The Digital Morphological Sampling Theorem

Robert M. Haralick; Xinhua Zhuang; Charlotte Lin; James Lee

doi:10.1117/12.942722

19 February 1988 The Digital Morphological Sampling Theorem

Robert M. Haralick, Xinhua Zhuang, Charlotte Lin, James Lee

Proceedings Volume 0848, Intelligent Robots and Computer Vision VI; (1988) https://doi.org/10.1117/12.942722
Event: Advances in Intelligent Robotics Systems, 1987, Cambridge, CA, United States

Abstract

There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems.

Citation Download Citation

Robert M. Haralick, Xinhua Zhuang, Charlotte Lin, and James Lee "The Digital Morphological Sampling Theorem", Proc. SPIE 0848, Intelligent Robots and Computer Vision VI, (19 February 1988); https://doi.org/10.1117/12.942722

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