Transport-based distances, such as the Wasserstein distance and earth mover’s distance, have been shown to be an effective tool in signal and image analysis. The success of transport-based distances is in part due to their Lagrangian nature which allows it to capture the important variations in many signal classes. However, these distances require the signal to be non-negative and normalised. Furthermore, the signals are considered as measures and compared by redistributing (transporting) them, which does not directly take into account the signal intensity. Here, we study a transport-based distance, called the \(TL^p\) distance, that combines Lagrangian and intensity modelling and is directly applicable to general, non-positive and multichannelled signals. The distance can be computed by existing numerical methods. We give an overview of the basic properties of this distance and applications to classification, with multichannelled non-positive one-dimensional signals and two-dimensional images, and colour transfer.

中文翻译：

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用于信号分析的传输 Lp 距离。

基于运输的距离，例如 Wasserstein 距离和推土机距离，已被证明是信号和图像分析的有效工具。基于传输的距离的成功部分归功于其拉格朗日性质，这使得它能够捕获许多信号类别的重要变化。然而，这些距离要求信号为非负且标准化。此外，信号被视为度量并通过重新分配（传输）它们进行比较，这不直接考虑信号强度。在这里，我们研究了一种基于传输的距离，称为\(TL^p\)距离，它结合了拉格朗日和强度建模，并且直接适用于一般、非正和多通道信号。该距离可以通过现有的数值方法来计算。我们概述了该距离的基本属性以及分类应用，包括多通道非正一维信号和二维图像以及颜色传递。