Satellite imagery solutions are widely used to study and monitor different regions of the Earth. However, a single satellite image can cover only a limited area. In cases where a larger area of interest is studied, several images must be stitched together to create a single larger image, called a mosaic, that can cover the area. Today, with the increasing number of satellite images available for commercial use, selecting the images to build the mosaic is challenging, especially when the user wants to optimize one or more parameters, such as the total cost and the cloud coverage percentage in the mosaic. More precisely, for this problem the input is an area of interest, several satellite images intersecting the area, a list of requirements relative to the image and the mosaic, such as cloud coverage percentage, image resolution, and a list of objectives to optimize. We contribute to the constraint and mixed integer lineal programming formulation of this new problem, which we call the \textit{satellite image mosaic selection problem}, which is a multi-objective extension of the polygon cover problem. We propose a dataset of realistic and challenging instances, where the images were captured by the satellite constellations SPOT, Pl\'eiades and Pl\'eiades Neo. We evaluate and compare the two proposed models and show their efficiency for large instances, up to 200 images.

翻译：卫星图像解决方案被广泛应用于研究和监测地球的不同区域。然而，单幅卫星图像只能覆盖有限区域。当需要研究更大区域时，必须将多幅图像拼接成一幅更大的图像（称为镶嵌图）以覆盖目标区域。如今，随着商业可用卫星图像数量的增加，如何选择用于构建镶嵌图的图像变得具有挑战性，尤其是在用户希望优化一个或多个参数（如总成本和镶嵌图中的云覆盖百分比）时。更精确地说，该问题的输入包括：目标区域、与区域相交的多幅卫星图像、与图像及镶嵌图相关的一系列需求（如云覆盖百分比、图像分辨率）以及一系列需要优化的目标。我们针对这一新问题（称为“卫星图像镶嵌选择问题”）提出了约束规划和混合整数线性规划模型，该问题是多边形覆盖问题的多目标扩展。我们构建了一个包含真实且具挑战性实例的数据集，其中图像由SPOT、Pléiades和Pléiades Neo卫星星座捕获。我们对两种模型进行了评估与比较，并展示了它们在处理多达200幅图像的大规模实例时的效率。