融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测

融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测 Hyperspectral Anomaly Detection via Combining Adaptive Window Saliency Detection and Improved Superpixel Segmentation 1 first-author 钱晓亮，研究方向为模式识别与人工智能/遥感图像场景分类与目标检测。E-mail：qxl_sunshine@163.com 钱晓亮，研究方向为模式识别与人工智能/遥感图像场景分类与目标检测。E-mail：qxl_sunshine@163.com qxl_sunshine@163.com 1 2 corresp 林生，研究方向为高光谱图像异常检测/遥感图像目标检测。E-mail：ls1425854658@163.com 林生，研究方向为高光谱图像异常检测/遥感图像目标检测。E-mail：ls1425854658@163.com ls1425854658@163.com 3 1 1 郑州轻工业大学 电气信息工程学院, 郑州450002 郑州轻工业大学 电气信息工程学院, 郑州450002 College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China 西安电子科技大学 空间科学与技术学院, 西安710126 西安电子科技大学 空间科学与技术学院, 西安710126 School of Aerospace Science and Technology, Xidian University, Xi'an 710126, China School of Aerospace Science and Technology, Xidian University, Xi'an 710126, China 河南工业大学 信息科学与工程学院, 郑州450001 河南工业大学 信息科学与工程学院, 郑州450001 College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou 450002, China School of Aerospace Science and Technology, Xidian University, Xi'an 710126, China School of Aerospace Science and Technology, Xidian University, Xi'an 710126, China College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China College of Information Science and Engineering, Henan University of Technology, Zhengzhou 450001, China 高光谱异常检测旨在识别与周围像素具有显著光谱差异的像素，由于不需要先验光谱信息的特点，其在军事和民用领域发挥重要价值。实现高光谱异常检测的一个重要手段是局部对比度计算，现有方法通常采用双窗口法进行计算，然而，窗口尺寸通常依据经验值进行手工设定，泛化能力不足。为了解决上述问题，本文提出了一种融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测方法。该方法先利用对抗自编码网络对高光谱图像进行降维，以降低模型计算复杂度。其次，引入正交投影散度来改进超像素分割中的光谱距离度量方式，提升分割精度。然后，提出一种自适应窗口显著性检测算法来初步定位异常目标，该算法依据超像素分割结果来自适应确定双窗口，提高显著性检测的精度和泛化能力。最后，采用域变换递归滤波和阈值化操作对初始检测结果进行后处理，降低虚警率。消融实验表明，本文所提基于正交投影散度的改进超像素分割算法较基于传统光谱距离度量方式的算法性能更优，所提自适应窗口显著性检测算法的性能优于传统手工设定窗口尺寸的算法；与7种流行算法的主、客观对比实验表明，本文方法在总检测精度和异常-背景像素分离度上均优于流行算法。综上所述，本文所提改进超像素分割算法能提升现有高光谱图像超像素分割的效果，以此为基础所设计的自适应窗口显著性检测算法不仅能克服现有双窗口算法泛化能力不足的问题，还能获得优于流行算法的异常检测效果。 Objective Hyperspectral anomaly detection is used to identify the pixels which have significant spectral contrast with their surrounding pixels, and plays a valuable role in military and civilian fields due to the characteristic that the priori spectral information is not required. The existing local contrast based methods usually adopt dual rectangular windows scheme for hyperspectral anomaly detection, however, they empirically set the size of dual window, which limits their generalization capability. Method To address above issue, a hyperspectral anomaly detection method via combining adaptive window saliency detection and improved superpixel segmentation is proposed in this paper. To reduce the computation complexity of the proposed method, an adversarial autoencoder is firstly introduced to reduce the dimension of the hyperspectral image. Secondly, the compressed hyperspectral image is segmented by improved superpixel segmentation. The existing spectral distance measurements used in the superpixel segmentation is effective under the condition that the relationship between the spectral value and the intensity of each pixel is linear, however, the condition cannot be guaranteed in practical applications. To solve this problem, the improved superpixel segmentation adopts the orthogonal projection divergence to measure the spectral distance. Afterwards, an adaptive window based saliency detection algorithm is proposed and used to obtain the initial detection results. Specifically, the size of the inner window is adaptively determined by the superpixels, which ensures that the pixels belonging to the same inner window are homogeneous, and the outer window can be obtained by enlarging the inner window with fixed size. Finally, to reduce the false alarm rate, the domain transform recursive filter and thresholding operation are employed to optimize the initial detection results. Result The comparisons between the orthogonal projection divergence and three common spectral distance measurements (euclidean distance, spectral angular mapping and spectral information divergence) in terms of AUC show that the orthogonal projection divergence based method gets the highest score on 5 datasets. The comparisons between the adaptive window and traditional manual setting dual window in terms of AUC show that the adaptive window based method gets the highest score on 5 datasets. To validate the overall performance of the proposed method, the comprehensive comparisons between proposed method and 7 state-of-the-art methods on 5 public datasets are implemented. To be specific, the subjective comparisons show that the anomalous pixels detected by proposed method are more precise and have stronger contrast with background regions, the objective comparisons demonstrate that the overall detection accuracy of proposed method is highest and separability between the anomalous pixels and background pixels of proposed method is best. Conclusion In summary, three conclusions can be derived from this paper. First of all, the improved superpixel segmentation algorithm can improve the segmentation results and the proposed adaptive window scheme can improve the performance of saliency detection. Secondly, the proposed method has excellent detection accuracy, false alarm rate and separability between the anomalous pixels and background pixels. Finally, the overall performance of the proposed method is superior to state-of-the-art methods. 异常检测 高光谱图像 正交投影散度 超像素分割 自适应窗口 显著性检测 anomaly detection hyperspectral image orthogonal projection divergence superpixel segmentation adaptive window saliency detection 1　引 言 1 高光谱图像是将光谱与成像技术相结合形成的三维立体图，它具有宽的光谱波段，高的光以及谱分辨率和低的空间分辨率（ Bioucas-Dias等， 2013 Bioucas-Dias等， 2013 ； Liu等， 2020 Liu等， 2020 ； Qian等， 2020 Qian等， 2020 ）。在光谱维上，高光谱图像具有数百个连续的光谱波段，其中包含了大量有价值的光谱信息，因此，可以利用其光谱特性对特定目标进行辨别和定位。