Faithful least-squares fitting of spheres, cylinders, cones and tori for reliable segmentation

  • Gabor Lukács
  • Ralph Martin
  • Dave Marshall
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)


This paper addresses a problem arising in the reverse engineering of solid models from depth-maps. We wish to identify and fit surfaces of known type wherever these are a good fit. This paper presents a set of methods for the least-squares fitting of spheres, cylinders, cones and tori to three-dimensional point data. Least-squares fitting of surfaces other planes, even of simple geometric type, has been little studied.

Our method has the particular advantage of being robust in the sense that as the principal curvatures of the surfaces being fitted decrease (or become more equal), the results which are returned naturally become closer and closer to those surfaces of ‘simpler type’, i.e. planes, cylinders, cones, or spheres which best describe the data, unlike other methods which may diverge as various parameters or their combination become infinite.


Distance Function Base Point Principal Curvature Reverse Engineering Range Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Gabor Lukács
    • 1
    • 2
  • Ralph Martin
    • 2
  • Dave Marshall
    • 2
  1. 1.Computer and Automation Research InstituteHungarian Academy of SciencesBudapestHungary
  2. 2.Dept of Computer ScienceCardiff UniversityCardiffUK

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