Matched Shrunken Cone Detector (MSCD): Bayesian Derivations and Case Studies for Hyperspectral Target Detection

Hyperspectral images (HSIs) possess non-negative properties for both hyperspectral signatures and abundance coefficients, which can be naturally modeled using cone-based representation. However, in hyperspectral target detection, cone-based methods are barely studied. In this paper, we propose a new regularized cone-based representation approach to hyperspectral target detection, as well as its two working models by incorporating into the cone representation l2-norm and l1-norm regularizations, respectively. We call the new approach the matched shrunken cone detector (MSCD). Also important, we provide principled derivations of the proposed MSCD from the Bayesian perspective: we show that MSCD can be derived by assuming a multivariate half-Gaussian distribution or a multivariate half-Laplace distribution as the prior distribution of the coefficients of the models. In the experimental studies, we compare the proposed MSCD with the subspace methods and the sparse representation-based methods for HSI target detection. Two real hyperspectral data sets are used for evaluating the detection performances on sub-pixel targets and full-pixel targets, respectively. Results show that the proposed MSCD can outperform other methods in both cases, demonstrating the competitiveness of the regularized cone-based representation

MSDH: matched subspace detector with heterogeneous noise

The matched subspace detector (MSD) is a classical subspace-based method for hyperspectral subpixel target detection. However, the model assumes that noise has the same variance over different bands, which is usually unrealistic in practice. In this letter, we relax the equal variance assumption and propose a matched subspace detector with heterogeneous noise (MSDH). In essence, the noise variances are different for different bands and they can be estimated by using iteratively reweighted least squares methods. Experiments on two benchmark real hyperspectral datasets demonstrate the superiority of MSDH over MSD for subpixel target detection

Constrained mutual convex cone method for image set based recognition

In this paper, we propose convex cone-based frameworks for image-set classification. Image-set classification aims to classify a set of images, usually obtained from video frames or multi-view cameras, into a target object. To accurately and stably classify a set, it is essential to accurately represent structural information of the set. There are various image features, such as histogram-based features and convolutional neural network features. We should note that most of them have non-negativity and thus can be effectively represented by a convex cone. This leads us to introduce the convex cone representation to image-set classification. To establish a convex cone-based framework, we mathematically define multiple angles between two convex cones, and then use the angles to define the geometric similarity between them. Moreover, to enhance the framework, we introduce two discriminant spaces. We first propose a discriminant space that maximizes gaps between cones and minimizes the within-class variance. We then extend it to a weighted discriminant space by introducing weights on the gaps to deal with complicated data distribution. In addition, to reduce the computational cost of the proposed methods, we develop a novel strategy for fast implementation. The effectiveness of the proposed methods is demonstrated experimentally by using five databases