而高光谱异常检测作为高光谱图像领域的研究热点之一，其目的是挖掘出与背景区域具有明显光谱差异的目标区域，该任务因不需要提供目标光谱的任何先验信息就能有效地标记出目标这一特点，在病虫害检测（ Vanegas等， 2018 Vanegas等， 2018 ）、战场搜救（ Stein等， 2002 Stein等， 2002 ）、地物勘探（ Peyghambari和Zhang， 2021 Peyghambari和Zhang， 2021 ）、场景分类（ 钱晓亮等， 2018 钱晓亮等， 2018 ）等领域得到广泛应用。 在高光谱图像中，异常目标区域与背景区域之间具有较大对比度，即显著性较强，根据对比度计算方式的不同，现有高光谱异常检测方法可大致分为两大类：基于全局的方法和基于局部的方法。在基于全局的方法中，高光谱图像是作为整体进行数据处理，该方法根据高光谱图像的所有数据计算背景统计量，实现对异常像素的检测。其中，最经典的全局方法是由Reed等人于1990年提出的Reed-Xiaoli （RX）算法（ Reed和Yu， 1990 Reed和Yu， 1990 ），该方法假设高光谱图像背景特征服从多元高斯分布，它首先根据整幅图像计算背景特征的均值向量和协方差矩阵，然后利用马氏距离度量待测像素与参考背景统计特性的偏离程度，并以此作为判别异常的标准。然而，由于真实高光谱图像的复杂性，基于全局的高斯分布往往难以拟合真实的背景分布，并且在计算背景的均值向量和协方差矩阵时，易受到异常像素的干扰，因此，其他研究学者提出了多种基于RX的改进算法，如高斯混合模型方法（ Stein等， 2002 Stein等， 2002 ）利用局部高斯分布、高斯混合和线性混合三种模型构建多元高斯分布的混合，对背景统计信息进行建模，并依据多个决策统计分布检测异常目标区域，从而提高检测性能。在文献（ Guo等， 2014 Guo等， 2014 ）中，提出了Weighted-RX方法用于高光谱异常检测，该方法在RX方法基础上对背景进行建模，并对不同背景赋予不同权重，以减少RX方法中异常像素和噪声对背景信息估计的干扰。Kernel-RX （KRX）算法（ Kwon和Nasrabadi， 2005 Kwon和Nasrabadi， 2005 ）是将原始光谱空间扩展到更高维的特征空间，并在高维特征空间中进行全局背景估计。其它基于RX的全局方法还有Subspace RX （SSRX）算法（ Schaum， 2004 Schaum， 2004 ）和线性RX（ Williams等， 2013 Williams等， 2013 ）等。此外，其他非RX的全局方法也获得了迅速发展。为了分离异常和背景像素，Kang等人提出了一种基于属性和边缘保持滤波的异常检测方法（ Kang等， 2017 Kang等， 2017 ），该方法先利用属性滤波和布尔映射的融合方法对具有特定区域特性和明显光谱差异的像素进行检测，得到初始检测结果；然后充分利用相邻像素之间的空间相关性，采用边缘保持滤波对初始检测结果进行优化。文献（ Du和Zhang， 2010 Du和Zhang， 2010 ）提出了一种基于随机选择的异常检测方法，该方法在高光谱图像上随机选择背景像素并计算其统计信息，然后采用随机选择和融合的方法以避免背景统计数据受到污染，从而实现异常检测任务。Li等人（ Li等， 2015 Li等， 2015 ）提出了基于背景联合稀疏表示（BJSR）的异常检测算法，该方法先利用BJSR算法来估计自适应正交背景互补子空间，以自适应地选择最具代表性的背景基；然后，提出了一种无监督自适应子空间模型来抑制背景，同时突出异常分量。由于高光谱图像中背景是低秩的，异常目标是稀疏的，由此Chen等人（ Chen和Yang， 2013 Chen和Yang， 2013 ）提出了基于低秩表示（LRR）的异常检测方法，该方法本质是通过低秩表示对背景进行建模，并利用表示残差确定异常目标。Xu等人（ Xu等， 2015 Xu等， 2015 ）提出了低秩稀疏表示（LRASR）模型来分离背景和异常。Niu等人（ Niu和Wang， 2016 Niu和Wang， 2016 ）通过学习词典改进了LRASR方法，并将张量分解应用于异常检测。 在地物场景比较复杂的高光谱图像中，异常目标通常只在局部范围内与背景之间具有较强对比度，根据全局方法计算对比度通常不准确，由此，研究者们对基于局部的异常检测方法展开研究，该方法通常采用双窗口法来计算待测像素与其局部邻域之间的对比度。Molero等人提出了Local-RX（LRX）检测方法（ Molero等， 2013 Molero等， 2013 ），该方法对高光谱图像中每个像素周围的单个局部窗口应用RX，并通过内外窗口间的像素来估计背景统计信息，实现高光谱异常检测。Li等人（ Li和Du， 2014 Li和Du， 2014 ）提出了基于协同表示（CRD）的异常检测方法，该方法假设背景像素可以被其邻域内像素线性表示，而异常像素不能被其线性表示，通过对待测像素构建内外窗口，实现对测试像素的线性表示，并利用表示误差判别异常。在基于稀疏表示的异常检测方法（ Paris等， 2013 Paris等， 2013 ； Bacher等， 2017 Bacher等， 2017 ； Chen等， 2011 Chen等， 2011 ）中，假设背景字典由窗口外区域的像素组成，这可以很好地用字典表示背景，并对所表示的系数有不同的约束条件；相反，异常则无法很好地用背景字典表示。局部求和异常检测方法（ Du等， 2016 Du等， 2016 ）将待测像素周围相邻局部窗口的多个局部分布与空间-光谱特征相结合，充分考虑了待测像素周围邻域背景分布与局部空间邻域之间的关系，通过综合局部背景统计，实现异常目标检测。 尽管现有基于双窗口的局部对比度计算方法在高光谱异常检测中取得了较好的效果，但是，该类方法通常依据经验值来手工设定双窗口的尺寸，考虑到实际应用中异常目标的尺寸多样性，手工设定窗口尺寸的处理方式会显著降低此类方法的泛化能力。针对上述问题，本文提出了一种融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测方法 （Hyperspectral Anomaly Detection via Combining Adaptive Window Saliency Detection and Improved Superpixel Segmentation， ISPS-AWSD）。如 图1 图1 所示，本文先利用对抗自编码网络对高光谱图像进行降维，以降低算法计算的复杂度。其次，提出一种改进的超像素分割算法对降维后的高光谱图像进行分割，该算法引入正交投影散度（ Tu等， 2019 Tu等， 2019 ）对超像素分割过程中光谱距离的度量方式进行改进。然后，提出了一种自适应窗口显著性检测算法来初步定位异常目标区域，该算法依据超像素分割结果来自适应确定双窗口，即：以每个超像素块作为内窗，将超像素块的外接四边形扩大后作为对应的外窗，该设定方式能确保内窗中所有像素具有同质性，这与异常目标区域内所有像素具有同质性相一致，从而对异常目标的尺度变化进行自动匹配。最后，采用域变换递归滤波和阈值化处理对初始检测结果进行后处理，以获得具有较低虚警率的检测结果。 本文的主要贡献如下： （1）提出了一种基于正交投影散度的高光谱图像超像素分割改进算法。在对高光谱图像进行超像素分割过程中涉及到光谱距离度量，而常见的欧式距离、光谱角距离以及光谱信息散度等度量方式受光照条件影响，因此，本文引入正交投影散度来改进超像素分割中光谱距离度量方式，提升高光谱图像的分割精度，为后续自适应窗口显著性检测提供依据。 （2）提出了一种自适应窗口显著性检测算法。现有的基于双窗口的显著性检测方法通常依据经验值来手工设定双窗口的尺寸，在实际应用中难以适应异常目标的尺度变化，因此，本文提出依据超像素分割结果来自适应地确定双窗口，确保内窗中所有像素具有同质性，从而对异常目标的尺度变化进行自动匹配，提升高光谱异常检测方法的精度和泛化能力。 2　融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测方法（ISPS-AWSD） 1 本文所提ISPS-AWSD方法总框图如 图1 图1 所示，该方法主要包含四个部分，按照计算流程依次是：基于对抗自编码网络的高光谱图像降维、基于正交投影散度的超像素分割、自适应窗口显著性检测以及后处理。各部分的具体细节如下。 2.1　基于对抗自编码网络的高光谱图像降维 2 由于高光谱图像具有上百个光谱波段，有的波段包含很多噪声或其他冗余信息，不利于异常检测任务，且逐像素逐波段计算的复杂度太高。 由此，对高光谱图像进行降维处理十分重要。本文采用对抗自编码网络（ Jiang等， 2020 Jiang等， 2020 ）实现高光谱图像降维，该网络在自编码器（ Larochelle等， 2007 Larochelle等， 2007 ）的基础上，通过引入对抗思想，使重构图像更加逼近原始输入图像，从而倒逼自编码网络的隐式特征尽可能多的包含原始高光谱图像信息。 图1 图1 所示对抗自编码网络中的隐式特征 z i 即为降维后的数据。具体细节如下。 整个对抗自编码网络包含两个子网络：自编码器和判别器。其中自编码器由编码器和解码器共同构成，分别用于高光谱图像的隐式特征提取和重构，其数学表达式如下： <math display="block" id="M1"><msub><mrow><mi mathvariant="bold-italic">z</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>E</mi><mi>n</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi 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mathvariant="normal">2</mn></mrow></msub></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906116&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906114&type= 57.65800095 5.24933338 <math display="block" id="M2"><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>D</mi><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="bold-italic">W</mi></mrow><mrow><mi mathvariant="bold">D</mi><mi mathvariant="bold">e</mi></mrow></msub><msub><mrow><mi mathvariant="bold-italic">z</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>+</mo><msub><mrow><mi mathvariant="bold-italic">b</mi></mrow><mrow><mi mathvariant="bold">D</mi><mi mathvariant="bold">e</mi></mrow></msub><mo stretchy="false">)</mo><mo>,</mo><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>∈</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906119&type= 43.34933472 5.16466665 其中， <math id="M3"><msub><mrow><mi>f</mi></mrow><mrow><mi>E</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906126&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906125&type= 6.77333355 4.74133301 和 <math id="M4"><msub><mrow><mi>f</mi></mrow><mrow><mi>D</mi><mi>e</mi></mrow></msub><mo stretchy="false">(</mo><mo>⋅</mo><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906130&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906128&type= 6.68866634 4.74133301 分别表示编码器和解码器的映射函数， <math id="M5"><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906395&type= 2.53999996 3.72533321 表示输入高光谱图像中第 i 个像素的光谱向量， N 表示像素总个数， N 1 表示光谱向量的维数， N 2 表示隐式特征的维数， <math