Globally Optimal Surfaces by Continuous Maximal Flows

摘要

In this paper we solve the problem of computing exact continuous optimal curves and surfaces for image segmentation and 3D reconstruction, using a maximal flow approach expressed by means of a PDE model. Previously existing techniques yield either grid-biased (graph-based approaches) or sub-optimal answers (active contours and surfaces). The proposed algorithm simulates the flow of an ideal fluid with spatially varying velocity constraint. A proof is given that the algorithm gives the globally maximal flow at convergence, along with an implementation method. The globally minimal surface may be obtained trivially from its output. The new algorithm is applied to segmentation in 2D and 3D medical images and to 3D reconstruction from a stereo image pair. The results in 2D agree remarkably well with an existing planar minimal surface algorithm and the results in 3D segmentation and reconstruction demonstrate that the new algorithm does not exhibit grid bias.