Codimension - Two Geodesic Active Contours for the Segmentation of Tubular Structures

Curve evolution schemes for segmentation, implemented with level set methods, have become an important approach in computer vision. Previous work has modeled evolving contours which are curves in 2D or surfaces in 3D. Our ob- jective is to explore recent mathematical work enabling the evolution of manifolds of higher co-dimension. We consider 1D curves in 3D (codimension-two) for the application of automatically segmenting blood vessels in volumetric mag- netic resonance angiography (MRA) images. This paper de- scribes the theoretical foundations of our system, CURVES, then provides segmentation results compared against seg- mentations obtained interactively by a neurosurgeon. Seg- mentations of bronchi in lung computed tomography (CT) scans are also presented. The new experiments, compar- isons to manual segmentations, and sample comparison to the use of a codimension-one regularization force are the primary contributions of this report.