| Nonrigid point set registration has been a key and difficult problem in the fields of image processing and computer vision.It has been widely used in medical image processing,remote sensing image processing,video processing,image fusion,target recognition,stereo vison,and so on.Point set refers to the feature points that are extracted from the corresponding images.The goal of point set registration is to recover the spatial transformation between two point sets using a group of complicate interpolation functions.There are two difficulties for the nonrigid point set registration:First,image degradations,such as large deformation,noise,occlusion,outliers and rotation,can significantly affect the performance of the algorithms.Second,it would have a heavy computational burden when there are a large number of points.They limit the scope of application and reduce the practical value of the algorithms.In the light of the problems above,by using the abundant structural information that lie in the point sets,we develop the nonrigid point set registration algorithms with robust and accurate performance.Further,we also design fast implementation to calculate the nonrigid spatial transformation,which can improve the real-time performance of the algorithm.The main content is as follows:First,in order to efficiently utilize the abundant structrual information in the point sets,we propose a robust nonrigid point set registration method that is based on collaborative correspondences.In order to establish accurate corresponding relationship between two point sets,we fuse the two complementary structural features,including the spatial location of a point and the local structure around it.The former is used to define the absolute distance(AD),and the latter is exploited to define the relative distance(RD).The AD-correspondences and the RD-correspondences can be established based on AD and RD,respectively.The neighboring corresponding consistency is employed to assign the confidence for each RD-correspondence.The proposed heuristic method combines the AD-correspondences and the RD-correspondences to determine the corresponding relationship between two point sets,which can significantly improve the corresponding accuracy.Subsequently,the thin plate spline(TPS)is employed as the transformation function.At each step,the closed-form solutions of the affine and nonaffine parts of TPS can be independently and robustly solved.It facilitates to analyze and control the registration process.Experimental results demonstrate that our method can achieve better performance than several existing state-of-the-art methods.Second,in order to reduce the computing complexity to calculate the spatial transformation functions,we propose the fast coherent point drift(fast-CPD).CPD is a classical method for nonrigid point set registration.However,to solve spatial transformation functions,CPD has to compute inversion of a M×M matrix per iteration with time complexity O(M ~3).By introducing a simple corresponding constraint,we develop a fast implementation of CPD.The most advantage of our method is to avoid matrix-inverse operation when calculating the spatial transformation.Before the iteration begins,our method requires to take eigenvalue decomposition of a M×M matrix once.After iteration begins,our method only needs to update a diagonal matrix,and perform matrix multiplication operation with time complexity approximately O(M ~2)in each iteration.Besides,our method can be further accelerated by the low-rank matrix approximation.Experimental results in 3D point cloud data show that our method can significantly reduce computation burden of the registration process,and keep comparable performance with CPD on accuracy.Third,in order to well assign the points that are along the boundaries of the units of the shape descriptors,we propose the Gaussian shape context(GSC).Around the reference point,the GSC sets up a group of Gaussian window functions.Using the Euclidean distance between the centers of the Gaussian functions and the sampling points,the GSC establishes shape descriptors based on the outputs of the Gaussian functions.The GSC is utilized to describe the spatial distributions surrounding the reference point.More accurate correspondences between two shapes are determined by comparing the similarities of the shape descriptors.Experimental results show that the GSC can find more accurate correspondence relations.The proposed descriptors can also make the algorithm converge faster,and keep more robust performance compared with shape contexts.Forth,in order to more efficiently deal with scale changes of shapes,we propose the scale shape descriptors(SSD).The scale shape descriptors(SSD)are designed by utilizing shape contexts(SC)or Gaussian shape contexts(GSC)with different scales as the basis shape descriptors.Firstly,the scales of shape descriptors are determined as the intra-layer scales based on the model shape.Different inter-layer scales used to establish scale cubes of the model shape.Secondly,calculate the mean distance between every layer of the scale cubes and the scene shape,and search the nearest scale of the scene shape based on the mean distance.Thirdly,the spline interpolation is used to more accurately estimate the optimal scale.Then shape descriptors are built based on the optimal scale and the point-to-point correspondences are exactly determined,and the spatial transformation is calculated.Experimental results show the SSD can well overcome the difficulties caused by scale changes of the shapes. |
