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The key idea is to compute the scalar field in a joint spatial\u2010range domain (i.e., bilateral domain) and resample its values on an image manifold. We introduce a new formulation of Hermite radial basis function (HRBF) interpolation to obtain the scalar field in the bilateral domain. In contrast to previous implicit methods, bilateral HRBF (B\u2010HRBF) generates a segmentation boundary that passes through all contours, fits high\u2010contrast image edges if they exist, and has a smooth shape in blurred areas of images. We also propose an acceleration scheme for computing B\u2010HRBF to support a real\u2010time and intuitive segmentation interface. 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