A Variational Surface Deformation and Subdivision-Based Modeling Framework for Noisy and Small n-Furcated Tube-Like Structures

Abstract

It is challenging to construct an accurate and smooth mesh for noisy and small n-furcated tube-like structures, such as arteries, veins, and pathological vessels, due to tiny vessel size, noise, n -furcations, and irregular shapes of pathological vessels. We propose a framework by dividing the modeling process into mesh construction and mesh refinement. In the first step, we focus on mesh topological correctness, and just create an initial rough mesh for the n-furcated tube-like structures. In the second step, we propose a variational surface deformation method to push the initial mesh to structure boundaries for positional accuracy improvement. By iteratively solving Euler-Lagrange equations derived from the minimization of the shell and distance energies, the initial mesh can be gradually pushed to the boundaries. A mesh dilation method is proposed to prevent the extremely deviated initial mesh moving toward wrong boundaries. We combine deformation and subdivision to propose a coarse-to-fine modeling framework for the improvement of efficiency and accuracy. Experiments show our method can construct an accurate and smooth mesh for noisy and small n-furcated tube-like structures, and it is useful in hemodynamics, quantitative measurement, and analysis of vessels.