id="M6"><msub><mrow><mi mathvariant="bold-italic">W</mi></mrow><mrow><mi mathvariant="bold">E</mi><mi mathvariant="bold">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906139&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906137&type= 5.58799982 3.72533321 和 <math id="M7"><msub><mrow><mi mathvariant="bold-italic">b</mi></mrow><mrow><mi mathvariant="bold">E</mi><mi mathvariant="bold">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906144&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906142&type= 4.23333359 3.72533321 分别表示编码层的权重和偏置， <math id="M8"><msub><mrow><mi mathvariant="bold-italic">W</mi></mrow><mrow><mi mathvariant="bold">D</mi><mi mathvariant="bold">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906148&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906146&type= 5.58799982 3.72533321 和 <math id="M9"><msub><mrow><mi mathvariant="bold-italic">b</mi></mrow><mrow><mi mathvariant="bold">D</mi><mi mathvariant="bold">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906153&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906151&type= 4.23333359 3.72533321 分别表示解码层的权重和偏置， <math id="M10"><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906176&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906174&type= 2.53999996 3.89466691 表示由 z i 重构的光谱向量。 自编码器的重构损失函数 <math id="M11"><msub><mrow><mi>L</mi></mrow><mrow><mi>r</mi><mi>e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906162&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906159&type= 3.47133350 3.72533321 表达式为： <math display="block" id="M12"><msub><mrow><mi>L</mi></mrow><mrow><mi>r</mi><mi>e</mi></mrow></msub><mo>=</mo><msub><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>-</mo><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow></mfenced></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906164&type= 22.69066620 6.18066692 在对抗学习阶段，自编码器作为生成器 G ，与判别器 D 共同构成生成式对抗网络，判别器的两个输入分别为原始光谱向量 <math id="M13"><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906395&type= 2.53999996 3.72533321 和重构光谱向量 <math id="M14"><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906176&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906174&type= 2.53999996 3.89466691 。生成器生成的重构光谱向量试图愚弄判别器，而判别器则努力将 <math id="M15"><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906176&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906174&type= 2.53999996 3.89466691 判别为假，两者互相博弈，其对抗损失函数 <math id="M16"><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi><mi>A</mi><mi>N</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906181&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906178&type= 5.67266655 3.72533321 表达式如下： <math display="block" id="M17"><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi><mi>A</mi><mi>N</mi></mrow></msub><mo>=</mo><munder><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mrow><mi>G</mi></mrow></munder><munder><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi>D</mi></mrow></munder><mi mathvariant="double-struck">E</mi><mtext> </mtext><mo stretchy="false">[</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mi>D</mi><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>+</mo><mi mathvariant="double-struck">E</mi><mtext> </mtext><mo stretchy="false">[</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">g</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>D</mi><mo stretchy="false">(</mo><msub><mrow><mover accent="true"><mi mathvariant="bold-italic">x</mi><mo>̂</mo></mover></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906184&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906182&type= 76.70800018 4.82600021 其中， <math id="M18"><mi mathvariant="double-struck">E</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906189&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906186&type= 2.53999996 2.53999996 表示数学期望。 对抗自编码网络的总损失函数 L 为： <math display="block" id="M19"><mi>L</mi><mo>=</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>r</mi><mi>e</mi></mrow></msub><mo>+</mo><mi>α</mi><mo>⋅</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>G</mi><mi>A</mi><mi>N</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906193&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906191&type= 25.65399933 3.72533321 其中， <math id="M20"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906197&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906195&type= 2.20133328 2.62466669 表示重构损失和生成对抗损失的权衡参数。对抗自编码网络的自监督训练完成后，将高光谱图像各像素的光谱向量依次输入自编码器中，获取隐式特征 z i ，并将所有隐式特征合并，得到降维后的高光谱图像Z，作为后续超像素分割操作的输入。 2.2　基于正交投影散度的超像素分割 2 为了充分利用高光谱图像中的光谱信息，尽可能地将异常像素聚合，本文对降维后的高光谱图像XZ进行超像素分割。在现有的超像素分割算法中，简单线性迭代聚类（Simple Linear Iterative Clustering， SLIC）（ Achanta等， 2012 Achanta等， 2012 ）具有速度快、分割效率高且边界保持性好的特点，是目前最常用的超像素分割方法。在高光谱图像SLIC超像素分割过程中涉及光谱距离的度量，现有的度量方式主要采用欧式距离、光谱角距离或光谱信息散度等，然而这些方式需要假设像素的光谱值与光照条件之间是线性关系，但在实际情况中，这种线性关系往往并不成立，光谱值会受多种环境因素影响（ Su等， 2012 Su等， 2012 ）。 针对上述问题，本文提出了一种基于正交投影散度的高光谱图像超像素分割改进算法，该算法采用正交投影散度来度量光谱距离，这种度量方式不需要以像素光谱值与光照条件之间存在线性关系为前提。改进后的高光谱图像超像素分割算法具体流程如下： 第一步，设定超像素块个数 K ，并根据设定的超像素块个数初始化聚类中心。 