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1.6.1. Subdivision

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Digital image processing has a long history, and the subdivision of images has been widely used for various image processing tasks. For example, JPEG and MPEG image/video compression standards still use block-based predictions and transforms, even in their most recent standards. Moreover, graph-based image processing also uses such a subdivision as preprocessing. It can also be combined with the following fast computation approaches.

A simple solution for image subdivision is the block-based approach. It divides the input image into an equal-sized subblocks (these blocks can be overlapped with an appropriate window function), after which the favorite image processing tasks can be performed. The advantage it provides is simplicity: we only have to consider the size of subblocks to make a trade-off between performance and complexity. Sizes of the consistent image regions vary significantly; as a result, a recursive subdivision, called quadtree decomposition, provides a good trade-off.

More complex image subdivisions are also possible by utilizing an image segmentation. Although these segmentated sub-images are not rectangular in general, we can directly perform graph-based image processing in such non-rectangular regions by using appropriate graphs.

Graph Spectral Image Processing

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