Approximation methods for the recovery of shapes and images from gradients

Vishal M. Patel, Rama Chellappa

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations


Recovery of shapes and images from gradients is an important problem in many fields such as computer vision, computational photography, and remote sensing. For instance, techniques such as photometric stereo and shape from Shading recover the underlying 3D shape by integrating an estimated surface gradient field or surface normals. In applications such as image stitching and image editing, gradients of given images are first manipulated. The final image is then reconstructed from the modified gradient field. The estimated or modified gradient field is usually nonintegrable due to the presence of noise, outliers in the estimation process, and inherent ambiguities. This chapter reviews some approximation-based methods for surface reconstruction from the given nonintegrable gradient field with applications to 3D modeling and image reconstruction.

Original languageEnglish (US)
Title of host publicationExcursions in Harmonic Analysis
Subtitle of host publicationThe February Fourier Talks at the Norbert Wiener Center
PublisherBirkhauser Boston
Number of pages22
ISBN (Electronic)9780817683764
ISBN (Print)9780817683757
StatePublished - Jan 1 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Compressive sampling
  • Image gradients
  • Image recovery
  • Photometric stereo
  • Poisson solver
  • Shape from shading
  • Shape recovery
  • Shapelets
  • Sparsity
  • Surface reconstruction


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