English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The Ambrosio-Tortorelli functional is a phase-field approximation of theMumford-Shah functional that has been widely used for image segmentation. Theapproximation has the advantages of being easy to implement, maintaining thesegmentation ability, and $\Gamma$-converging to the Mumford-Shah functional.However, it has been observed in actual computation that the segmentationability of the Ambrosio-Tortorelli functional varies significantly withdifferent values of the parameter and it even fails to $\Gamma$-converge to theoriginal functional for some cases. In this paper we present an asymptoticanalysis on the gradient flow equation of the Ambrosio-Tortorelli functionaland show that the functional can have different segmentation behavior for smallbut finite values of the regularization parameter and eventually loses itssegmentation ability as the parameter goes to zero when the input image istreated as a continuous function. This is consistent with the existingobservation as well as the numerical examples presented in this work. Aselection strategy for the regularization parameter and a scaling procedure forthe solution are devised based on the analysis. Numerical results show thatthey lead to good segmentation of the Ambrosio-Tortorelli functional for realimages.

Selection of the Regularization Parameter in the Ambrosio-Tortorelli Approximation of the Mumford-Shah Functional for Image Segmentation