Abstract: A distance transform will convert a bi-level image into a gray scale image, where the intensity of the object pixels is proportional to their distance from the nearest back-ground pixel. This can be computed in two passes through an image, and has been used to encode all binary erosions and dilations into one `globally eroded' image. It is also possible to encode all possible binary openings and closings as gray levels, allowing any particular opening or closing to be achieved through a simple thresholding operation, or by non-destructive comparisons. We define nodal points in the distance transform as those which have no neighbors having the maximum possible value (For example, 7 for diagonal pixels, and 12 for others using Euclidean distance). At each of these points a digital circle can be drawn, whose values equal that of the significant point. A simple histogram of the thus encoded image yields the roughness spectrum, but the spectrum found using only the significant points may be just as useful. !9
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