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When remote sensing meets topological data analysis

机译：当遥感遇到拓扑数据分析时

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Author Summary: Hyperspectral remote sensing plays an increasingly important role in many scientific domains and everyday life problems. Indeed, this imaging concept ends up in applications as varied as catching tax-evaders red-handed by locating new construction and building alterations, searching for aircraft and saving lives after fatal crashes, detecting oil spills for marine life and environmental preservation, spying on enemies with reconnaissance satellites, watching algae grow as an indicator of environmental health, forecasting weather to warn about natural disasters and much more. From an instrumental point of view, we can say that the actual spectrometers have rather good characteristics, even if we can always increase spatial resolution and spectral range. In order to extract ever more information from such experiments and develop new applications, we must, therefore, propose multivariate data analysis tools able to capture the shape of data sets and their specific features. Nevertheless, actual methods often impose a data model which implicitly defines the geometry of the data set. The aim of the paper is thus to introduce the concept of topological data analysis in the framework of remote sensing, making no assumptions about the global shape of the data set, but also allowing the capture of its local features.
机译：作者摘要：高光谱遥感在许多科学领域和日常生活中起着越来越重要的作用。的确，这种成像概念最终在各种应用中得到应用，例如通过查找新建筑和建筑物改建来逃税，寻找飞机并在致命坠机后挽救生命，检测溢油以保护海洋生物和环境保护，监视敌人借助侦察卫星，可以观察藻类的生长，以此作为环境健康的指标，并预测天气以警告自然灾害等等。从仪器的角度来看，即使可以始终提高空间分辨率和光谱范围，我们也可以说实际的光谱仪具有相当好的特性。因此，为了从此类实验中提取更多信息并开发新的应用程序，我们必须提出能够捕获数据集的形状及其特定功能的多元数据分析工具。但是，实际方法通常会施加一个数据模型，该模型隐式定义数据集的几何形状。因此，本文的目的是在遥感框架中引入拓扑数据分析的概念，不对数据集的整体形状进行任何假设，但也可以捕获其局部特征。

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