第二步，计算 <math id="M21"><mn mathvariant="normal">2</mn><mi>S</mi><mo>×</mo><mn mathvariant="normal">2</mn><mi>S</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906202&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906200&type= 11.93799973 2.70933342 （ <math id="M22"><mi>S</mi><mo>=</mo><mroot><mrow><mi>N</mi><mo>/</mo><mi>K</mi></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906206&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906204&type= 15.49400043 4.31799984 ，其中 N 为像素总数）邻域内所有像素与该邻域内所有聚类中心之间的距离，该距离包括空间距离和光谱距离，其表达式如下： <math display="block" id="M23"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mroot><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906210&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906208&type= 58.41999817 5.67266655 <math display="block" id="M24"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">[</mo><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>T</mi></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup></mrow><mrow><mo>⊥</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo>+</mo><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mi>T</mi></mrow></msup><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup></mrow><mrow><mo>⊥</mo></mrow></msubsup><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><msup><mrow><mo stretchy="false">]</mo></mrow><mrow><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">2</mn></mrow></msup></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⊥</mo></mrow></msubsup><mo>=</mo><mi mathvariant="bold-italic">I</mi><mo>-</mo><mi mathvariant="bold-italic">s</mi><mo stretchy="false">(</mo><msup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mi mathvariant="bold-italic">T</mi></mrow></msup><msup><mrow><mi mathvariant="bold-italic">s</mi><mo stretchy="false">)</mo></mrow><mrow><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msup><msup><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mi mathvariant="bold-italic">T</mi></mrow></msup><mo> </mo><mo> </mo><mo stretchy="false">(</mo><mi mathvariant="bold-italic">s</mi><mo>=</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906214&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906212&type= 64.60066223 11.26066685 <math display="block" id="M25"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>u</mi><mi>m</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mi>ω</mi><mo>×</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ω</mi><mo stretchy="false">)</mo><mo>×</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msubsup><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906218&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906216&type= 85.25933075 5.07999992 其中， <math id="M26"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906281&type= 3.04800010 4.82600021 和 <math id="M27"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906285&type= 3.04800010 4.82600021 分别表示降维后的高光谱图像 Z 中第 i 和第 j 个像素点， <math id="M28"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>a</mi><mi>l</mi></mrow></msub><mfenced separators="|"><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906229&type= 18.88066673 5.16466665 ， <math id="M29"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mfenced separators="|"><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906236&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906233&type= 19.55800056 5.16466665 和 <math id="M30"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>u</mi><mi>m</mi></mrow></msub><mfenced separators="|"><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906238&type= 16.84866714 5.16466665 分别代表 <math id="M31"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906281&type= 3.04800010 4.82600021 与 <math id="M32"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906285&type= 3.04800010 4.82600021 之间的空间距离，光谱距离以及空间-光谱总距离，（ <math id="M33"><msubsup><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi mathvariant="normal">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906252&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906250&type= 2.53999996 4.06400013 ， <math id="M34"><msubsup><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906256&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906254&type= 2.87866688 4.06400013 ）和（ <math id="M35"><msubsup><mrow><mi>r</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906260&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906258&type= 2.62466669 4.06400013 ， <math id="M36"><msubsup><mrow><mi>c</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906264&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906262&type= 2.87866688 4.06400013 ）分别表示 <math id="M37"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906281&type= 3.04800010 4.82600021 和 <math id="M38"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906285&type= 3.04800010 4.82600021 的空间坐标， <math id="M39"><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906274&type= 3.21733332 4.06400013 和 <math id="M40"><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906279&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906277&type= 3.21733332 4.06400013 分别表示 <math id="M41"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906283&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906281&type= 3.04800010 4.82600021 和 <math id="M42"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>j</mi></mrow><mrow><mi>Z</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906287&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906285&type= 3.04800010 4.82600021 的光谱向量， <math id="M43"><msubsup><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">s</mi></mrow><mrow><mo>⊥</mo></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906293&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906289&type= 4.14866638 4.06400013 表示 <math id="M44"><mi>s</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906296&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906295&type= 1.26999998 2.62466669 的正交子空间， <math id="M45"><mi mathvariant="bold-italic">I</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906301&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906298&type= 1.43933344 2.62466669 表示单位矩阵， <math id="M46"><mi>ω</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906305&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906303&type= 2.45533323 2.62466669 是用于平衡空间距离和光谱距离的权重参数。 