Three-dimensional object recognition
ACM Computing Surveys (CSUR) - Annals of discrete mathematics, 24
Analysis and interpretation of range images
IEEE Transactions on Pattern Analysis and Machine Intelligence
A buyer's guide to conic fitting
BMVC '95 Proceedings of the 6th British conference on Machine vision (Vol. 2)
Use of the Hough transformation to detect lines and curves in pictures
Communications of the ACM
Pros and Cons of Euclidean Fitting
Proceedings of the 23rd DAGM-Symposium on Pattern Recognition
Using a geometric formulation of annular-like shape priors for constraining variational level-sets
Pattern Recognition Letters
Plausible 3d colour surface completion using non-parametric techniques
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
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The focus of our paper is on the fitting of general curves and surfaces to 3D data. In the past researchers have used approximate distance functions rather than the Euclidean distance because of computational efficiency. We now feel that machine speeds are sufficient to ask whether it is worth considering Euclidean fitting again. Experiments with the real Euclidean distance show the limitations of suggested approximations like the Algebraic distance or Taubin's approximation. In this paper we present our results improving the known fitting methods by an (iterative) estimation of the real Euclidean distance. The performance of our method is compared with several methods proposed in the literature and we show that the Euclidean fitting guarantees a better accuracy with an acceptable computational cost.