Non-convex regularization in remote sensing

In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parametrization. We consider regularization via traditional squared (2) and sparsity-promoting (1) norms, as well as more unconventional nonconvex regularizers (p and Log Sum Penalty). We compare their properties and advantages on several classification and linear unmixing tasks and provide advices on the choice of the best regularizer for the problem at hand. Finally, we also provide a fully functional toolbox for the community.Comment: 11 pages, 11 figure

Constrained Convex Neyman-Pearson Classification Using an Outer Approximation Splitting Method

This paper presents an algorithm for Neyman-Pearson classification. While empirical riskminimization approaches focus on minimizing a global risk, the Neyman-Pearson frameworkminimizes the type II risk under an upper bound constraint on the type I risk. Sincethe 0=1 loss function is not convex, optimization methods employ convex surrogates thatlead to tractable minimization problems. As shown in recent work, statistical bounds canbe derived to quantify the cost of using such surrogates instead of the exact 1/0 loss.However, no specific algorithm has yet been proposed to actually solve the resulting minimizationproblem numerically. The contribution of this paper is to propose an efficientsplitting algorithm to address this issue. Our method alternates a gradient step on the objectivesurrogate risk and an approximate projection step onto the constraint set, which isimplemented by means of an outer approximation subgradient projection algorithm. Experimentson both synthetic data and biological data show the efficiency of the proposed method

DREAM²S: Deformable Regions Driven by an Eulerian Accurate Minimization Method for Image and Video Segmentation

This paper deals with image and video segmentation using active contours. We propose a general form for the energy functional related to region-based active contours. We compute the associated evolution equation using shape derivation tools and accounting for the evolving region-based terms. Then we apply this general framework to compute the evolution equation from functionals that include various statistical measures of homogeneity for the region to be segmented. Experimental results show that the determinant of the covariance matrix appears to be a very relevant tool for segmentation of homogeneous color regions. As an example, it has been successfully applied to face segmentation in real video sequences

k-NN Boosting Prototype Learning for Object Classification

Object classification is a challenging task in computer vision. Many approaches have been proposed to extract meaningful descriptors from images and classifying them in a supervised learning framework. In this paper, we revisit the classic k-nearest neighbors (k-NN) classification rule, which has shown to be very effective when dealing with local image descriptors. However, k-NN still features some major drawbacks, mainly due to the uniform voting among the nearest prototypes in the feature space. In this paper, we propose a generalization of the classic k-NN rule in a supervised learning (boosting) framework. Namely, we redefine the voting rule as a strong classifier that linearly combines predictions from the k closest prototypes. To induce this classifier, we propose a novel learning algorithm, MLNN (Multiclass Leveraged Nearest Neighbors), which gives a simple procedure for performing prototype selection very efficiently. We tested our method on 12 categories of objects, and observed significant improvement over classic k-NN in terms of classification performances

Active contour segmentation with a parametric shape prior: Link with the shape gradient

International audienceActive contours are adapted to image segmentation by energy minimization. The energies often exhibit local minima, requiring regularization. Such an a priori can be expressed as a shape prior and used in two main ways: (1) a shape prior energy is combined with the segmentation energy into a trade-off between prior compliance and accuracy or (2) the segmentation energy is minimized in the space defined by a parametric shape prior. Methods (1) require the tuning of a data-dependent balance parameter and methods (1) and (2) are often dedicated to a specific prior or contour representation, with the prior and segmentation aspects often meshed together, increasing complexity. A general framework for category (2) is proposed: it is independent of the prior and contour representations and it separates the prior and segmentation aspects. It relies on the relationship shown here between the shape gradient, the prior-induced admissible contour transformations, and the segmentation energy minimization