A Computational Approach to Edge Detection
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We propose a new edge detector for 3D gray-scale images, extending the 2D edge detector of Desolneux et al. (J. Math. Imaging Vis. 14(3):271---284, 2001). While the edges of a planar image are pieces of curve, the edges of a volumetric image are pieces of surface, which are more delicate to manage. The proposed edge detector works by selecting those pieces of level surface which are well-contrasted according to a statistical test, called Helmholtz principle. As it is infeasible to treat all the possible pieces of each level surface, we restrict the search to the regions that result of optimizing the Mumford-Shah functional of the gradient over the surface, throughout all scales. We assert that this selection device results in a good edge detector for a wide class of images, including several types of medical images from X-ray computed tomography and magnetic resonance.