第三步，将所有像素分配至距离其最近的聚类中心，然后计算每个聚类所有像素的均值，并以该聚类中距离均值最近的像素作为新的聚类中心，重复步骤二和三，直至聚类中心不再变化，最终得到超像素分割结果 <math id="M47"><mi>S</mi><mi>P</mi><mo>=</mo><mfenced open="{" close="}" separators="|"><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>,</mo><mo>⋯</mo><mo>,</mo><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906307&type= 39.45466614 5.16466665 。 图2 图2 给出了采用四种不同光谱距离度量方式的超像素分割图，与其他三种光谱距离度量方法相比，基于正交投影散度的超像素分割算法具有更好的分割效果，即：更有效度量异常目标与背景之间的差异，为后续自适应窗口显著性检测提供依据。 1,2;3,4; 2.3　自适应窗口显著性检测 2 ITTI等（ Itti等， 1998 Itti等， 1998 ）指出与局部邻域具有较强对比度的图像区域往往能吸引人眼注意，即：具有较强显著性，而在高光谱图像中，异常目标区域与其邻域通常也具有较强对比度，因此，本文提出通过显著性检测来检测异常目标区域。 受ITTI等（ Itti等， 1998 Itti等， 1998 ）启发，如 图3 图3 所示，本文采用双窗口法来计算高光谱图像的显著性，即：以内窗与其邻域（内外窗之间的区域）之间的对比度来定义显著性，但现有双窗口的设计方式存在缺陷，本文因此提出了一种自适应窗口显著性检测算法。具体细节如 图3 图3 所示。 1,2; 如 图3（a） 图3（a） 所示，传统待测像素的局部窗口通常由矩形内外窗构成，这种双窗口设计方式是以待测像素为中心，内窗尺寸 <math id="M48"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi><mi>n</mi><mi>n</mi><mi>e</mi><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906362&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906359&type= 6.43466663 3.72533321 和外窗尺寸 <math id="M49"><msub><mrow><mi>R</mi></mrow><mrow><mi>o</mi><mi>u</mi><mi>t</mi><mi>e</mi><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906366&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906364&type= 6.26533365 3.72533321 是依据经验值来手工设定，在实际应用中难以适应异常目标的尺度变化，因此，为了提高检测精度和泛化能力，本文提出了一种自适应窗口显著性检测算法。如 图3（b） 图3（b） 所示，对任意待测像素，将包含该像素的超像素块作为其内窗（绿色实线框），寻找该超像素块的外接四边形（绿色虚线框）并以特定尺寸进行放大，获取该像素的外窗（红色实线框），内外窗间距为 R 。显然，本文设计的内外窗是由超像素分割结果自适应确定，该设计思路能确保内窗中所有像素具有同质性，这与异常目标区域内所有像素具有同质性相一致，从而对异常目标的尺度变化进行自动匹配。 在内外窗确定后，高光谱图像的显著性计算（ Goferman等， 2012 Goferman等， 2012 ； Tan等， 2014 Tan等， 2014 ）如下： <math display="block" id="M50"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mfenced separators="|"><mrow><mfrac><mrow><mfenced open="<" close=">" separators="|"><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">h</mi></mrow><mrow><mi mathvariant="bold-italic">s</mi><msub><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">g</mi></mrow></msub></mrow></msubsup></mrow></mfenced></mrow><mrow><mfenced open="|" close="|" separators="|"><mrow><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow></mfenced><mo>⋅</mo><mfenced open="|" close="|" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">h</mi></mrow><mrow><mi mathvariant="bold-italic">s</mi><msub><mrow><mi mathvariant="bold-italic">p</mi></mrow><mrow><mi mathvariant="bold-italic">g</mi></mrow></msub></mrow></msubsup></mrow></mfenced></mrow></mfrac></mrow></mfenced><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>,</mo><mi>h</mi><mo>∈</mo><mo stretchy="false">[</mo><mn mathvariant="normal">1</mn><mo>,</mo><mi>H</mi><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906371&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906368&type= 80.09466553 12.78466606 <math display="block" id="M51"><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mroot><mrow><mo stretchy="false">(</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow/></mroot></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906376&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906374&type= 60.28266144 6.01133299 <math display="block" id="M52"><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">1</mn><mo>+</mo><mi>C</mi><mo>⋅</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906380&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906378&type= 56.30332947 9.82133293 <math display="block" id="M53"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>y</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msubsup><mo>∑</mo><mrow><mi>h</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi>H</mi></mrow></msubsup><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></mrow></mrow><mrow><mi>H</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906382&type= 48.00600052 8.72066593 其中， <math id="M54"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906456&type= 2.37066650 4.57200003 表示高光谱图像中第 i 个像素点（位于超像素块 sp g 内）， <math id="M55"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906452&type= 4.06400013 3.97933316 表示 sp g 对应邻域内第 h 个像素点， H 表示 sp g 对应邻域内像素点的数量， <math id="M56"><msub><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906396&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906395&type= 2.53999996 3.72533321 和 <math id="M57"><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi mathvariant="bold-italic">S</mi><msub><mrow><mi mathvariant="bold-italic">P</mi></mrow><mrow><mi mathvariant="bold-italic">g</mi></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906400&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906399&type= 4.99533367 3.89466691 分别表示 <math id="M58"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906456&type= 2.37066650 4.57200003 和 <math id="M59"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906452&type= 4.06400013 3.97933316 的光谱向量， <math id="M60"><mfenced open="<" close=">" separators="|"><mrow><mtext> </mtext><mo>⋅</mo><mtext> </mtext></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906410&type= 6.94266701 3.47133350 表示内积运算， <math id="M61"><mfenced open="|" close="|" separators="|"><mrow><mtext> </mtext><mo>⋅</mo><mtext> </mtext></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906417&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906415&type= 5.84200001 3.80999994 表示向量的模， <math id="M62"><mo stretchy="false">(</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>c</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906422&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906420&type= 8.97466660 4.57200003 和 <math id="M63"><mo stretchy="false">(</mo><msubsup><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo>,</mo><msubsup><mrow><mi>c</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906426&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906424&type= 12.36133385 3.89466691 分别表示 <math id="M64"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906456&type= 