On the relation between constraint regularization, level sets, and shape optimization

TL;DR

This paper explores how constraint regularization methods, combining Tikhonov regularization and projection strategies, connect level set methods with inverse problems, scale-space theory, and shape optimization.

Contribution

It introduces a unified framework linking constraint regularization to level set methods and related fields, providing new insights into their interrelations.

Findings

Constraint regularization leads to straightforward derivation of level set methods.

The approach links asymptotic regularization to inverse problems theory.

Connects scale-space theory to computer vision and shape optimization.

Abstract

We consider regularization methods based on the coupling of Tikhonov regularization and projection strategies. From the resulting constraint regularization method we obtain level set methods in a straight forward way. Moreover, we show that this approach links the areas of asymptotic regularization to inverse problems theory, scale-space theory to computer vision, level set methods, and shape optimization.