What Is the Range of Surface Reconstructions from a Gradient Field?

  • Amit Agrawal
  • Ramesh Raskar
  • Rama Chellappa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)


We propose a generalized equation to represent a continuum of surface reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algorithm are special cases of this generalized equation. For a N × N pixel grid, the subspace of all integrable gradient fields is of dimension N 2 – 1. Our framework can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the integration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using binary weights, where the parameter α allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continuous weights and (c) Diffusion using affine transformation of gradients. We provide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.


Span Tree Surface Reconstruction Laplacian Matrix Photometric Stereo Correction Gradient 
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 2006

Authors and Affiliations

  • Amit Agrawal
    • 1
  • Ramesh Raskar
    • 2
  • Rama Chellappa
    • 1
  1. 1.Center for Automation ResearchUniversity of MarylandCollege ParkUSA
  2. 2.Mitsubishi Electric Research Labs (MERL)CambridgeUSA

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