A Novel Multi-Purpose Matching Representation of Local 3D Surfaces: A Rotationally Invariant, Efficient, and Highly Discriminative Approach With an Adjustable Sensitivity

In this paper, a novel approach to local 3D surface matching representation suitable for a range of 3D vision applications is introduced. Local 3D surface patches around key points on the 3D surface are represented by 2D images such that the representing 2D images enjoy certain characteristics which positively impact the matching accuracy, robustness, and speed. First, the proposed representation is complete, in the sense, there is no information loss during their computation. Second, the 3DoF 2D representations are strictly invariant to all the 3DoF rotations. To optimally avail surface information, the sensitivity of the representations to surface information is adjustable. This also provides the proposed matching representation with the means to optimally adjust to a particular class of problems/applications or an acquisition technology. Each 2D matching representation is a sequence of adjustable integral kernels, where each kernel is efficiently computed from a triple of precise 3D curves (profiles) formed by intersecting three concentric spheres with the 3D surface. Robust techniques for sampling the profiles and establishing correspondences among them were devised. Based on the proposed matching representation, two techniques for the detection of key points were presented. The first is suitable for static images, while the second is suitable for 3D videos. The approach was tested on the face recognition grand challenge v2.0, the 3D twins expression challenge, and the Bosphorus data sets, and a superior face recognition performance was achieved. In addition, the proposed approach was used in object class recognition and tested on a Kinect data set.