A Volumetric Shape Registration Based on Locally Affine-Invariant Constraint

we present a method based on a locally affineinvariant constraint for volumetric registration of 3D solid shapes. The core idea of this method is that an affine combination of the given point in 3D solid shapes that are directly connected to the given point, and the corresponding weight of each neighboring point can be obtained by the method of generalized least square. The input of our method is a pair of 3D solid shapes that are represented by a tetrahedral mesh and a voxelized object consisting of a set of voxel cells segmented from Digital Imaging and Communications in Medicine(DICOM) scans. To achieve the registration between the two input DICOM images, we firstly need to do some preprocessing to segment the bones out from the DICOM images and represent the segmented healthy bone and lesion bone using a generic template tetrahedral mesh and a set of voxel cells, respectively. Secondly we apply the standard Iterative Closest Point (ICP) method to briefly align the tetrahedral mesh and the voxelized object. Thirdly we execute a novel registration process that uses as much volumetric information and local geometry information as possible while deforming the generic template tetrahedral mesh of a healthy human bone towards the undelying geometry of the voxel cells. Compared with the previous methods that are based on point or surface, our method requires less auxiliary variables and can better capture the volumetric information of the 3D solid shapes, such as the thickness of the bones. Besides that, using a tetrahedral mesh to represent a solid shape can make the precision of registration greatly improved. Our experimental results demonstrate that the proposed method is robust and is of high registration accuracy.