Modeling of Sparsely Sampled Tubular Surfaces Using Coupled Curves

Abstract: We present a variational approach to simultaneously trace the axis and determine the thickness of 3-D (or 2-D) tubular structures defined by sparsely and unevenly sampled noisy surface points. Many existing approaches try to solve the axis-tracing and the precise fitting in two subsequent steps. In contrast to this our model is initialized with a small cylinder segment and converges to the final tubular structure in a single energy minimization using a gradient descent scheme. The energy is based on the error of fit and simultaneously penalizes strong curvature and thickness variations. We demonstrate the performance of this closed formulation on volumetric microscopic data sets of the Arabidopsis root tip, where only the nuclei of the cells are visible.