Efficient distance estimation for fitting implicit quadric surfaces

This paper presents a novel approach for estimating the shortest Euclidean distance from a given point to the corresponding implicit quadric fitting surface. It first estimates the orthogonal orientation to the surface from the given point; then the shortest distance is directly estimated by intersecting the implicit surface with a line passing through the given point according to the estimated orthogonal orientation. The proposed orthogonal distance estimation is easily obtained without increasing computational complexity; hence it can be used in error minimization surface fitting frameworks. Comparisons of the proposed metric with previous approaches are provided to show both improvements in CPU time as well as in the accuracy of the obtained results. Surfaces fitted by using the proposed geometric distance estimation and state of the art metrics are presented to show the viability of the proposed approach.