2.37066650 4.57200003 和 <math id="M65"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906452&type= 4.06400013 3.97933316 的空间坐标， C 为常量， <math id="M66"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>p</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mtext> </mtext><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906439&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906437&type= 20.99733353 5.07999992 ， <math id="M67"><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mtext> </mtext><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906444&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906441&type= 21.16666603 5.07999992 和 <math id="M68"><msub><mrow><mi>d</mi></mrow><mrow><mi>c</mi><mi>o</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>s</mi><mi>t</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mtext> </mtext><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906449&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906446&type= 21.25133324 5.07999992 分别表示 <math id="M69"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906456&type= 2.37066650 4.57200003 和 <math id="M70"><msubsup><mrow><mi>p</mi></mrow><mrow><mi>h</mi></mrow><mrow><mi>s</mi><msub><mrow><mi>p</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906452&type= 4.06400013 3.97933316 之间的光谱角距离，欧式距离和对比度， <math id="M71"><msub><mrow><mi>d</mi></mrow><mrow><mi>s</mi><mi>a</mi><mi>l</mi><mi>i</mi><mi>e</mi><mi>n</mi><mi>c</mi><mi>y</mi></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906455&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906454&type= 14.30866718 5.16466665 表示 <math id="M72"><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906456&type= 2.37066650 4.57200003 的显著值。根据 公式（12） 公式（12） 将所有像素点的显著值计算完成后，可得到高光谱图像的显著图，以此作为高光谱异常检测的初始检测结果IR。 2.4　后处理 2 为了降低虚警率，本文对初始检测结果IR进行后处理，后处理操作主要包括两部分：图像滤波和阈值化处理。图像滤波部分，本文采用域变换递归滤波方法（ Gastal和Oliveira， 2011 Gastal和Oliveira， 2011 ）；阈值化处理部分，本文采用OTSU算法（ Otsu， 1979 Otsu， 1979 ）来自适应地选择阈值，进而获取最终的二值化检测结果。 （1）　域变换递归滤波 3 为了滤波后的图像不失真，通常采用具有边缘保持特性的滤波方法，常用的边缘保持滤波方法有双边滤波器（ Tomasi和Manduchi， 1998 Tomasi和Manduchi， 1998 ）和各向异性扩散（ Perona和Malik， 1990 Perona和Malik， 1990 ）等，前者需要变换至高维空间进行计算，后者需要迭代计算，均具有较高的计算复杂度。本文采用的域变换递归滤波既有边缘保持特性，又具有较低的计算复杂度。 以初始检测结果IR作为输入图像，以降维后的高光谱图像Z作为引导图像，则域变换递归滤波后的图像 J 可由下式获取（ Gastal和Oliveira， 2011 Gastal和Oliveira， 2011 ）： <math display="block" id="M73"><mtable columnalign="left"><mtr><mtd><msub><mrow><mi>J</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></msup><mo stretchy="false">)</mo><mi>I</mi><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>+</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></msup><msub><mrow><mi>J</mi></mrow><mrow><mi>i</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>a</mi><mo>=</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo><mroot><mrow><mn mathvariant="normal">2</mn></mrow><mrow/></mroot><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></msup></mtd></mtr><mtr><mtd><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>b</mi><mo>=</mo><mfrac><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></mrow></mfrac><msub><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup><mo>-</mo><msubsup><mrow><mi mathvariant="bold-italic">x</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow><mrow><mi mathvariant="bold-italic">Z</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906459&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906458&type= 36.32199860 19.98133469 其中， <math id="M74"><mi>I</mi><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906461&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906460&type= 4.23333359 3.72533321 表示IR中第 i 个像素点的值， <math id="M75"><msub><mrow><mi>J</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906464&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906462&type= 2.37066650 4.06400013 和 <math id="M76"><msub><mrow><mi>J</mi></mrow><mrow><mi>i</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906468&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906466&type= 5.75733376 4.06400013 分别表示 J 中第 i 和第 i -1个像素点的值， a 表示反馈系数， b 表示相邻像素间的相似性， <math id="M77"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906532&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906531&type= 3.30200005 3.72533321 和 <math id="M78"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906533&type= 3.30200005 3.72533321 用于控制滤波平滑度的参数。 （2）　阈值化处理 3 为了进一步降低虚警率并获得最终的二值化结果，本文对滤波后的图像J进行阈值化处理： <math display="block" id="M79"><msub><mrow><mi>R</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mn mathvariant="normal">1</mn><mo>,</mo><mo> </mo><msub><mrow><mi>J</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≥</mo><mi>T</mi><mi>H</mi></mtd></mtr><mtr><mtd><mn mathvariant="normal">0</mn><mo>,</mo><mo> </mo><mi mathvariant="normal">其</mi><mi mathvariant="normal">他</mi></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906475&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906474&type= 27.00866890 10.07533360 其中， R i 表示最终检测结果图 R 中第 i 个像素点的值， TH 是采用OTSU算法（ Otsu， 1979 Otsu， 1979 ）获取的阈值。 3　实验结果与分析 1 3.1　实验设置 2 3.1.1　数据集 3 本文采用San Diego-I（ Chen和Yang， 2013 Chen和Yang， 2013 ），San Diego-II（ Tomasi和Manduchi， 1998 Tomasi和Manduchi， 1998 ），Bay Champagne （ Williams等， 2013 Williams等， 2013 ），Cat Island（ Xie等， 2019 Xie等， 2019 ）和Los Angeles（ Williams等， 2013 Williams等， 2013 ）5个数据集进行实验对比。 （1）San Diego-I数据集是由机载可见光/红外成像光谱仪（AVIRIS）传感器采集的高光谱影像。该传感器的空间分辨率为3.5米，该高光谱影像像素为400×400，覆盖了美国加利福尼亚州的圣地亚哥机场区域。最初的波段数为224个，分布在370~2510nm波长范围内，去除无用的波段后仍保留189个波段。该数据集中的异常之处在于机场上有几架飞机，如 图4 图4 （a）所示。 （2）San Diego-II数据集是由机载可见光/红外成像光谱仪（AVIRIS）传感器采集的高光谱影像。该数据集像素大小为100×100，具有189个有效频谱通道，排除了低信噪比或其他不良频带，波长范围为370～2510nm，其中三架白色飞机被选为预期的异常目标，如 图4 图4 （b）所示。 （3）Cat Island数据集也是由AVIRIS传感器采集的猫岛场景，该数据集的空间像素为100×100，光谱波段为193，原始图像中的噪声带已被移除。