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Smooth Image Surface Approximation by Piecewise Cubic Polynomials

  • Oliver Matias van Kaick
  • Helio Pedrini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4756)

Abstract

The construction of surfaces from dense data points is an important problem encountered in several applications, such as computer vision, reverse engineering, computer graphics, terrain modeling, and robotics. Moreover, the particular problem of approximating digital images from a set of selected points allows to employ methods that are directed specifically to this task, which take advantage of the fact that all points belong to a common 2D domain. This paper describes a method for approximating images by fitting smooth surfaces to scattered points, where the smooth surfaces are constructed using piecewise cubic approximation. An incremental triangulation algorithm is used to iteratively refine a mesh until a specified error tolerance is achieved. The resulting surface is represented by a network of piecewise cubic triangular patches possessing C 1 continuity. The proposed method is compared against other surface approximation approaches and applied to several data sets in order to demonstrate its performance.

Keywords

Surface modeling image surface smooth interpolation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Oliver Matias van Kaick
    • 1
  • Helio Pedrini
    • 2
  1. 1.School of Computing Science, Simon Fraser University, Burnaby, BC, V5A 1S6Canada
  2. 2.Department of Computer Science, Federal University of Paraná, Curitiba, PR, 81531-990Brazil

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