Detecting anomalous changes in remote sensing images is a challenging problem, where many approaches and techniques have been presented so far. We rely on the standard field of multivariate statistics of diagnostic measures, which are concerned about the characterization of distributions, detection of anomalies, extreme events, and changes. One useful tool to detect multivariate anomalies is the celebrated Cook's distance. Instead of assuming a linear relationship, we present a novel kernelized version of the Cook's distance to address anomalous change detection in remote sensing images. Due to the large computational burden involved in the direct kernelization, and the lack of out-of-sample formulas, we introduce and compare both random Fourier features and Nyström implementations to approximate the solution. We study the kernel Cook's distance for anomalous change detection in a chronochrome scheme, where the anomalousness indicator comes from evaluating the statistical leverage of the residuals of regressors between time acquisitions. We illustrate the performance of all algorithms in a representative number of multispectral and very high resolution satellite images involving changes due to droughts, urbanization, wildfires, and floods. Very good results and computational efficiency confirm the validity of the approach.

中文翻译：

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用于遥感异常变化检测的高效内核库克距离

检测遥感图像中的异常变化是一个具有挑战性的问题，迄今为止已经提出了许多方法和技术。我们依赖于诊断措施的多元统计的标准领域，它关注分布特征、异常检测、极端事件和变化。检测多变量异常的一种有用工具是著名的库克距离。我们没有假设线性关系，而是提出了一种新的库克距离内核化版本，以解决遥感图像中的异常变化检测问题。由于直接核化涉及大量计算负担，并且缺少样本外公式，我们引入并比较随机傅立叶特征和 Nyström 实现以近似解。我们研究内核库克' s 计时色方案中异常变化检测的距离，其中异常指标来自评估时间获取之间回归量残差的统计杠杆。我们在具有代表性数量的多光谱和超高分辨率卫星图像中说明了所有算法的性能，这些卫星图像涉及干旱、城市化、野火和洪水引起的变化。非常好的结果和计算效率证实了该方法的有效性。我们在具有代表性数量的多光谱和超高分辨率卫星图像中说明了所有算法的性能，这些卫星图像涉及干旱、城市化、野火和洪水引起的变化。非常好的结果和计算效率证实了该方法的有效性。我们在具有代表性数量的多光谱和超高分辨率卫星图像中说明了所有算法的性能，这些卫星图像涉及干旱、城市化、野火和洪水引起的变化。非常好的结果和计算效率证实了该方法的有效性。