Abstract Image representation is the key factor influencing the accuracy of remote sensing image segmentation. Traditional algorithms rely on the pixel-wise characteristics exhibited in the feature space. They introduce spatial information by establishing the connections between neighboring pixels in the neighborhood system. But the spectral-spatial features cannot be well expressed. In this paper, a Riemannian manifold space is introduced to express the contextual information by jointly mapping the spectral features of a pixel and its neighboring ones on to it. To benefit from the expression ability and geometric properties of the Riemannian manifold, a data submanifold and a parameter submanifold are established to depict the characteristics of the detected image and all possible segmentation results. On the parameter submanifold, only points representing objects of the current segmentation are active. Then distance between a point on the data submanifold and an active point on the parameter submanifold is measured by a geodesic-kernel function. Consequently, four geodesic-kernel function-based manifold projection criteria are proposed to explore the complementation between features expressed in different feature spaces. Experiments on synthetic and real remote sensing images demonstrated that the proposed geodesic-kernel function-based manifold projection algorithm outperforms traditional ones and features expressed in different feature spaces did contain some complementary information.

中文翻译：

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使用测地线核函数和多特征空间的遥感图像分割

摘要 影像表征是影响遥感影像分割精度的关键因素。传统算法依赖于特征空间中展示的逐像素特征。它们通过在邻域系统中建立相邻像素之间的连接来引入空间信息。但是光谱空间特征不能很好地表达。在本文中，引入了黎曼流形空间，通过将像素及其相邻像素的光谱特征联合映射到其上来表达上下文信息。为了利用黎曼流形的表达能力和几何特性，建立了数据子流形和参数子流形来描述检测图像的特征和所有可能的分割结果。在参数子流形上，只有代表当前分割对象的点是活动的。然后数据子流形上的点与参数子流形上的活动点之间的距离由测地线核函数测量。因此，提出了四种基于测地线核函数的流形投影标准来探索不同特征空间中表达的特征之间的互补性。对合成和真实遥感图像的实验表明，所提出的基于测地线核函数的流形投影算法优于传统算法，并且在不同特征空间中表达的特征确实包含一些补充信息。然后数据子流形上的点与参数子流形上的活动点之间的距离由测地线核函数测量。因此，提出了四种基于测地线核函数的流形投影标准来探索不同特征空间中表达的特征之间的互补性。对合成和真实遥感图像的实验表明，所提出的基于测地线核函数的流形投影算法优于传统算法，并且在不同特征空间中表达的特征确实包含一些补充信息。然后数据子流形上的点与参数子流形上的活动点之间的距离由测地线核函数测量。因此，提出了四种基于测地线核函数的流形投影标准来探索不同特征空间中表达的特征之间的互补性。对合成和真实遥感图像的实验表明，所提出的基于测地线核函数的流形投影算法优于传统算法，并且在不同特征空间中表达的特征确实包含一些补充信息。