Pros and cons of euclidean fitting

Abstract

The purpose of this paper is to discuss pros and cons of fitting general curves and surfaces to 2D and 3D edge and range data using the Euclidean distance. In the past researchers have used approximate distance functions rather than the Euclidean distance. But the main disadvantage of the Euclidean fitting, computational cost, has become less important due to rising computing speed. Experiments with the real Euclidean distance show the limitations of suggested approximations like the Algebraic distance or Taubin’s approximation. We compare the performance of various fitting algorithms in terms of efficiency, correctness, robustness and pose invariance.