Joint Reconstruction-Segmentation on Graphs

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation, using each to guide the other. However, this work has so far employed relatively simple segmentation...

Theory and Applications of Differential Equation Methods for Graph-based Learning

A large number of modern learning problems involve working with highly interrelated and interconnected data. Graph-based learning is an emerging technique for approaching such problems, by representing this data as a graph (a.k.a. a network). That is, the points of data are represented by the vertices of the graph, and then the edges linking...

Mass-conserving diffusion-based dynamics on graphs

An emerging technique in image segmentation, semi-supervised learning and general classification problems concerns the use of phase-separating flows defined on finite graphs. This technique was pioneered in Bertozzi and Flenner (2012, Multiscale Modeling and Simulation 10(3), 1090-1118), which used the Allen-Cahn flow on a graph, and was then...

Classification and image processing with a semi-discrete scheme for fidelity forced Allen–Cahn on graphs

This paper introduces a semi-discrete implicit Euler (SDIE) scheme for the Allen-Cahn equation (ACE) with fidelity forcing on graphs. The continuous-in-time version of this differential equation was pioneered by Bertozzi and Flenner in 2012 as a method for graph classification problems, such as semi-supervised learning and image segmentation....

Criteria for hull-machinery rigidity compability

The design of a class of 28.000-ton tankers