TR2006-021

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


    •  Agrawal, A., Raskar, R., Chellappa, R., "What is the Range of Surface Reconstructions from a Gradient Field?", European Conference on Computer Vision (ECCV), May 2006.
      BibTeX TR2006-021 PDF
      • @inproceedings{Agrawal2006may,
      • author = {Agrawal, A. and Raskar, R. and Chellappa, R.},
      • title = {What is the Range of Surface Reconstructions from a Gradient Field?},
      • booktitle = {European Conference on Computer Vision (ECCV)},
      • year = 2006,
      • month = may,
      • url = {https://www.merl.com/publications/TR2006-021}
      • }
  • Research Area:

    Computer Vision

Abstract:

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 quation. For a N x N pixel grid, the subspace of all integrable gradient fields is of dimension N2-1. 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) a-surfaces using binary weights, where the parameter a allos 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 anisotrpoic treatment discounts noise while recovering salient features in reconstructions.

 

  • Related News & Events

    •  NEWS    ECCV 2006: 2 publications by Oncel Tuzel, Amit Agrawal and Ramesh Raskar
      Date: May 7, 2006
      Where: European Conference on Computer Vision (ECCV)
      Research Area: Computer Vision
      Brief
      • The papers "Region Covariance: A Fast Descriptor for Detection and Classification" by Tuzel, O., Porikli, F. and Meer, P. and "What is the Range of Surface Reconstructions from a Gradient Field?" by Agrawal, A., Raskar, R. and Chellappa, R. were presented at the European Conference on Computer Vision (ECCV).
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