  We propose and analyze a constrained level-set method for semi-automatic
image segmentation. Our level-set model with constraints on the level-set
function enables us to specify which parts of the image lie inside respectively
outside the segmented objects. Such a-priori information can be expressed in
terms of upper and lower constraints prescribed for the level-set function.
Constraints have the same conceptual meaning as initial seeds of the popular
graph-cuts based methods for image segmentation. A numerical approximation
scheme is based on the complementary-finite volumes method combined with the
Projected successive over-relaxation method adopted for solving constrained
linear complementarity problems. The advantage of the constrained level-set
method is demonstrated on several artificial images as well as on cardiac MRI
data.
