3D edge detection by selection of level surface patches

We propose a new edge detector for 3D gray-
scale images, extending the 2D edge detector of Desol-
neux 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 as-
sert that this selection device results in a good edge detector
for a wide class of images, including several types of med-
ical images from X-ray computed tomography and magnetic
resonance.