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3 July 2001 Design of connected operators using the image foresting transform
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The Image Foresting Transform (IFT) reduces optimal image partition problems from seed pixels into a shortest-path forest problem in a graph, whose solution can be obtained in linear time. It has allowed a unified and efficient approach to edge tracking, region growing, watershed transforms, multiscale skeletonization, and Euclidean distance transform. In this paper, we extend the IFT to introduce two connected operators: cutting-off-domes and filling-up-basins. The former simplifies grayscale images by reducing the height of its domes, while the latter reduces the depth of its basins. By automatically or interactively specifying seed pixels in the image and computing a shortest-path forest, whose trees are rooted at these seeds, the IFT creates a simplified image where the brightness of each pixel is associated with the length of the corresponding shortest-path. A label assigned to each seed is propagated, resulting a labeled image that corresponds to the watershed partitioning from markers. The proposed operators may also be used to provide regional image filtering and labeling of connected components. We combine the cutting-off-domes and filling-up-basins to implement regional minima/maxima, h-domes/basins, opening/closing by reconstruction, leveling, area opening/closing, closing of holes, and removal of pikes. Their applications are illustrated with respect to medical image segmentation.
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Alexandre Xavier Falcao, Bruno S. Cunha, and Roberto Alencar Lotufo "Design of connected operators using the image foresting transform", Proc. SPIE 4322, Medical Imaging 2001: Image Processing, (3 July 2001);

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