Structured Learning of Tree Potentials in CRF for Image Segmentation

We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of some pre-defined parametric models, and then methods like structured support vector machines (SSVMs) are applied to learn those linear coefficients. We instead formulate the unary and pairwise potentials as nonparametric forests---ensembles of decision trees, and learn the ensemble parameters and the trees in a unified optimization problem within the large-margin framework. In this fashion, we easily achieve nonlinear learning of potential functions on both unary and pairwise terms in CRFs. Moreover, we learn class-wise decision trees for each object that appears in the image. Due to the rich structure and flexibility of decision trees, our approach is powerful in modelling complex data likelihoods and label relationships. The resulting optimization problem is very challenging because it can have exponentially many variables and constraints. We show that this challenging optimization can be efficiently solved by combining a modified column generation and cutting-planes techniques. Experimental results on both binary (Graz-02, Weizmann horse, Oxford flower) and multi-class (MSRC-21, PASCAL VOC 2012) segmentation datasets demonstrate the power of the learned nonlinear nonparametric potentials.Comment: 10 pages. Appearing in IEEE Transactions on Neural Networks and Learning System

Efficient Optimization of Performance Measures by Classifier Adaptation

In practical applications, machine learning algorithms are often needed to learn classifiers that optimize domain specific performance measures. Previously, the research has focused on learning the needed classifier in isolation, yet learning nonlinear classifier for nonlinear and nonsmooth performance measures is still hard. In this paper, rather than learning the needed classifier by optimizing specific performance measure directly, we circumvent this problem by proposing a novel two-step approach called as CAPO, namely to first train nonlinear auxiliary classifiers with existing learning methods, and then to adapt auxiliary classifiers for specific performance measures. In the first step, auxiliary classifiers can be obtained efficiently by taking off-the-shelf learning algorithms. For the second step, we show that the classifier adaptation problem can be reduced to a quadratic program problem, which is similar to linear SVMperf and can be efficiently solved. By exploiting nonlinear auxiliary classifiers, CAPO can generate nonlinear classifier which optimizes a large variety of performance measures including all the performance measure based on the contingency table and AUC, whilst keeping high computational efficiency. Empirical studies show that CAPO is effective and of high computational efficiency, and even it is more efficient than linear SVMperf.Comment: 30 pages, 5 figures, to appear in IEEE Transactions on Pattern Analysis and Machine Intelligence, 201

Learning Structured Models for Segmentation of 2D and 3D Imagery

Efficient and accurate segmentation of cellular structures in microscopic data is an essential task in medical imaging. Many state-of-the-art approaches to image segmentation use structured models whose parameters must be carefully chosen for optimal performance. A popular choice is to learn them using a large-margin framework and more specifically structured support vector machines (SSVM). Although SSVMs are appealing, they suffer from certain limitations. First, they are restricted in practice to linear kernels because the more powerful non-linear kernels cause the learning to become prohibitively expensive. Second, they require iteratively finding the most violated constraints, which is often intractable for the loopy graphical models used in image segmentation. This requires approximation that can lead to reduced quality of learning. In this article, we propose three novel techniques to overcome these limitations. We first introduce a method to “kernelize” the features so that a linear SSVM framework can leverage the power of non-linear kernels without incurring much additional computational cost. Moreover, we employ a working set of constraints to increase the reliability of approximate subgradient methods and introduce a new way to select a suitable step size at each iteration. We demonstrate the strength of our approach on both 2D and 3D electron microscopic (EM) image data and show consistent performance improvement over state-of-the-art approaches

Transductive hyperspectral image classification: toward integrating spectral and relational features via an iterative ensemble system

Remotely sensed hyperspectral image classification is a very challenging task due to the spatial correlation of the spectral signature and the high cost of true sample labeling. In light of this, the collective inference paradigm allows us to manage the spatial correlation between spectral responses of neighboring pixels, as interacting pixels are labeled simultaneously. The transductive inference paradigm allows us to reduce the inference error for the given set of unlabeled data, as sparsely labeled pixels are learned by accounting for both labeled and unlabeled information. In this paper, both these paradigms contribute to the definition of a spectral-relational classification methodology for imagery data. We propose a novel algorithm to assign a class to each pixel of a sparsely labeled hyperspectral image. It integrates the spectral information and the spatial correlation through an ensemble system. For every pixel of a hyperspectral image, spatial neighborhoods are constructed and used to build application-specific relational features. Classification is performed with an ensemble comprising a classifier learned by considering the available spectral information (associated with the pixel) and the classifiers learned by considering the extracted spatio-relational information (associated with the spatial neighborhoods). The more reliable labels predicted by the ensemble are fed back to the labeled part of the image. Experimental results highlight the importance of the spectral-relational strategy for the accurate transductive classification of hyperspectral images and they validate the proposed algorithm