Kernel Correlation as an Affinity Measure in Point-Sampled Vision Problems

Abstract

Range sensors, such as laser range finder and stereo vision systems, return point-samples of a scene. Typical point-sampled vision problems include registration, regularization and merging. We introduce a robust distance minimization approach to solving the three classes of problems. The approach is based on correlating kernels centered at point-samples, a technique we call kernel correlation. Kernel correlation is an affinity measure, and it contains an M-estimator mechanism for distance mini- mization. Kernel correlation is also an entropy measure of the point set configuration. Maximizing kernel correlation implies enforcing compact point set. The effectiveness of kernel correlation is evaluated by the three classes of problems. First, the kernel correlation based registration method is shown to be efficient, accurate and robust, and its performance is com- pared with the iterative closest point (ICP) algorithm. Second, kernel correlation is adopted as an object space regularizer in the stereo vision problem. Kernel correlation is discontinuity preserving and usually can be applied in large scales, resulting in smooth appearance of the estimated model. The performance of the algorithm is evaluated both quantitatively and qualitatively. Finally, kernel correlation plays a point-sample merg- ing role in a multiple view stereo algorithm. Kernel correlation enforces smoothness on point samples from all views, not just within a single view. As a result we can put both the photo-consistency and the model merg- ing constraints into a single energy function. Convincing reconstruction results are demonstrated.