# Superpixel Segmentation of Hyperspectral Images Based on Entropy and Mutual Information
## 1 Introduction  
Hyperspectral images (HSIs) contain full spectral and spatial information, and the formed three-dimensional data block can effectively reflect much ground object information that cannot be detected in wide-band multi-spectral images [1]. In recent years, the classification of hyperspectral images has received extensive attention in the field of remote sensing image processing. In addition, hyperspectral images have the characteristics of high dimension and high information redundancy. Therefore, dimensionality reduction and image preprocessing (such as image segmentation) are important. At present, there are mainly two types of dimension reduction methods for hyperspectral images, i.e., feature extraction and band selection. Band selection is based on information measures and has been intensively studied. In the band selection method, Shannon entropy or its variations are typically used to evaluate image information. [PERSON] proposed a supervised band-selection algorithm, in which only the known class signatures were used while neither the original band nor a training sample was required [2]. Based on mutual information, [PERSON] et al. used a clustering method to select band and achieve dimensionality reduction [3]. Based on spatial entropy, [PERSON] et al. proposed a hyperspectral band selection algorithm for supervised classification [4]. On the other hand, many methods perform feature extraction on hyperspectral images to achieve dimensionality reduction. For example, [PERSON] and [PERSON] proposed a selection method using principal component analysis (PCA) [5]. [PERSON] et al. proposed a non-linear extraction method based on manifold learning [6]. The dimensionality of data can be reduced by finding the corresponding coordinates on low-dimensional manifold for the points in high-dimensional space. [PERSON] et al. proposed a dimensionality reduction method for hyperspectral images based on sparse representation [7]. [PERSON] et al. proposed a band transformation method that extends the color matching functions (CMF) to the entire image spectra, which provided a foundation for subsequent band selection [8]. In addition to the dimensionality reduction, hyperspectral image segmentation can also reduce the processing complexity of subsequent images. [PERSON] et al. proposed an HSIs segmentation algorithm based on statistical approach [9]. The proposed algorithm was completely unsupervised and only relied on the spectral information. [PERSON] et al. proposed a hyperspectral image segmentation method using a new spectral unmixing-based binary partition tree representation [10]. [PERSON] et al. proposed an intelligent image analysis framework for image enhancement, automatic global thresholding and segmentation [11]. However, the above traditional object-level segmentation algorithms have the common problem of under-segmentation, which has a significant impact on post-processing. In recent years, some researchers have proposed an over-segmentation scale called superpixel, which has adaptive sizes and shapes for different spatial structures. In the hyperspectral image classification process, segmentation using the superpixel method can effectively reduce the impact of the segmentation scale on the classification results [12]. Therefore, superpixel segmentation (SS) has become an important preprocessing method for HSIs. The concept of superpixel was firstly proposed by [PERSON] et al. [13]. In recent years, new superpixel segmentation algorithms have been continuously proposed. [PERSON] proposed an entropy rate-based objective function for superpixel segmentation. However, the proposed method was very computationally intensive and time consuming [14]. [PERSON] et al. proposed a superpixel segmentation algorithm via energy-driven sampling. However, the disadvantage of this method was that it cannot solve the problem of sudden colohr changes [15]. [PERSON] et al.