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We propose a nonlinear multiscale decomposition of signals defined on the vertex set of a general weighted graph. This decomposition is inspired by the hierarchical multiscale (BV,L 2) decomposition of Tadmor, Nezzar, and Vese (Multiscale Model. Simul. 2(4):554–579, 2004). We find the decomposition by iterative regularization using a graph variant of the(More)
The decomposition of images into their meaningful components is one of the major tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical decomposition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a(More)
A new hierarchical representation of general discrete data sets living on graphs is proposed. The approach takes advantage of recent works on graph regularization. The different levels of the hierarchy are discovered as the regularization process is performed. The role of the merging criterion that is common to hierarchical representations is greatly(More)
We propose a new hierarchical representation of discrete data sets living on graphs. The approach takes advantage of recent works on graph regularization. The role of the merging criterion that is common to hierarchical representations is greatly reduced due to the regulariza-tion step. The regularization is performed recursively with a decreasing fidelity(More)
We consider the problem of recovering a high-resolution image from a pair consisting of a complete low-resolution image and a high-resolution but incomplete one. We refer to this task as the image zoom completion problem. After discussing possible contexts in which this setting may arise, we introduce a nonlocal regularization strategy, giving full details(More)
—We propose a new multiscale transform for scalar functions defined on the vertex set of a general undirected weighted graph. The transform is based on an adaption of the lifting scheme to graphs. One of the difficulties in applying directly the lifting scheme to graphs is the partitioning of the vertex set. We follow a recent greedy approach and extend it(More)
—In this paper, we propose a nonlocal approach based on graphs to segment raw point clouds as a particular class of graph signals. Using the framework of Partial difference Equations (PdEs), we propose a transcription on graphs of recent continuous global active contours along with a minimization algorithm. To apply it on point clouds, we show how to(More)
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