Cross Cumulative Residual Entropy Research Articles

Hyperspectral Image Classification via Information Theoretic Dimension Reduction

Hyperspectral images (HSIs) are one of the most successfully used tools for precisely and potentially detecting key ground surfaces, vegetation, and minerals. HSIs contain a large amount of information about the ground scene; therefore, object classification becomes the most difficult task for such a high-dimensional HSI data cube. Additionally, the HSI’s spectral bands exhibit a high correlation, and a large amount of spectral data creates high dimensionality issues as well. Dimensionality reduction is, therefore, a crucial step in the HSI classification pipeline. In order to identify a pertinent subset of features for effective HSI classification, this study proposes a dimension reduction method that combines feature extraction and feature selection. In particular, we exploited the widely used denoising method minimum noise fraction (MNF) for feature extraction and an information theoretic-based strategy, cross-cumulative residual entropy (CCRE), for feature selection. Using the normalized CCRE, minimum redundancy maximum relevance (mRMR)-driven feature selection criteria were used to enhance the quality of the selected feature. To assess the effectiveness of the extracted features’ subsets, the kernel support vector machine (KSVM) classifier was applied to three publicly available HSIs. The experimental findings manifest a discernible improvement in classification accuracy and the qualities of the selected features. Specifically, the proposed method outperforms the traditional methods investigated, with overall classification accuracies on Indian Pines, Washington DC Mall, and Pavia University HSIs of 97.44%, 99.71%, and 98.35%, respectively.

Spectral segmentation based dimension reduction for hyperspectral image classification

ABSTRACT Hyperspectral images (HSI) contain a wide range of information, the most prominent technology for observing the earth. However, using an original HSI high-dimensional datacube, the classification task faces significant challenges since it has a high computational cost. As a result, dimensionality reduction is indispensable. A dimension reduction method has been introduced in this paper, including feature extraction and feature selection to obtain feature subsets. Minimum Noise Fraction (MNF) is a popular feature extraction method for HSI, requiring a high computational capability. We propose a segmented MNF that divides the complete HSI into groups utilising normalised cross-cumulative residual entropy (nCCRE). An nCCRE-based feature selection is also employed to improve the quality of the chosen features using the max-relevancy min-redundancy measure. The support vector machine (SVM) classifier is used on two real HSI to evaluate the efficiency of the extracted subsets.

Effective subspace detection based on the measurement of both the spectral and spatial information for hyperspectral image classification

ABSTRACT Subspace detection from high dimensional hyperspectral image (HSI) data cube has become an important area of research for efficient identification of ground objects. Standard feature extraction method such as Principal Component Analysis (PCA) has some drawbacks as it depends solely on global variance of the dataset generated. Folded-PCA (FPCA), an improvement of PCA, offers more benefits over PCA as it envisages both local and global structures of image contents and requires less computation and memory. These superior properties make FPCA more effective for feature extraction in high dimensional remote sensing images e.g. HSIs. Therefore, the proposed feature reduction method combines FPCA feature extraction with Normalized Cross Cumulative Residual Entropy (NCCRE) feature selection, termed as FPCA-NCCRE, for efficient features’ subspace detection. NCCRE is utilised as a means of feature selection over the new features generated from FPCA to obtain a more informative subspace. It is experimented on a real mixed agricultural and an urban hyperspectral dataset. Finally, Kernel Support Vector Machine (KSVM) is implemented to calculate the classification accuracy using the detected subspace. From the experiments, it is observed that the proposed method outperforms the baseline approaches and obtains the highest accuracy of 97.67 and 98.57% on the two real hyperspectral images.

Cross‐cumulative residual entropy‐based medical image registration via hybrid differential search algorithm

AbstractImage registration is the process of overlaying images of the same scene taken at different times by different sensors from different viewpoints. The cross‐cumulative residual entropy (CCRE)‐based medical image registration could achieve a high precision and a strong robustness performance. However, the optimization problem formulated by CCRE consists of some local extrema, especially for noise images. In order to address these difficulties, this article proposes a new optimization algorithm named hybrid differential search algorithm (HDSA) to optimize CCRE. As HDSA consists of simple control parameters, it is independent of the initial searching point. In addition, HDSA ameliorated the search method and the iterative conditions. As a result, the optimization process is more stable and efficient. Image registration experiments of HDSA are performed and compared with the conventional differential search algorithm (DSA) and adaptive differential evolution with optional external archive (JADE). The results show that HDSA does not only overcome the difficulties of sticking in the local extrema but also enhances the precision of registration. It is effective, robust, and fast for both the single‐mode rigid medical image registration and the multispectral‐mode rigid medical image registration.

Information theoretical measures from cumulative and survival densities in quantum systems

AbstractEntropic uncertainty and statistical correlation measures, based on survival and cumulative densities, are explored in some representative quantum systems. We illustrate how the cumulative residual entropy in the quantum well system recovers the correct classical behavior for larger quantum numbers while the Shannon entropy does not. Two interacting and noninteracting oscillators are used to examine two‐particle entropies and their related correlation measures. The joint cumulative residual entropy does distinguish between symmetric and antisymmetric wave functions in interacting systems as the interaction is turned on. The joint Shannon entropy does not distinguish between the symmetries even in the presence of interaction. Conversely, the joint Shannon entropy and joint cumulative residual entropy are both unable to distinguish between the symmetries for certain states of the noninteracting oscillators. As measures of statistical correlation, the mutual information and the cross cumulative residual entropy yield similar behaviors as a function of the strength of the interparticle interaction.

Robust Automatic Registration of Multimodal Satellite Images Using CCRE With Partial Volume Interpolation

One of the most important steps in data fusion is image registration. Automatic image-to-image registration for images captured by different sensors traditionally requires the use of information-theoretic similarity measures such as mutual information. Recently, a new similarity measure known as cross-cumulative residual entropy (CCRE) has been proposed for multimodal image registration in medical imaging applications. In this paper, we investigate the use of CCRE for multisensor registration of remote sensing imagery. In particular, we investigate the extreme case of registering synthetic aperture radar images to optical images. We also propose a novel extension to the Parzen-window optimization approach proposed by Thévenaz which involves applying partial volume interpolation in the calculation of the gradients of the similarity measure. Our experimental results show that our proposed approach which uses CCRE as the similarity measure and partial volume interpolation in the optimization procedure provides superior performance to other approaches investigated.

Registration for SAR and Optical Image via Cross Cumulative Residual Entropy and Ratio Operator

Optical and SAR images have different imaging modes and pixel expression formats, which caused much difficult for image registration. The paper proposes a registration algorithm combined Ratio gradient and Cross Cumulative Residual Entropy (CCRE) aimed at solving the problem of SAR image speckles. Compared with other traditional methods, the experiment results show that the CCRE combined with Ratio operator registration method performs satisfactorily in SAR and optical image registration and provides a significant improvement on the registration accuracy over the other algorithm

Registration for SAR and Optical Image via Cross Cumulative Residual Entropy and Ratio Operator

Optical and SAR images have different imaging modes and pixel expression formats, which caused much difficult for image registration. The paper proposes a registration algorithm combined Ratio gradient and Cross Cumulative Residual Entropy (CCRE) aimed at solving the problem of SAR image speckles. Compared with other traditional methods, the experiment results show that the CCRE combined with Ratio operator registration method performs satisfactorily in SAR and optical image registration and provides a significant improvement on the registration accuracy over the other algorithm

Non-Rigid Multi-Modal Image Registration Using Cross-Cumulative Residual Entropy.

In this paper we present a new approach for the non-rigid registration of multi-modality images. Our approach is based on an information theoretic measure called the cumulative residual entropy (CRE), which is a measure of entropy defined using cumulative distributions. Cross-CRE between two images to be registered is defined and maximized over the space of smooth and unknown non-rigid transformations. For efficient and robust computation of the non-rigid deformations, a tri-cubic B-spline based representation of the deformation function is used. The key strengths of combining CCRE with the tri-cubic B-spline representation in addressing the non-rigid registration problem are that, not only do we achieve the robustness due to the nature of the CCRE measure, we also achieve computational efficiency in estimating the non-rigid registration. The salient features of our algorithm are: (i) it accommodates images to be registered of varying contrast+brightness, (ii) faster convergence speed compared to other information theory-based measures used for non-rigid registration in literature, (iii) analytic computation of the gradient of CCRE with respect to the non-rigid registration parameters to achieve efficient and accurate registration, (iv) it is well suited for situations where the source and the target images have field of views with large non-overlapping regions. We demonstrate these strengths via experiments on synthesized and real image data.