title: Shape from defocus via diffusion.
abstract: 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.
authors.affiliation: School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, UK. p.favaro@hw.ac.uk
authors.forename: Paolo
authors.initials: P
authors.lastname: Favaro
authors.forename: Stefano
authors.initials: S
authors.lastname: Soatto
authors.forename: Martin
authors.initials: M
authors.lastname: Burger
authors.forename: Stanley J
authors.initials: SJ
authors.lastname: Osher
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001185:Artificial Intelligence; D004058:Diffusion; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity