Local operations on labelled dot patterns

Abstract: When a local operation is performed on the pixels in an array, the new value of the pixel is a function of the old values of the pixel and its neighbors. This paper introduces the more general concept of local operations on labelled dot patterns, where the new label of a dot is a function of the old labels of the dot and a set of its neighbors (e.g., its Voronoi neighbors). Such operations may change the positions of the dots, in addition to changing their "values'. We illustrate these ideas by giving examples of operations that perform local feature detection (e.g., isolated dot detection, cluster edge detection, dotted curve detection) and 'enhancement' (e.g., 'smoothing' the dot spacing or 'sharpening" the edges of diffuse clusters), as well as 'morphological' operations. Local operations on labelled graphs are also briefly discussed.