedded in the Riemannian manifold by the Laplace-Beltrami operator, and described in terms of a heat kernel signature. The descriptor are utilized to initialize the matching probability matrix of Relaxation labeling. Then relaxation labeling is adopted to update the probability matrix and refine the matching based on preserving topology structures of local neighborhood. Subsequently, the mismatching elimination method is used to eliminate the residual mismatching points.In order to verify the feasibility of our method, we compared the methods of SIFT, SURF, and our method experimentally. The experimental results showed that our method outperformed the single SURF and SIFT methods, whether on the number of the feature points or on the correct radio of match.