Continuous Maximal Flows and Wulff Shapes: Application to MRFs.

Area of Science:

• Computer Vision
• Image Processing
• Computational Mathematics

Background:

• Low-level vision problems benefit from convex and continuous energy formulations for efficient global optimization.
• The isotropic capacity-based maximal flow framework is well-established for such problems.

Purpose of the Study:

• To extend the continuous maximal flow framework to the anisotropic setting.
• To develop a simple and efficient minimization procedure for anisotropic energy formulations.
• To unify this approach with Markov random field formulations for enhanced prior incorporation.

Main Methods:

• Leveraging convex analysis for deriving minimization procedures.
• Extending the continuous, isotropic capacity-based maximal flow to anisotropic settings.
• Unifying the anisotropic maximal flow with convex continuous Markov random field formulations.

Main Results:

• A very simple and efficient minimization procedure for anisotropic settings was derived.
• Key properties, such as globally optimal binary results via thresholding, carry over.
• The approach was unified with Markov random fields, allowing more general smoothness priors.

Conclusions:

• The proposed anisotropic maximal flow framework offers an efficient method for solving low-level vision problems.
• The framework supports globally optimal binary solutions and incorporates general smoothness priors.
• Demonstrated capabilities through dense stereo vision results.