Nearest-neighbor clutter removal for estimating features in spatial point processes

We consider the problem of detecting features in spatial point processes in the presence of substantial clutter. One example is the detection of minefields using reconnaissance aircraft images that identify many objects that are not mines. Our solution uses Kth nearest neighbor distances of points in the process to classify them as clutter or otherwise. The observed Kth nearest neighbor distances are modeled as a mixture distribution, the parameters of which are estimated by a simple EM algorithm. This method allows for detection of generally shaped features that need not be path connected. In the minefield example this method yields high detection and low false-positive rates. Another application, to outlining seismic faults, is considered with some success. The method works well in high dimensions. The method can also be used to produce very high-breakdown-point-robust estimators of a covariance matrix.