The performance of braided ceramic matrix composites has been shown to depend on the spatial arrangement of tows; therefore, a new class of tools is required to measure irregularities in the composite architecture for components with intricate geometries. We report a scalable and robust reconstruction technique built upon stereoscopic digital image correlation that is able to efficiently measure the position of tows in arbitrarily shaped composites. This method was applied to triaxially braided ceramic matrix composite tubes intended for use as nuclear fuel cladding, which revealed both long-range systematic tow packing defects associated with the manufacturing process and short-range intrinsic defects due to the braid architecture. These findings suggested that the character of tow spacing variation in braided composite tubes was substantially more complex than in planar woven composites. These measurements are expected to lead to improved processing of braided composites and to facilitate the design of statistically representative virtual specimens for finite element modeling.