Microvascular networks are challenging to model because these structures are currently near the diffraction limit for most advanced three-dimensional imaging modalities, including confocal and light sheet microscopy. This makes semantic segmentation difficult, because individual components of these networks fluctuate within the confines of individual pixels. Level set methods are ideally suited to solve this problem by providing surface and topological constraints on the resulting model, however these active contour techniques are extremely time intensive and impractical for terabyte-scale images. We propose a reformulation and implementation of the region-scalable fitting (RSF) level set model that makes it amenable to three-dimensional evaluation using both single-instruction multiple data (SIMD) and single-program multiple-data (SPMD) parallel processing. This enables evaluation of the level set equation on independent regions of the data set using graphics processing units (GPUs), making large-scale segmentation of high-resolution networks practical and inexpensive. We tested this 3D parallel RSF approach on multiple data sets acquired using state-of-the-art imaging techniques to acquire microvascular data, including micro-CT, light sheet fluorescence microscopy (LSFM) and milling microscopy. To assess the performance and accuracy of the RSF model, we conducted a Monte-Carlo-based validation technique to compare results to other segmentation methods. We also provide a rigorous profiling to show the gains in processing speed leveraging parallel hardware. This study showcases the practical application of the RSF model, emphasizing its utility in the challenging domain of segmenting large-scale high-topology network structures with a particular focus on building microvascular models.