图像的主要背景是海洋和岛屿，而在这个场景中有19个空间像素的船被视为异常，伪彩色图像和真值图如 图4 图4 （c）所示。 （4）Bay Champagne数据集是由AVIRIS传感器采集的高光谱影像，该影像的空间分辨率为4.4m，包含188个波段，场景覆盖区域的像素为100×100，异常共由11个像素组成，对应的伪彩图和真值图如 图4 图4 （d）所示。 （5）Los Angeles数据集是由机载可见光/红外成像光谱仪（AVIRIS）传感器获得的洛杉矶场景，具有205个波段和7.1米的空间分辨率，场景由100×100像素组成，异常目标为建筑物，总共占据272个像素，伪彩图和真值图如 图4 图4 （e）所示。 3.1.2　评估指标 3 本文采用三个最常用的指标来定量评估本文所提方法的性能。 （a） San Diego-I dataset （b） San Diego-II dataset （c） Cat Island dataset （d） Bay Champagne dataset （e） Los Angeles dataset （1）受试者工作特征曲线（Receiver Operating Characteristic Curve，ROC）（ Bradley， 1997 Bradley， 1997 ）。ROC由基于真值图的各种阈值τ下的真阳性率（TPR）和假阳性率（FPR）绘制，该指标可以从检测精度和虚警率两个方面来评估检测性能。在相同的虚警条件下，当检测概率高于其他检测器时，异常检测器的性能更好。 （2）Area Under Roc Curve （AUC）（ Flach等， 2011 Flach等， 2011 ）。AUC是ROC曲线下的面积。AUC值越接近1，说明检测性能越好。 （3）异常背景可分性箱线图（ Manolakis和Shaw， 2002 Manolakis和Shaw， 2002 ）。该指标得出的是可分性范围，它表示不同检测方法从背景中提取异常的能力，检测方法越好，异常和背景之间的分离越明显。 3.1.3　对比算法 3 本文与7种主流的异常检测方法进行对比，主要包括RX（ Reed和Yu， 1990 Reed和Yu， 1990 ）、LRX（ Niu和Wang， 2016 Niu和Wang， 2016 ）、CRD（ Molero等， 2013 Molero等， 2013 ）、LSMAD（ Zhang等， 2016 Zhang等， 2016 ）、LRASR（ Chen和Yang， 2013 Chen和Yang， 2013 ）、AED（ Li等， 2018 Li等， 2018 ）和LSDM-MoG（ Li等， 2021 Li等， 2021 ）。其中，RX通过计算测试像素和图像背景之间的马氏距离实现异常目标的检测，是无监督异常检测领域中广泛使用的检测方法；LRX通过计算测试像素和局部图像背景之间的距离来检测异常，是基于RX改进的方法；CRD使用相邻像素进行协同表示，以实现异常检测；LSMAD和LRASR是两种典型的基于低秩和稀疏表示的异常检测方法；AED是基于形态学的异常检测方法；LSDM-MoG在低秩稀疏分解模型中引入混合噪声模型，从而更准确的描述复杂的背景分布。 3.1.4　实验细节 3 2.1节中，自编码器包含5层，节点数分别为（200，80，40，80，200），判别器包含4层，节点数分别为（200，80，40，1），激活函数均采用Leaky ReLU，负值斜率为0.2；对抗自编码网络的优化器采用Adam，自编码器和判别器的学习率分别为1e-3和1e-4，总迭代次数为500次。2.1节中， 公式（1） 公式（1） 中 N 2 设置为40； 公式（5） 公式（5） 中 α 设置为0.1。2.2节中，超像素块数量 K =300； 公式（8） 公式（8） 中 w 设置为0.1。2.3节中，内外窗间距 R =6。2.4节中， 公式（9） 公式（9） 中 C 设置为1。 对抗自编码网络的处理过程均在GeForce RTX2080Ti显卡上，其运行环境为python 3.6.13、Pytorch 1.8.2以及CUDA 10.2。同时，所有对比算法运行环境均在MATLAB R2017b。 3.2　实验结果对比及分析 2 图5　本文方法与7种流行方法在5个数据集上的主观对比 Fig.5　Subjective comparisons between the proposed method and 7 state-of-the-art methods on 5 datasets. 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17.99099922 17.72699928 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906672&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906674&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906673&type= 17.99099922 17.72699928 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906675&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906677&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906676&type= 17.99099922 17.99099922 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906678&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906680&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906679&type= 17.99099922 17.99099922 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906681&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906683&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906682&type= 17.99099922 17.99099922 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906684&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906686&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906685&type= 17.99099922 17.99099922 3.2.1　主观对比 3 本文方法与7种流行方法的主观对比结果如图5所示。如图5（a）所示，LRX的结果完全未检测出异常目标，LRASR和AED的异常检测效果相对较好，但是本文方法检测效果最佳，即：异常目标区域与背景区域之间对比度最高，异常目标的位置和轮廓定位最准。如图5（b）所示，LRX仍然未检测出异常目标，AED和本文方法对异常目标的检测效果更好，但AED的检测结果中有其他被误检的背景目标，本文方法既能精确地检测出异常目标，同时在背景区域又具有较低的误检率。如图5（c）和（d）所示，LRASR在两个数据集上都将沙滩、海面等背景误检为异常，AED和本文方法对异常目标的检测效果一如既往的稳定，异常目标的位置明确，但是在Cat Island数据集上，AED还是误检出部分背景，本文方法依然具有较低的误检率。如图5（e）所示，LRX、CRD和LSMAD的异常检测结果很差，仍然是AED检测效果更好，但与本文方法相比，存在漏检异常目标的问题。总体来看，在7种流行方法中，AED的检测效果相对较好，但本文方法相比AED检测效果更好，主要体现在两个方面：对于异常目标，本文方法漏检更少，且异常目标区域与背景区域之间具有更高对比度；在背景区域，本文方法误检更少。 3.2.2　客观对比 3 如 表1 表1 所示，本文方法在5个数据集上的AUC结果均为第一，综合表现最好；在7种流行方法中，AED的AUC结果在4个数据集上排名第二，1个数据集上排名第三，综合表现仅次于本文方法，这与主观对比的结论一致。观察图6可以得到同样的结论，即：本文方法的ROC曲线最高，AED次之。 注： 黑色粗体为最优的AUC结果。 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906687&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906689&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906688&type= 33.36999893 7.61999989 数据集 检测算法 San Diego-I San Diego-II Cat Island Bay Champagne Los Angeles RX 0.9403 0.9111 0.9807 0.9999 0.9887 LRX 0.8428 0.6929 0.9956 0.9995 0.8081 CRD 0.9412 0.9791 0.9916 0.9998 0.9794 LSMAD 0.9701 0.9731 0.9661 0.9997 0.9814 LRASR 0.8950 0.9853 0.4203 0.7536 0.8748 AED 0.9846 0.9979 0.9974 0.9997 0.9912 LSDM-MoG 0.9339 0.9320 0.9942 0.9996 0.9745 ISPS-AWSD 0.9850 0.9996 0.9999 0.9999 0.9934 为了进一步比较本文方法与7种异常检测方法的检测性能， 图7 图7 分别绘制了5个数据集上各检测方法的异常背景可分性箱线图。与其他7种异常检测方法相比，本文方法在各数据集上的红框下限和 1,2,3;4,5; 图6　本文方法与7种流行方法在5个数据集上的ROC曲线对比 Fig.6　Comparisons of ROC curves between the proposed method and 7 state-of-the-art methods on 5 datasets. 3 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906690&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906692&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906691&type= 6.61400032 0.26400000 RX LRX CRD LSMAD LRASR AED LSDM-MoG ISPS-AWSD http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906693&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906694&type= 46.83100128 35.71799850 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906696&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906698&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906697&type= 47.88899994 36.77700043 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906699&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906701&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906700&type= 48.94699860 37.30599976 （a） San Diego-I数据集 （a） San Diego-I dataset （b） San Diego-II数据集 （b） San Diego-II dataset （c） Cat Island数据集 （c） Cat Island dataset 2 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906702&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906704&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906703&type= 46.30199814 35.45399857 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906705&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906707&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906706&type= 47.36000061 36.51200104 2 （d） Bay Champagne数据集 （d） Bay Champagne dataset （e） Los Angeles数据集 （e） Los Angeles dataset 绿框上限之间的距离更大，表明本文方法对异常目标区域与背景区域的可分性更好。 