Gravitation-Based Edge Detection in Hyperspectral Images

Genyun Sun, Aizhu Zhang, Jinchang Ren, Jingsheng Ma, Peng Wang, Yuanzhi Zhang, Xiuping Jia
2017 Remote Sensing  
Edge detection is one of the key issues in the field of computer vision and remote sensing image analysis. Although many different edge-detection methods have been proposed for gray-scale, color, and multispectral images, they still face difficulties when extracting edge features from hyperspectral images (HSIs) that contain a large number of bands with very narrow gap in the spectral domain. Inspired by the clustering characteristic of the gravitational theory, a novel edge-detection algorithm
more » ... detection algorithm for HSIs is presented in this paper. In the proposed method, we first construct a joint feature space by combining the spatial and spectral features. Each pixel of HSI is assumed to be a celestial object in the joint feature space, which exerts gravitational force to each of its neighboring pixel. Accordingly, each object travels in the joint feature space until it reaches a stable equilibrium. At the equilibrium, the image is smoothed and the edges are enhanced, where the edge pixels can be easily distinguished by calculating the gravitational potential energy. The proposed edge-detection method is tested on several benchmark HSIs and the obtained results were compared with those of four state-of-the-art approaches. The experimental results confirm the efficacy of the proposed method. Remote Sens. 2017, 9, 592 2 of 23 the imaged scenes are complex scenes and may not have clear boundaries, image segmentation is always a big challenging task. Effective edge detection algorithms have been found useful for image segmentation since they delineate boundaries of regions and determine segmentation results [2, 3] . Especially for the advanced HSIs with high spatial resolution, the clearly depicted edges could be of great benefit in characterizing the spatial structures of landscapes [4] . Over the past few decades, a large number of edge-detection techniques have been proposed, such as Canny [5] , Marr [6], SUSAN (Univalue Segment Assimilating Nucleus) [7] and active contour based methods [8] . However, these approaches are designed primarily for gray, color or multispectral images and few studies have paid attention to edge detection on HSIs [9, 10] . In previous studies [10, 11] , edge-detection tasks are completed by adapting color or multispectral approaches to hyperspectral images (HSIs). Accordingly, existing approaches for color or multispectral based edge detection are discussed as follows. In general, most approaches for color or multispectral based edge detection can be grouped into three categories: (1) monochromatic approaches; (2) vector based approaches; and (3) feature-space based approaches. Monochromatic approaches combine all edge maps after applying well-established gray-scale edge detectors on each band, and typical rules for combining edges include the maximum rule [12] , the summation rule [13] and the logic OR operation [14] . Although the fine spectral resolution of HSI provides invaluable and abundant information regarding the physical nature of different materials [10], edge features may be only observable over a small subset of bands in the HSI [15] . That is to say, different spectral bands may even contain inconsistent edges, which can easily leads to false edges by simple combination. To overcome this drawback caused by the combination rules, Lei and Fan combined the first principal component and hue component of color images to obtain complete object edges [16] . Different from monochromatic approaches, vector-based approaches consider each pixel as a spectral vector and then use vector operations to detect edges [17] [18] [19] [20] [21] [22] [23] [24] . In these approaches, the gradient magnitude and direction are defined in a vector field by extending the gray-scale edge definition [11] . Di Zenzo's gradient operator [17] , which uses the tensor gradient to define the edge magnitude and direction, is a widely used vector-based method. However, Di Zeno's method is sensitive to small changes in intensity because it is based on the measure of the squared local contrast variation of multispectral images. To overcome this problem, in Drewniok [19], Di Zeno's method is combined with the Canny edge detector with a Gaussian pre-filter model applied to each band for smoothing the image. Drewniok's method has better effectiveness, but it results in a localization error when the Gaussian scale parameter is large [25] . To remove both the effect of noise and the localization error caused by pre-filtering, a novel method based on robust color morphological gradient (RCMG) is proposed, where the edge strength of a pixel is defined as the maximum distance between any two pixels in its surrounding window [24] . The RCMG is robust to noise and helps top reserve accurate spatial structures due to a non-linear scheme is implied in the process [10] . Generally speaking, vector based approaches are superior to monochromatic approaches in multispectral edge detection since they take the spectral correlation of the bands into consideration. Different from color images or multispectral images, however, HSIs usually consist of hundreds of contiguous spectral bands. Although