Abstract
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.
Highlights
Feature curves are a key element in the analysis and synthesis of digital shapes
For recognising curves expressed in implicit form, we extend the approach described in [27], which required the intermediate step of projecting the curves on a plane, while for parametric curve representations, we generalise to space curves the method for plane curves proposed in [15]
We report the family of space curves, the parameters of the mathematical curve, the curve parameters that differ from the original ones as recognised by the Hough transform (HT) algorithms, for the implicit and parametric curve expressions, respectively, on the perturbed curve samples
Summary
Feature curves are a key element in the analysis and synthesis of digital shapes. They are significant for shape interpretation and perception studies support these curves as an effective choice for representing the salient parts of a 3D model [5]. Our HT-based recognition method recognises a large number of space curves, including both those that directly have a space representation, such as the helix of Fig. 2, and those that can be represented with a projection onto quadrics or planes This method deals with curves expressed in both implicit and parametric form; it evaluates the quality of the curve approximation, for both implicit and parametric representations, and it is robust to noise and outliers. It provides a comparative analysis of the HTbased recognition algorithm for curves represented either in parametric or implicit form with respect to both a number of measures of quality of the curve fitting and the computational time.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
