A closed form solution to natural image matting

Anat Levin*, Dani Lischinski, Yair Weiss

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

433 Scopus citations

Abstract

Interactive digital matting, the process of extracting a foreground object from an image based on limited user input, is an important task in image and video editing. From a computer vision perspective, this task is extremely challenging because it is massively ill-posed - at each pixel we must estimate the foreground and the background colors, as well as the foreground opacity ("alpha matte") from a single color measurement. Current approaches either restrict the estimation to a small part of the image, estimating foreground and background colors based on nearby pixels where they are known, or perform iterative nonlinear estimation by alternating foreground and background color estimation with alpha estimation. In this paper we present a closed form solution to natural image matting. We derive a cost function from local smoothness assumptions on foreground and background colors, and show that in the resulting expression it is possible to analytically eliminate the foreground and background colors to obtain a quadratic cost function in alpha. This allows us to find the globally optimal alpha matte by solving a sparse linear system of equations. Furthermore, the closed form formula allows us to predict the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms. We show that high quality mattes can be obtained on natural images from a surprisingly small amount of user input.

Original languageAmerican English
Title of host publicationProceedings - 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2006
Pages61-68
Number of pages8
DOIs
StatePublished - 2006
Event2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2006 - New York, NY, United States
Duration: 17 Jun 200622 Jun 2006

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume1
ISSN (Print)1063-6919

Conference

Conference2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2006
Country/TerritoryUnited States
CityNew York, NY
Period17/06/0622/06/06

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