Matching of irreversibly deformed images in microscopy based on piecewise monotone subgradient optimization using parallel processing

Abstract

Image registration tasks are often formulated in terms of minimization of a functional consisting of a data fidelity term penalizing the mismatch between the reference and the target image, and a term enforcing smoothness of shift between neighboring pairs of pixels (a min-sum problem). For registration of neighboring physical slices of microscopy specimens with discontinuities, Janacek [1] proposed earlier an L1-distance data fidelity term and a total variation (TV) 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 et. aI. [10] presented an equivalent transformation of max-sum problems to the problem of minimizing a dual quantity called problem power, which is - contrary to the original max-sum (min-sum) functional - convex (concave). We applied Schlesinger's approach to develop an alternative, multi-label, L1-TV minimization algorithm by maximization of the dual problem. We compared experimentally results obtained by the multi-label dual solution with a graph cut based minimization. For Schlesinger's subgradient algorithm we proposed a step control heuristics which considerably enhances both speed and accuracy compared with known stepsize strategies for subgradient methods. The registration algorithm is easily parallelizable, since the dynamic programming maximization of the functional along a horizontal (resp. vertical) gridline is independent of maximization along any other horizontal (resp. vertical) gridlines. We have implemented it both on Core Quad or Core Duo PCs and CUDA Graphic Processing Unit, thus significantly speeding up the computation.