Image colorization based on numerical modeling gives a highly accurate restoration result when colors are given to enough regions. A lot of numerical models focus on the relation between adjacent pixels; therefore, it is required to give the same color to various regions, and high spatial frequency regions are not colored properly. This letter proposes a colorization algorithm using graph signal processing. The key novelty of our algorithm is a new modeling method for a chrominance image using two different graphs. The first graph is a global graph, which connects the important pixels on an image. The second graph is a local graph, which connects the global graph and each pixel. Based on the hierarchical combination of these two graphs, color image is recovered. Numerical experiments show the effectiveness of the proposed algorithm by comparing with four existing methods.

中文翻译：

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图像着色的局部和全局图方法

当颜色被赋予足够的区域时，基于数值建模的图像着色可提供高度准确的恢复结果。许多数值模型关注相邻像素之间的关系；因此，需要给不同的区域赋予相同的颜色，而高空间频率区域没有正确着色。这封信提出了一种使用图形信号处理的着色算法。我们算法的关键新颖之处在于一种使用两个不同图形的色度图像的新建模方法。第一个图是全局图，它连接图像上的重要像素。第二个图是局部图，它连接全局图和每个像素。基于这两个图的层次组合，恢复彩色图像。