Since their introduction in a classic paper by Rudin, Osher and Fatemi [26], total variation
minimizing models have become one of the most popular and successful methodology for …

Partial differential equations (PDEs) have led to an entire new field in image processing and
computer vision. Hundreds of publications have appeared in the last decade, and PDE …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus
of Variations | SpringerLink Skip to main content Advertisement Springer Nature Link Account …

We propose the use of nonlocal operators to define new types of flows and functionals for
image processing and elsewhere. A main advantage over classical PDE-based algorithms …

No time in human history has ever witnessed such explosive influence and impact of image
processing on modern society, sciences, and technologies. From nanotechnologies …

Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

We propose a novel class of graph neural networks based on the discretized Beltrami flow, a
non-Euclidean diffusion PDE. In our model, node features are supplemented with positional …

In this paper, we focus on techniques for vector-valued image regularization, based on
variational methods and PDE. Starting from the study of PDE-based formalisms previously …

Geodesic active contours and graph cuts are two standard image segmentation techniques.
We introduce a new segmentation method combining some of their benefits. Our main …