Cubature Split Covariance Intersection Filter-Based Point Set Registration

Point set registration is a basic but still an open problem in numerous computer vision tasks. In general, there are more than one type of error sources for registration, for example, noise, outliers, and false initialization, may exist simultaneously. These errors could influence the registration independently and dependently. Previous works usually test performance under one of the two types of errors at one time, or they do not perform well under some extreme situations with both of the error sources. This paper presents a robust point set registration algorithm under a filtering framework, which aims to be robust under various types of errors simultaneously. The point set registration problem can be cast into a non-linear state space model. We use a split covariance intersection filter (SCIF) to capture the correlation between the state transition and the observation (moving point set). The two above-mentioned types of errors can be represented as dependent and independent parts in the SCIF. The covariance of the two types of errors will be updated every iteration. Meanwhile, the non-linearity of the observation model is approximated by a cubature transformation. First, the recursive cubature split covariance intersection filter is derived based on the non-linear state space model. Then, we use this algorithm to solve the point set registration problem. This algorithm can approximate non-linearity by a third-order term and consider correlations between the process model and the observation model. Compared with other filtering-based methods, this algorithm is more robust and precise. Tests on both public data sets and experiments validate the precision and robustness of this algorithm to outliers and noise. Comparison experiments show that this algorithm outperforms the state-of-the-art point set registration algorithms in certain respects.