the high spectral resolution of HSIs provides potential for more accurate identification of targets, it still suffers from three problems in edge detection, various interferences that lead to low homogeneity inside regions [26] , spectral mixtures or edges that appear in a small subset of bands often cause weak edges [26] and inconsistent edges from narrow and abundant channels [27] , which have made edge detection more challenging in HSIs. Dimension reduction has been investigated using signal subspace approach and proposed the local rank based edge detection method [28] , however the performance is limited. It is necessary to consider the spatial relationships between spectral vectors [29] . In Reference [30], a modified Simultaneous Spectral/Spatial Detection of Edges (SSSDE) [31] for HSIs was proposed to exploit spectral information and identify boundaries (edges) between different materials. This is a kind of constructive attempt to joint utilization of Remote Sens. 2017, 9, 592 3 of 23 spatial and spectral information. Recently, many researchers have tried to develop feature-based new edge-detection methods because edge pixels have saliency in the feature space [32] . In Lin [32], color image edge detection is proposed based on a subspace classification in which multivariate features are utilized to determine edge pixels. In Dinh [27] , MSI edge detection is achieved via clustering the gradient feature. The feature space is suitable to analyze HSIs because it is capable of showing data from various land cover types in groups [33] . In particular, a spatial-spectral joined feature space, which takes into consideration both the spatial and spectral correlation between pixels, has attracted increasing attention [1, 29] . In addition to edge detection, feature space has also been widely used in other fields of image processing, such as hyperspectral feature selection [34, 35] , target detection [36] , and image segmentation [37, 38] . However, few studies focus on edge detection for HSIs using feature space. Physical models that mimic real-world systems can be used to analyze complex scientific and engineering problems [37, 39, 40] . The ongoing research of physical models has motivated the exploration of new ways to handle image-processing tasks. As a typical physical model, Newton's law of universal gravitation [41] has received considerable attention, based on which, a series of image-processing algorithms has been proposed, such as the stochastic gravitational approach to feature-based color image segmentation (SGISA) [37], the improved gravitational search algorithm for image multi-level image thresholding [42] and the gravitational collapse (CTCGC) approach for color texture classification [43] . Other gravitation model based approaches for classification include data gravitation classification (DGC) [44] [45] [46] and gravitational self-organizing maps (GSOM) [47] . The advantages of the gravity field model have inspired the development of new edge-detection method for gray-scale images [48, 49] . Although the image-processing procedure using gravitational theory is relatively easy for understanding, this theory is rarely used in edge detection for HSIs. As the gravitational theory describes the movements of objects in the three-dimensional feature space of the real world, we can easily extend it to n-dimensional feature space and apply it for edge detection in HSIs. In this paper, a novel edge-detection method for HSIs based on gravitation (GEDHSI) is proposed. The main ideas of the proposed GEDHSI are as follows: (1) there exists a type of "force", called gravitation, between any two pixels in the feature space; (2) computational gravitation obeys the law of gravitation in the physical world; (3) all pixels move in the feature space according to the law of motion until the stopping criteria are satisfied, and then the image system reaches a stable equilibrium; and (4) the edge pixels and non-edge pixels are classified into two different clusters. Therefore, in the equilibrium system, edge responses can be obtained by computing the gravitational potential energy due to the relative positions. Different from our previous approach for gravitation based edge detection in gray-scale images [49], the proposed method features a dynamic scheme. By imitating the gravitational theory, all pixels move in the joint spatial-spectral feature space, which makes the GEDHSI more attractive and effective for HSIs. The experiment results illustrate both the efficiency and efficacy of the proposed method for HSI edge-detection problems. The rest of the paper is organized as follows: The law of universal gravity is briefly reviewed in Section 2. The proposed gravitation-based edge detection method is presented in Section 3. The experimental validations of the proposed algorithm using both artificial and real HSIs are given in Section 4. Finally, the paper is concluded in Section 5. Background of the Universal Law of Gravitation According to gravitational theory [35], any two objects exert gravitational force onto each other. The forces between them are equal to each other but reverse in direction. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them, as shown in Equation (1) : Remote Sens. 2017, 9, 592 4 of 23 →
doi:10.3390/rs9060592 fatcat:67fqcfnuhbfn7pniekkm256ewi