Granulometry (morphology)

Granulometry
Basic concepts
Particle size · Grain size Size distribution · Morphology
Methods and techniques
Mesh scale · Optical granulometry Sieve analysis · Soil gradation
Related concepts
Granulation · Granular material Mineral dust · Pattern recognition Dynamic light scattering

In mathematical morphology, granulometry is an approach to compute a size distribution of grains in binary images, using a series of morphological opening operations. It was introduced by Georges Matheron in the 1960s, and is the basis for the characterization of the concept of size in mathematical morphology.

Let B be a structuring element in an Euclidean space or grid E, and consider the family ${\displaystyle \{B_{k}\}}$, ${\displaystyle k=0,1,\ldots }$, given by:

where ${\displaystyle \oplus }$ denotes morphological dilation. By convention, ${\displaystyle B_{0}}$ is the set containing only the origin of E, and ${\displaystyle B_{1}=B}$.

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