Morphological scale space for 2D shape smoothing

We describe a multiple-scale boundary representation based on morphological operations. An object boundary is first progressively smoothed by a number of opening and closing operations using a set of structuring elements of increasing size, generating a multiple scale representation of the object. Then, corresponding features of the smoothed boundary across a continuum of scales are extracted and linked together forming a map called the morphological scale space. Properties of this scale space map are investigated and presented. A shape smoothing algorithm, which is based on this map and its properties, is proposed to show how the scale space representation could be applied to solve practical image processing problems. Specifically, in line with Witkin's (1983) Gaussian scale space filtering, boundary features that are explicitly related across scales by the morphological scale space map are organized into global region information and local boundary features. From the organization, perceptually dominant features are determined and a shape is smoothed without the requirement of prior knowledge of the object boundary nor its noise.