Pattern spectrum of images and morphological shape-size complexity

By using morphological opening and closing set operations, a pattern spectrum of binary images can be developed, which measures the image content relative to patterns of arbitrary shape and size. In this paper, the pattern spectrum of discrete images is further generalized, is directly related to the skeleton (medial axis) transform, is used to derive a shape-size complexity measure of the image and its immediate background, and all these concepts are extended to graytone images. The results of this study indicate that the pattern spectrum can be used to analyze and enrich the medial axis (or other skeleton-like) transforms, and quantify the roughness of the image boundary or surface.