In this paper, we introduce a new (constructive) characterization of tight wavelet frames on
non-flat domains in both continuum setting, ie on manifolds, and discrete setting, ie on …

In this study, our goal is to integrate classical mathematical models with deep neural
networks by introducing two novel deep neural network models for image segmentation …

This paper is a republication of an MMS paper [AL Bertozzi and A. Flenner, Multiscale
Model. Simul., 10 (2012), pp. 1090--1118] describing a new class of algorithms for …

The graph Laplacian and the graph cut problem are closely related to Markov random fields,
and have many applications in clustering and image segmentation. The diffuse interface …

Hyperspectral imagery is a challenging modality due to the dimension of the pixels which
can range from hundreds to over a thousand frequencies depending on the sensor. Most …

Learning a good graph similarity matrix in data clustering is very crucial. The goal of
clustering is to construct a good graph similarity matrix such that the similarity of points …

We present an accurate and efficient graph-based algorithm for semi-supervised
classification that is motivated by recent successful threshold dynamics approaches and …

In this paper we propose two variational models for semi-supervised clustering of high-
dimensional data. The new models produce substantial improvements of the classification …

Networks capture pairwise interactions between entities and are frequently used in
applications such as social networks, food networks, and protein interaction networks, to …

We consider the problem of scale detection in images where a region of interest is present
together with a measurement tool (eg a ruler). For the segmentation part, we focus on the …