Outlier detection and inlier fusion

As measurement noise we assume a contaminated Gaussian distribution with a main peak within a small interval (of 1 pixel) and a small percentage of outliers. Inlier noise is caused by the limited resolution of the disparity matcher and by the interpolation artifacts. Outliers are undetected correspondence failures and may be arbitrarily large. As threshold to detect the outliers we utilize the depth uncertainty interval $e_k$. The detection of an outlier at $k$ terminates the linking at $k-1$. All depth values $[d_k, d_{k+1}, . . ., d_{l-1}]$ are inlier depth values that fall within the uncertainty interval around the mean depth estimate. They are fused by a simple 1-D kalman filter to obtain an optimal mean depth estimate.

Figure 7.17(right) explains the outlier selection and link termination for the up-link. The outlier detection scheme is not optimal since it relies on the position of the outlier in the chain. Valid correspondences behind the outlier are not considered anymore. It will, however, always be as good as a single estimate and in general superior to it. In addition, since we process bidirectionally up- and down-link, we always have two correspondence chains to fuse which allows for one outlier per chain.