Boundary Smoothing via Symmetry Transforms

  • Authors:

  • Hüseyin Tek;Benjamin B. Kimia

  • Affiliations:

  • Imaging and Visualization Department, Siemens Corporate Research, Inc., 755 College Road East, Princeton, NJ 08540, USA. htek@scr.siemens.com;LEMS, Division of Engineering, Brown University, 182 Hope Street, Providence RI 02912, USA. kimia@lems.brown.edu

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2001

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Abstract

This paper proposes a smoothing technique for shape based on a perturbation analysis of the underlying medial axis, and by iteratively removing skeletal branches. While medial axis regularization usually aims at dealing with its sensitivity in the context of applications such as recognition, we use it here to smooth shape. The approach overcomes a basic drawback with current smoothing techniques, namely, the rounding of perceptually salient corners. The key idea is that the instability of the skeleton under a family of deformations can be dealt with via a symmetry transform which is applied to all related symmetry branches so as to effect an appropriate change in the shape. This leads to the notion of a splice transform which removes a branch coupled with simultaneous changes in the skeleton. In contrast to point-based pruning techniques which use local salience and which cannot construct coarse-scale corners, our approach constructs and preserves coarse-scale curvature extrema, leading to a “scale-discrete scale-space” for shape. The approach is also applicable to the smoothing of incomplete shapes represented as a set of curve segments.