## Computing Feret diameters from the convex hull

Monday, February 13th, 2012

Some time ago I wrote about how to compute the Feret diameters of a 2D object based on the chain code of its boundary. The diameters we computed were the longest and shortest projections of the object. The shortest projection, or smallest Feret diameter, is equivalent to the size measured when physically passing objects through sieves (i.e. sieve analysis, as is often done, e.g., with rocks). The longest projection, or largest Feret diameter, is useful as an estimate of the length of elongated objects.

The algorithm I described then simply rotated the object in two-degree intervals, and computed the projection length at each orientation. The problem with this algorithm is that the width estimated for very elongated objects is not very accurate: the orientation that produces the shortest projection could be up to 1 degree away from the optimal orientation, meaning that the estimated width is *length*⋅sin(*π*/180) too large. This doesn’t sound like much, but if the aspect ratio is 100, meaning the length is 100 times the width, we can overestimate the width by up to 175%!