The kernel-based spatial-spectral approach has been widely used for hyperspectral image (HSI) classification in recent years, where composite kernel (CK) and spatial-spectral kernel (SSK) are the most representative methods. Unlike CK, SSK measures the similarity of two clusters in kernel space to capture the hidden manifold in HSI, which has proven to be powerful to handle the well-known sample selection bias problem. However, the cluster feature in kernel space is always handled by a spatial filter which treats a cluster as a collection of individually independent pixels. This is neither efficient nor robust. Therefore, in this paper, we propose a method which treats each cluster as the combination of several subclusters. On the basis of the assumption that each manifold within a local region is a homeomorphic subspace in Euclidean space, we consider computing subcluster-based spatial-spectral features in the original input space and measure the similarities between subclusters to construct the proposed generalized SSK (GSSK). Moreover, due to the powerful ability to preserve the object boundaries, the adjacent superpixels (ASs) under an over-segmentation condition seem to be perfect candidates that serve as the subclusters. Therefore, we propose AS-based GSSK (ASGSSK) for HSI classification. Furthermore, the superpixel-based multiscale strategy is utilized in the framework of ASGSSK (termed ASMGSSK) to further explore the multiscale structures of HSI for improving the classification performance and sidestepping the selection of an optimal superpixel scale. Compared with the classic SSK method, the proposed ASMGSSK achieves 2.2% and 3.8% higher overall accuracy on average, with only 25% and 20% computational consumption for the Indian Pines and University of Pavia datasets, respectively. Experiments on two real HSI datasets demonstrate the superiority of the proposed method.

Fourier-Mellin transform (FMT) has been widely used for the extraction of rotation- and scale-invariant features. However, affine transform is a more reasonable approximation model for real viewpoint change. Due to shearing, the integral along the angular direction in the calculation of FMT cannot be used to extract the inherent features of an image undergoing affine transform. To eliminate the effect of shearing, whitening transform should be conducted on the integral along the radial direction. FMT can hardly be modified by conventional whitening-based methods with low computational cost due to additional processes. In this paper, two factors are constructed and embedded into FMT. Quasi Fourier-Mellin transform (QFMT) is proposed. The embedding of these factors is equivalent to whitening transform and can eliminate the effect of shearing in the affine transform. In particular, QFMT can also be calculated by integrating along the radial direction followed by integrating along the angular direction, as in FMT. Based on QFMT, the quasi Fourier-Mellin descriptor (QFMD) is constructed for the extraction of affine invariant features. Some experiments have also been conducted to test the performance of the proposed method.

The existing output signal-to-noise ratio (SNR) optimization model seems not accurate enough to characterize the closed-form instantaneous cross-correlation function type of Wigner distribution’s optimum detection performance, resulting in an unsatisfactory optimal linear canonical transform free parameters selection strategy. A more appropriate output SNR definition, the so-called variance-SNR, is then proposed to model a new kind of optimization, the variance-SNR optimization model. By integrating these two optimization models, it follows a multiobjective optimization, whose solutions to noisy single component linear frequency-modulated signals are also deduced. The newly derived strategy on determination of the optimal parameters implies the previous one so that there is a better detection performance in terms of noise suppression.

It is often a difficult task to accurately segment brain magnetic resonance (MR) images with intensity in-homogeneity and noise. This paper introduces a novel level set method for simultaneous brain MR image segmentation and intensity inhomogeneity correction. To reduce the effect of noise, novel anisotropic spatial information, which can preserve more details of edges and corners, is proposed by incorporating the inner relationships among the neighbor pixels. Then the proposed energy function uses the multivariate Student's t-distribution to fit the distribution of the intensities of each tissue. Furthermore, the proposed model utilizes Hidden Markov random fields to model the spatial correlation between neigh-boring pixels/voxels. The means of the multivariate Student's t-distribution can be adaptively estimated by multiplying a bias field to reduce the effect of intensity inhomogeneity. In the end, we reconstructed the energy function to be convex and calculated it by using the Split Bregman method, which allows our framework for random initialization, thereby allowing fully automated applications. Our method can obtain the final result in less than 1 second for 2D image with size 256 × 256 and less than 300 seconds for 3D image with size 256 × 256 × 171. The proposed method was compared to other state-of-the-art segmentation methods using both synthetic and clinical brain MR images and increased the accuracies of the results more than 3%.

To tackle a challenge in high-dimensional complex features information processing, this study extends the permanent scale Wigner distribution and the single scale k -Wigner distribution (kWD, formerly known as τ-Wigner distribution) to a novel multiscale parameterized Wigner distribution. That is the so-called K-Wigner distribution (KWD) which is able to use different scales to extract different types of features at different dimensions. Heisenberg-type uncertainty inequalities of the KWD are established, giving rise to the tightest universal attainable lower bound for all functions on the uncertainty product in time-KWD and Fouier transform-KWD domains, and two versions of attainable lower bounds for complex-valued functions. The obtained results solve an important concern regarding the limit of the KWD’s time-frequency resolution influenced by the parameter matrix. As an application, the derived uncertainty inequalities are applied to estimate the bandwidth in KWD domains. The time-frequency resolution performance of the multiscale KWD, as compared with that of the single scale kWD, is investigated in details. The optimal parameter matrix of the KWD achieving the best performance is then generated, which solves an important concern regarding the KWD’s parameter matrix selection. Examples are also carried out to demonstrate the usefulness and effectiveness of the proposed technique.