Hough transform based recognition of space curves

Given a set of points representing a curve embedded in the Euclidean space and a family of space curves, we face the problem of finding the curve of the family that best fits these points. For our purposes, we apply the Hough transform (HT), which allows the recognition of a template curve from a set of points and its exact representation. Our method directly applies to digital models of 3D objects and combines the HT based recognition of curves expressed in both implicit and parametric form in a single flow. Furthermore, we extend the number of space curves that can be recognised, by including also those curves whose profile P can be approximated as the intersection of a quadric surface and a cylinder generated by a plane curve.