Extending Graph-Cut to Continuous Value Domain Minimization

In this paper we propose two methods for minimizing objective functions of discrete functions with continuous value domain. Many practical problems in the area of computer vision are continuous-valued, and discrete optimization methods of graph-cut type cannot be applied directly. This is different with the proposed methods. The first method is an add-on for multiple-label graph-cut. In the second one, binary graph-cut is firstly used to generate regions of support within different ranges of the signal. Secondly, a robust error minimization is approximated based on the previously determined regions. The advantages and properties of the new approaches are explained and visualized using synthetic test data. The methods are compared to ordinary multi-label graph-cut and robust smoothing for the application of disparity estimation. They show better quality of results compared to the other approaches and the second algorithm is significantly faster than multi-label graph-cut.