Morphological Scale Space for 2D Shape Smoothing

In this paper, 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 structuring element of increasing size, generating a multiple scale representation of the object. Then, smooth boundry segments across a continuum of scales are extracted and linked together creating a pattern called the morphological scale space. Properties of this scale space pattern are investigated and contrasted with those of Gaussian scale space. A shape smoothing algorithm based on this scale space is proposed to show how the scale space representation could be applied to image analysis. Specifically, in line with Witkin's scale space filtering, boundary features that are explicitly related across scales by the morphological scale space are organized into global regions and local boundary features. From the organization, perceptually dominant features for a smooth boundary are determined without the requirement of prior knowledge of the object nor input parameters. Extensive experiments were conducted to show the performance of morphological scale space for 2D shape smoothing.