The authors address the problem of editing signals such as 2D colour images or 3D coloured meshes that are represented under the general framework of graph signals. As state-of-the-art editing approaches decompose an image into several layers in order to manipulate them, they propose a hierarchical multi-layer decomposition of graph signals that relies on morphological filtering. Since morphological filtering operators require a complete lattice, a dedicated approach for the morphological processing of vectorial data on graphs is used. By iterating the application of morphological filterings of decreasing sizes, the graph signal is decomposed into several detail layers, each capturing a given detail level. Editing applications such as abstraction, sharpness enhancement and tone mapping are shown to illustrate the benefits of the proposed approach.

中文翻译：

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用于编辑应用程序的分层形态图信号多层分解

作者解决了编辑信号的问题，例如在图形信号的一般框架下表示的2D彩色图像或3D彩色网格。随着最新的编辑方法将图像分解为多层以进行操作，他们提出了依赖形态过滤的图形信号分层多层分解方法。由于形态过滤运算符需要完整的晶格，因此使用了专用的方法对图形上的矢量数据进行形态处理。通过迭代减小大小的形态过滤的应用，图形信号被分解为几个细节层，每个细节层捕获一个给定的细节级别。显示了诸如抽象，清晰度增强和色调映射之类的编辑应用程序，以说明该方法的好处。