For registration of neighboring physical slices of microscopy specimens with discontinuities, Janáček proposed earlier an L1-based data fidelity term and a total variation (TV) based smoothness term, and used a graph-cut based iterative steepest descent algorithm for minimization.

The L1-TV functional is in general non-convex, and thus a steepest descent algorithm is not guaranteed to converge to the global minimum. Schlesinger presented a transformation of min-sum problems to their dual problem, which is - contrary to the original min-sum functional - convex. We applied Schlesinger's approach to an alternative, multi-label, L1-TV minimization by maximization of the dual problem. We compared experimentally the graph cut based minimization with the multi-label dual solution.

For Schlesinger´s subgradient algorithm we proposed a step control heuristics which leads to acceptable speed. It turns out that the graph-cut based solution is about three times faster than a parallel implementation of the iterative solution based on the maximization of the dual problem, but the dual maximization achieves consistently better matching of the images in terms of lower values of the L1-TV functional, and sometimes yields visually better results.