Summary: Implicit Medial Representation for Vessel Segmentation
Guillaume Pizaineab, Elsa Angelinib, Isabelle Blochb, Sherif Makram-Ebeida
a Medisys Research Lab, Philips Healthcare, Suresnes, France.
b Institut Telecom, Telecom ParisTech, CNRS LTCI, Paris, France.
In the context of mathematical modeling of complex vessel tree structures with deformable models, we present
a novel level set formulation to evolve both the vessel surface and its centerline. The implicit function is
computed as the convolution of a geometric primitive, representing the centerline, with localized kernels of
continuously-varying scales allowing accurate estimation of the vessel width. The centerline itself is derived
as the characteristic function of an underlying signed medialness function, to enforce a tubular shape for the
segmented object, and evolves under shape and medialness constraints. Given a set of initial medial loci and
radii, this representation first allows for simultaneous recovery of the vessels centerlines and radii, thus enabling
surface reconstruction. Secondly, due to the topological adaptivity of the level set segmentation setting, it can
handle tree-like structures and bifurcations without additional junction detection schemes nor user inputs. We
discuss the shape parameters involved, their tuning and their influence on the control of the segmented shapes,
and we present some segmentation results on synthetic images, 2D angiographies, 3D rotational angiographies
and 3D-CT scans.
Keywords: vessel segmentation, tree-like structures, level sets, variational methods, shape constraint
Vascular tree segmentation is a challenging task for fully automated approaches and remains one of the most