Oriented smoothness constraints for adaptive active contour models

We show how introducing oriented smoothness constraints results in a novel class of active contour models for segmentation extending standard isotropic inhomogeneous membrane/thin-plate stabilizers. These constraints, equivalent to directional adaptive stretching and bending densities, are expressed as 2nd-order positive definite tensors which are invariant with respect to rigid motions in the image plane and preserve the differential properties (metric and curvature) of the intensity surface. Optimization of the model is discussed in details. Its accuracy and robustness have been established on MR cardiac images.