Shape from focus and defocus: Convexity, quasiconvexity and defocus-invariant textures

Paolo Favaro

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

In this paper we analyze the convexity and the quasiconvexity of shape from focus/defocus and image restoration. We show that these problems are strictly quasiconvex for a family of Bregman's divergences, and in particular for least-squares. In addition to giving novel analytical insight to these problems, this study can be readily exploited to design algorithms: One can do away with global minimizers and obtain the same optimal solution by employing simple and efficient local methods. We experimentally validate this investigation by comparing two minimization algorithms: one based on a local method (gradient-flow) and another based on a global method (graph cuts). We show that both algorithms find the global optimum. Finally, we fully characterize defocus-invariant textures, a class of textures that do not allow depth recovery. We show how to decompose textures into defocus-invariant and defocus-varying components, and how this decomposition can be used to dramatically improve depth estimates. ©2007 IEEE.

Original languageEnglish
Title of host publicationProceedings of the IEEE International Conference on Computer Vision
DOIs
Publication statusPublished - 2007
Event2007 IEEE 11th International Conference on Computer Vision - Rio de Janeiro, Brazil
Duration: 14 Oct 200721 Oct 2007

Conference

Conference2007 IEEE 11th International Conference on Computer Vision
Abbreviated titleICCV
CountryBrazil
CityRio de Janeiro
Period14/10/0721/10/07

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  • Cite this

    Favaro, P. (2007). Shape from focus and defocus: Convexity, quasiconvexity and defocus-invariant textures. In Proceedings of the IEEE International Conference on Computer Vision https://doi.org/10.1109/ICCV.2007.4409024