TVL\({}_1\) Planarity Regularization for 3D Shape Approximation

  • Eugen FunkEmail author
  • Laurence S. Dooley
  • Anko Börner
Part of the Communications in Computer and Information Science book series (CCIS, volume 598)


The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.

This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy.


Radial Basis Function Move Little Square Radial Basis Function Shape Approximation Total Variation Regularization 
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 International Publishing Switzerland 2016

Authors and Affiliations

  • Eugen Funk
    • 1
    • 2
    Email author
  • Laurence S. Dooley
    • 1
  • Anko Börner
    • 2
  1. 1.Department of Computing and CommunicationsThe Open UniversityMilton KeynesUK
  2. 2.Department of Information Processing for Optical Systems, Institute of Optical Sensor SystemsGerman Aerospace Center (DLR)BerlinGermany

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