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Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows
, 2011
"... We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to take into account the problem structure, and automatically select a subgraph with a small number of connected components. By exp ..."
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We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to take into account the problem structure, and automatically select a subgraph with a small number of connected components. By exploiting prior knowledge, one can indeed improve the prediction performance and/or obtain better interpretable results. Regularization or penalty functions for selecting features in graphs have recently been proposed but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and “well connected” subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called “path coding ” penalties. Unlike existing regularization functions, path coding penalties can both model long range interactions between features in the graph and be tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and lead to more connected subgraphs than other regularization functions for graphs.
1Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
"... Abstract—We present two graphbased algorithms for multiclass segmentation of highdimensional data on graphs. The algorithms use a diffuse interface model based on the GinzburgLandau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex ..."
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Abstract—We present two graphbased algorithms for multiclass segmentation of highdimensional data on graphs. The algorithms use a diffuse interface model based on the GinzburgLandau functional, related to total variation and graph cuts. A multiclass extension is introduced using the Gibbs simplex, with the functional’s doublewell potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm uses a graph adaptation of the classical numerical MerrimanBenceOsher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, image labeling, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current stateoftheart in multiclass graphbased segmentation algorithms for highdimensional data.
Convex Optimization for Image Segmentation
"... Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar ..."
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Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar motion). Segmentation is a highly ambiguous task, and usually requires some prior knowledge. This can either be obtained by interactive user input in an supervised manner, or completely unsupervised using strong prior knowledge. In this thesis we use continuous energy minimization to tackle all of these problems. Continuous energy minimization provides an elegant way to model a problem like image segmentation. If the problem is convex, there are powerful optimization algorithms available. Additionally, we are guaranteed to find the globally optimal solution. We give an extensive introduction to convex optimization methods in computer vision. A great part of this thesis is devoted to basic image segmentation. We investigate the continuous maximum flow model for the two label segmentation, as well as optimization problems for multilabel segmentation. To obtain good segmentation results in a reasonable time, it is important that the energy,
Active Contours on Graphs: Multiscale Morphology and Graphcuts
"... Abstract—In this paper we propose two novel methods for formulating and implementing the methodology of geodesic active contours on arbitrary graphs, as applied to multiscale morphology and segmentation. Firstly, we propose approximations to the calculation of the gradient and the divergence of vect ..."
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Abstract—In this paper we propose two novel methods for formulating and implementing the methodology of geodesic active contours on arbitrary graphs, as applied to multiscale morphology and segmentation. Firstly, we propose approximations to the calculation of the gradient and the divergence of vector functions defined on graphs and use these approximations to apply the technique of geodesic active contours for object detection on graphs. To this end, we extend existing work on graph morphology to multiscale dilation and erosion and implement them recursively usinglevel sets of functions defined on the graph. Second, we propose a graphcut based solution to the geodesic active contour problem on graphs. Appropriate weights are calculated for each edge for which the Riemannian length of a contour can be approximated by the weighted sum of intersections of the contour with the edges of the graph. Finding the minimum Riemannian length contour then becomes equivalent to solving a max flow problem for which efficient solutions have been proposed in the literature. Index Terms—Geodesic active contours, graphcuts, image analysis, image edge detection, image segmentation, morphological operations, object detection. I.
Seeded Segmentation Methods for Medical Image Analysis
, 2011
"... Segmentation is one of the key tools in medical image analysis. The objective of segmentation is to provide reliable, fast, and effective organ delineation. While traditionally, particularly in computer vision, segmentation is seen as an early vision tool used for subsequent recognition, in medical ..."
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Segmentation is one of the key tools in medical image analysis. The objective of segmentation is to provide reliable, fast, and effective organ delineation. While traditionally, particularly in computer vision, segmentation is seen as an early vision tool used for subsequent recognition, in medical imaging the opposite is often true. Recognition can be performed interactively by clinicians or automatically using robust techniques, while the objective of segmentation is to precisely delineate contours and surfaces. This can lead to effective techniques known as “intelligent scissors ” in 2D and their equivalent in 3D. This chapter is divided as follows. Section 3.1 starts off with a more “philosophical” section setting the background for this study. We argue for a segmentation context where highlevel knowledge, object information, and segmentation method are all separate. In Sect. 3.2, we survey in some detail a number of segmentation methods that are wellsuited to image analysis, in particular of medical images. We illustrate this, make some comparisons and some recommendations. In Sect. 3.3, we introduce very recent methods that unify many popular discrete segmentation methods and we introduce a new technique. In Sect. 3.4, we give some remarks about recent advances in seeded, globally optimal active contour methods that are of interest for this study. In Sect. 3.5, we compare all presented methods qualitatively. We then conclude and give some indications for future work.
Chambolle’s Projection Algorithm for Total Variation
"... This article is available online with supplementary materials, software, datasets and online demo at ..."
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This article is available online with supplementary materials, software, datasets and online demo at