Shape from defocus via diffusion

Paolo Favaro, Stefano Soatto, Martin Burger, Stanley J. Osher

Research output: Contribution to journalArticlepeer-review

146 Citations (Scopus)


Defocus can be modeled as a diffusion process and represented mathematically using the heat equation, where image blur corresponds to the diffusion of heat. This analogy can be extended to non-planar scenes by allowing a space-varying diffusion coefficient. The inverse problem of reconstructing 3-D structure from blurred images corresponds to an "inverse diffusion" that is notoriously ill-posed. We show how to bypass this problem by using the notion of relative blur. Given two images, within each neighborhood, the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene. This can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image, using only forward diffusion. © 2008 IEEE.

Original languageEnglish
Pages (from-to)518-531
Number of pages14
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number3
Publication statusPublished - Mar 2008


  • And deblurring
  • Depth cues
  • Gradient methods
  • Inverse problems
  • Iterative methods
  • Partial differential equations
  • Reconstruction
  • Shape
  • Sharpening


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