Fitting cylinders computation with an application to measuring 3D shapes

Abstract

This paper observes a fitting cylinders problem for 3D shapes. The method presented defines two cylinders that fit well with the shape considered. These cylinders are easy and fast to compute. Would the 3D shape considered be digitized, i.e. represented by the set of voxels, the computation is asymptotically optimal. Precisely, the time required for the computation is O(N) , where N is the number of voxels inside the shape. Next, we show how these fitting cylinders can be used to measure 3D shapes. More precisely, we define a new 3D shape measure that numerically evaluates how mach a shape given looks like a cylinder. Interestingly, both fitting cylinders have to be used to define such a measure—just one of them is not sufficient. The new measure is invariant with respect to translation, rotation, and scaling transformations, and ranges over the interval [0; 1], and takes the value 1 if and only if the shape considered is a perfect cylinder. It is robust and simple to compute.