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We present a framework for segmenting and storing filament networks from scalar volume data. Filament networks are encountered more and more commonly in biomedical imaging due to advances in high-throughput microscopy. These data sets are characterized by a complex volumetric network of thin filaments embedded in a scalar volume field. High-throughput microscopy volumes are also difficult to manage since they can require several terabytes of storage, even though the total volume of the embedded structure is much smaller. Filaments in microscopy data sets are difficult to segment because their diameter is often near the sampling resolution of the microscope, yet these networks can span large regions of the data set. We describe a novel method to trace filaments through scalar volume data sets that is robust to both noisy and undersampled data. We use graphics hardware to accelerate the tracing algorithm, making it more useful for large data sets. After the initial network is traced, we use an efficient encoding scheme to store volumetric data pertaining to the network.