Hough Transform for Detecting Space Curves in Digital 3D Models

We present and analyse the Hough transform (HT) to recognise and approximate space curves in digital models, a problem that is not currently addressed by the standard HT. Our method works on meshes and point clouds and applies to models even incomplete or affected by noise, thus being suitable for the analysis of digital models deriving from 3D scans. In our approach we take advantage of a recent HT formulation for algebraic curves to define both parametric and implicit space curve representations. We also provide a comparative analysis of the HT-based method when dealing with both curve representations, discussing the computational performance and the approximation accuracy of both strategies.

Automated summary

This article presents a method for recognizing and approximating space curves in digital models, which works on incomplete or noisy models and is suitable for analyzing digital models derived from 3D scans. The method utilizes a recent formulation of the Hough Transform for algebraic curves to define both parametric and implicit space curve representations, and compares the computational performance and approximation accuracy of both strategies.