Implicit vessel surface reconstruction for visualization and CFD simulation

Abstract

Objective: Accurate and high-quality reconstructions of vascular structures are essential for vascular disease diagnosis and blood flow simulations.These applications necessitate a trade-off between accuracy and smoothness. An additional requirement for the volume grid generation for Computational Fluid Dynamics (CFD) simulations is a high triangle quality. We propose a method that produces an accurate reconstruction of the vessel surface with satisfactory surface quality. Methods: A point cloud representing the vascular boundary is generated based on a segmentation result. Thin vessels are subsampled to enable an accurate reconstruction. A signed distance field is generated using Multi-level Partition of Unity Implicits and subsequently polygonized using a surface tracking approach. To guarantee a high triangle quality, the surface is remeshed. Results: Compared to other methods, our approach represents a good trade-off between accuracy and smoothness. For the tested data, the average surface deviation to the segmentation results is 0.19 voxel diagonals and the maximum equi-angle skewness values are below 0.75. Conclusions: The generated surfaces are considerably more accurate than those obtained using model-based approaches. Compared to other model-free approaches, the proposed method produces smoother results and thus better supports the perception and interpretation of the vascular topology.Moreover, the triangle quality of the generated surfaces is suitable for CFD simulations.

Implicit Reconstruction of Vasculatures Using Bivariate Piecewise Algebraic Splines

“…As discussed in the last section, the accuracy and the smoothness of the reconstructed surface from the discrete point sets needs to be balanced. Generally, our method can achieve highly accurate reconstructed surface, of which the mean deviation is as small as 0.20 mm, which is quite smaller than the mean distance (0.39 mm) presented in [6] and the median of the deviations (0.30 mm) presented in [19]. Furthermore, the mean deviation is much less than half of the mean diagonal voxel size (1.28 mm) of the used datasets (0.96 mm for the CTA carotid artery dataset, 1.05 mm for the MRA cerebral vessel dataset, 1.17 mm for the MRA abdominal aorta dataset, and 1.94 mm for the segmented liver portal vein).…”

“…9 shows a detailed look at the reconstructed cerebral vessels. As is presented in the gure, the isosurface rendering of the binary data (top left) suffers from strong aliasing artifacts like staircases, which has a strong divergence with real vessels and might hamper the visual interpretation of the vessel surface [19]. Although the segmentation result based on level set method [37] (top right) can achieve certain smooth surface when compared to the binary data, the visualization result is still poor, and needs further smoothing steps.…”

“…The reconstruction method based on MPUI (bottom left) can construct smooth surface with certain visual quality. However, due to the complex and ne nature of most vascular tree, the quality of the resulting surfaces is still not good enough and has to be improved using an additional remeshing step [19], which subsequently increases the effort required from the reconstruction process and inevitably introduces further errors. In contrast, our approach can achieve superior visual quality and produce smooth transitions at branchings (bottom right).…”

“…Schumann et al [5], [19] have proposed a method based on multi-level partition of unity (MPU) implicits [20], which provides a superior quality of visualizing results when compared to CESN. The basic principle of this method is to convert the segmentation result into a point cloud that is transformed into a surface representation by means of MPU Implicits, which ts a smooth quadratic surface locally to each local subdataset.…”

“…Generally, the implicit surfaces are able to represent a given geometry smoothly without explicitly constructing the geometry [1]. However, due to the complex and ne nature of most vascular tree, the quality of the resulting surfaces is usually poor and has to be improved using an additional remeshing step [19], either based on parameterization, or tting of subdivision surfaces [21], which subsequently increases the effort required from the reconstruction process and inevitably introduces further errors.…”