MATHEMATICAL MORPHOLOGY BASED CHARACTERIZATION OF BINARY IMAGE

Authors

  • Raghvendra Sharma Indian Statistical Institute, Bangalore
  • B. S. Daya Sagar Indian Statistical Institute, Bangalore

DOI:

https://doi.org/10.5566/ias.1291

Keywords:

dilation asymmetry, erosion asymmetry, close-hull, open-skull, degree of stability, hull fragments, skull fragments

Abstract

This paper reports the results of a theoretical study on morphological characterization of foreground (X) and background (Xc) of a discrete binary image. Erosion asymmetry and dilation asymmetry, defined to elaborate smoothing of an image respectively by contraction and expansion, are generalized for multiscale smoothing, and their relationships with morphological skeleton and ridge (background skeleton) transformations are discussed. Then we develop algorithms identifying image topology in terms of critical scales corresponding to close-hulls and open-skulls, along with a few other salient characteristics, as respective smoothing by expansion and contraction proceeds. For empirical demonstration of these algorithms, essentially to unravel the hidden characteristics of topological and geometrical relevance, we considered deterministic and random binary Koch quadric fractals. A shape-size based zonal quantization technique for image and its background is introduced as analytical outcome of these algorithms. The ideas presented and demonstrated on binary fractals could be easily extended to the grayscale images and fractals.

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Published

2015-06-29

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Section

Original Research Paper

How to Cite

Sharma, R., & Sagar, B. S. D. (2015). MATHEMATICAL MORPHOLOGY BASED CHARACTERIZATION OF BINARY IMAGE. Image Analysis and Stereology, 34(2), 111-123. https://doi.org/10.5566/ias.1291