Interpolating Orientation Fields: An Axiomatic Approach

We develop an axiomatic approach of vector field interpolation, which is useful as a feature extraction preprocessing step. Two operators will be singled out: the curvature operator, appearing in the total variation minimisation for image restoration and inpainting/disocclusion, and the Absolutely Minimizing Lipschitz Extension (AMLE), already known as a robust and coherent scalar image interpolation technique if we relax slightly the axioms. Numerical results, using a multiresolution scheme, show that they produce fields in accordance with the human perception of edges.