Multiscale Nonlinear Decomposition: The Sieve Decomposition Theorem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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In this paper we propose a series of novel morphological operators that are anisotropic, and adapt themselves to the local orientation in the image. This new morphology is therefore rotation invariant; i.e. rotation of the image before or after the operation yields the same result. We present relevant properties required by morphology, as well as other properties shared with common morphological operators. Two of these new operators are increasing, idempotent and absorbing, which are required properties for a morphological operator to be used as a sieve. A sieve is a sequence of filters of increasing size parameter, that can be used to construct size distributions. As an example of the usefulness of these new operators, we show how a sieve can be build to estimate a particle or pore length distribution, as well as the elongation of those features.