MENU

You are here

Minimal partitions and image classification using a gradient-free perimeter approximation

TitleMinimal partitions and image classification using a gradient-free perimeter approximation
Publication TypePreprint
2013
AuthorsAmstutz, S, Van Goethem, N, Novotny, AAndré
InstitutionSISSA
Image classification, deblurring, optimal partitions, perimeter approximation

In this paper a new mathematically-founded method for the optimal partitioning of domains, with applications to the classification of greyscale and color images, is proposed.
Since optimal partition problems are in general ill-posed, some regularization strategy is required.
Here we regularize by a non-standard approximation of the total interface length, which does not involve the gradient of approximate characteristic functions, in contrast to the classical Modica-Mortola approximation. Instead, it involves a system of uncoupled linear partial differential equations and nevertheless shows $\Gamma$-convergence properties in appropriate function spaces.
This approach leads to an alternating algorithm that ensures a decrease of the objective function at each iteration, and which always provides a partition, even during the iterations.
The efficiency of this algorithm is illustrated by various numerical examples. Among them we consider binary and multilabel minimal partition problems including supervised or automatic image classification, inpainting, texture pattern identification and deblurring.

http://hdl.handle.net/1963/6976

Sign in