Neighborhood and Window Operations

Abstract

When processing spatial grids, it is often necessary to preprocess them to improve the results of later stages. Preprocessing may be to remove noise, to smooth over abrupt variations, to identify edges, or to fill gaps. In this chapter, we discuss neighborhood and window operations that may be used for these purposes. Smoothing can be carried out using a variety of windowing operations: the boxcar, Gaussian, and median filters are most commonly used. Because the boxcar filter is subject to ringing artifacts, we recommend the use of either the Gaussian filter (to mitigate abrupt changes) or the median filter (to mitigate the impact of noise). A matched filter may be used to extract specific shapes from a spatial grid but requires that you know the exact shape and orientation beforehand. Directional smoothing is commonly achieved using a filter bank of oriented filters. Separability is a concern, however. We discuss a couple of edge filtering techniques and point out the use of median filters in speckle removal. Morphological operations for dilation and erosion are described and the use of combinations of morphological operations for denoising and gap filling described. Finally, we discuss skeletonization and thinning algorithms.