Finding the Minimum-Cost Path Without Cutting Corners

Applying a minimum-cost path algorithm to find the path through the bottom of a curvilinear valley yields a biased path through the inside of a corner. DNA molecules, blood vessels, and neurite tracks are examples of string-like (network) structures, whose minimum-cost path is cutting through corners and is less flexible than the underlying centerline. Hence, the path is too short and its shape too stiff, which hampers quantitative analysis. We developed a method which solves this problem and results in a path whose distance to the true centerline is more than an order of magnitude smaller in areas of high curvature. We first compute an initial path. The principle behind our iterative algorithm is to deform the image space, using the current path in such a way that curved string-like objects are straightened before calculating a new path. A damping term in the deformation is needed to guarantee convergence of the method.