Shape factor (image analysis and microscopy)

Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from two-dimensional cross-sections or projections, as in a microscope field, but shape factors also apply to three-dimensional objects. The particles could be the grains in a metallurgical or ceramic microstructure, or the microorganisms in a culture, for example. The dimensionless quantities often represent the degree of deviation from an ideal shape, such as a circle, sphere or equilateral polyhedron. Shape factors are often normalized, that is, the value ranges from zero to one. A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube.

The most common shape factor is the aspect ratio, a function of the largest diameter and the smallest diameter orthogonal to it:

The normalized aspect ratio varies from approaching zero for a very elongated particle, such as a grain in a cold-worked metal, to near unity for an grain. The reciprocal of the right side of the above equation is also used, such that the AR varies from one to approaching infinity.

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