The notion of viscosity solutions of scalar fully nonlinear partial differential equations of
second order provides a framework in which startling comparison and uniqueness …

We propose a new model for active contours based on a geometric partial differential
equation. Our model is intrinsec, stable (satisfies the maximum principle) and permits a …

A stable algorithm is proposed for image restoration based on the “mean curvature motion”
equation. Existence and uniqueness of the “viscosity” solution of the equation are proved, a …

Image-processing transforms must satisfy a list of formal requirements. We discuss these
requirements and classify them into three categories:“architectural requirements” like …

There are several interesting examples of equations governing motion of hypersurfaces
bounding two phases of materials in various sciences. Such a hypersurface is called an …

In this note I discuss in some detail, but without all the occasionally cumbersome
technicalities, a general theory about propagating fronts, ie" hypersurfaces" moving with …

This book contains both a synthesis and mathematical analysis of a wide set of algorithms
and theories whose aim is the automatic segmen tation of digital images as well as the …

The connection between the weak theories for a class of geometric equations and the
asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established …

Recent theoretical advances in the mathematical treatment of geometric interface motion
make more tractable the theory of a wide variety of materials science problems where the …

Although research in curve shortening flow has been very active for nearly 20 years, the
results of those efforts have remained scattered throughout the literature. For the first time …