基于上述分析，可以确认本文方法总体性能优于对比的７种方法，是一种非常有竞争力的异常检测方法。 3.2.3　消融实验 3 本节对前言中所提的两个创新点进行逐一验证。 （1）基于正交投影散度的高光谱图像超像素分割改进算法的有效性验证。 表2 表2 将超像素分割改进算法中采用的正交投影散度与欧式距离、光谱角距离以及光谱信息散度这三种常用光谱距离度量方式在5个数据集上进行了AUC值对比，为保证实验的公平性，除光谱距离度量方式外，其余设置均保持一致。如 表2 表2 所示，采用正交投影散度的AUC值在5个数据集上均优于其他三种光谱距离度量方式。这表明采用正交投影散度来度量光谱距离可以有效提升超像素分割的效果。 注： 黑色粗体为最优的AUC结果。 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906708&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906710&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906709&type= 23.44899940 7.46099997 度量方式 数据集 欧氏 距离 光谱角 距离 光谱信息 散度 正交投影 散度 San Diego-I 0.9840 0.9840 0.9843 0.9850 San Diego-II 0.9976 0.9976 0.9978 0.9996 Cat Island 0.9947 0.9948 0.9962 0.9999 Bay Champagne 0.9952 0.9952 0.9963 0.9999 Los Angeles 0.9902 0.9902 0.9916 0.9934 （2）自适应窗口显著性检测算法的有效性验证。 表3 表3 将采用自适应窗口与四种手工设定尺寸的双窗口在5个数据集上进行了AUC值对比，为保证实验的公平性，除内窗尺寸外（外窗由内窗按照固定间距 R 扩充所得，如 图3 图3 所示），其余设置均保持一致。如 表3 表3 所示，采用自适应窗口的AUC值在5个数据集上均优于四种手工设定尺寸的双窗口的AUC值，尤其在Los Angeles数据集上，与第二名得分相比提升了10个百分点。上述分析充分表明本文所提自适应窗口显著性检测算法的有效性。 注： 黑色粗体为最优的AUC结果。 http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906711&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906713&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906712&type= 23.66500092 7.35500002 内窗尺寸 数据集 3 5 7 9 自适应 San Diego-I 0.9763 0.9782 0.9803 0.9821 0.9850 San Diego-II 0.9968 0.9971 0.9960 0.9950 0.9996 Cat Island 0.9921 0.9872 0.9826 0.9795 0.9999 Bay Champagne 0.9876 0.9896 0.9920 0.9823 0.9999 Los Angeles 0.8924 0.8696 0.8642 0.8539 0.9934 3.3　参数分析 2 本节将与算法性能密切相关的超像素块数量 K 、内外窗间距 R 以及域变换递归滤波中的平滑度参数 <math id="M80"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906532&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906531&type= 3.30200005 3.72533321 和 <math id="M81"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906514&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906513&type= 3.30200005 3.72533321 进行参数分析。 图8 图8 给出了AUC值随 K 值变化的曲线，在4个公开的数据集上（除Cat Island外），AUC值均呈现先上升后下降的趋势，且均在 K =300时取得最大值；Cat Island数据集在 K =300时的AUC取值与最 大值较为接近。综合分析， K =300时本文方法取得最佳效果。 图9 图9 给出了AUC值随 R 值变化的曲线，在San Diego-I和Los Angeles数据集上，AUC均在 R =6时取得最大值；其余3个数据集的AUC值对 R 的变化不敏感。综合分析， R =6时本文方法取得最佳效果。 图10 图10 给出了AUC值随 <math id="M82"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906532&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906531&type= 3.30200005 3.72533321 和 <math id="M83"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906533&type= 3.30200005 3.72533321 值变化的三维立体图，在San Diego-I和Los Angeles数据集上，AUC均在 <math id="M84"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906532&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906531&type= 3.30200005 3.72533321 =1时取得最大值，其中San Diego-I数据集在 <math id="M85"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906533&type= 3.30200005 3.72533321 =20时AUC值最大，Los Angeles数据集在 <math id="M86"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906533&type= 3.30200005 3.72533321 =20和30时AUC值接近；其余3个数据集对 <math id="M87"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906532&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906531&type= 3.30200005 3.72533321 和 <math id="M88"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906534&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906533&type= 3.30200005 3.72533321 的变化不敏感。综合分析， <math id="M89"><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906536&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906535&type= 9.65200043 3.72533321 ， <math id="M90"><msub><mrow><mi>σ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">20</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906538&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=24906537&type= 11.51466751 3.80999994 时本文方法取得最佳效果。 1,2,3;4,5; 4　结 论 1 本文提出了一种融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测方法并得到以下结论： （1）现有高光谱图像超像素分割算法常采用欧式距离、光谱角距离或光谱信息散度等方式进行光谱距离度量，然而这些方式需要假设像素的光谱值与光照条件之间是线性关系，但实践中这种假设一般不成立。本文采用的正交投影散度能突破上述假设的限制，消融实验结果表明，基于正交投影散度的改进超像素分割算法优于现有超像素分割算法的表现。 （2）现有基于局部对比度的高光谱异常检测方法通常采用双窗口法，但该类方法通常根据经验值来设置双窗口尺寸，难以适应异常目标的尺度变化，泛化能力不足。考虑到异常目标区域内像素间的同质性，本文在超像素分割的基础上自适应地设定双窗口尺寸，确保内窗中所有像素具有同质性，从而自动匹配异常目标的尺度变化，解决了传统双窗口法泛化能力不足的问题。消融实验结果表明，自适应窗口显著性检测算法的性能优于现有双窗口算法。 （3）在5个公开的数据集上与7种流行方法的主观对比结果表明，本文方法对异常目标的漏检更少，在背景区域的误检更低，且异常目标区域与背景区域之间具有更强对比度；客观对比结果表明，本文方法的总体检测精度和异常背景可分性均优于7种流行方法，充分验证了本文方法的优越性。 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A low-rank and sparse matrix decomposition-based mahalanobis distance method for hyperspectral anomaly detection 10.11834/jrs.20222004 TP701 A 钱晓亮，曾银凤，林生，张博，任航丽，王慰.XXXX.融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测.遥感学报，XX（XX）： 1-14 钱晓亮，曾银凤，林生，张博，任航丽，王慰.XXXX.融合自适应窗口显著性检测和改进超像素分割的高光谱异常检测.遥感学报，XX（XX）： 1-14 QIAN Xiaoliang，ZENG Yinfeng，LIN Sheng，ZHANG Bo，REN Hangli，WANG Wei. XXXX. Hyperspectral Anomaly Detection via Combining Adaptive Window Saliency Detection and Improved Superpixel Segmentation. National Remote Sensing Bulletin， XX（XX）：1-14 QIAN Xiaoliang，ZENG Yinfeng，LIN Sheng，ZHANG Bo，REN Hangli，WANG Wei. XXXX. Hyperspectral Anomaly Detection via Combining Adaptive Window Saliency Detection and Improved Superpixel Segmentation. National Remote Sensing Bulletin， XX（XX）：1-14 国家自然科学基金（编号： 62076223， 62003311）， 河南省科技攻关项目（编号： 202102210347， 202102210143）， 河南省自然科学基金（编号： 202300410503）. Supported by Supported by National Science Foundation of China (Grant No. 62076223, 62003311), Key Science and Technology Program of Henan Province (Grant No. 202102210347, 202102210143), Natural Science Foundation of Henan Province (Grant No. 202300410503). 2022-03-07 遥感学报