Properties of crystalline and amorphous materials are characterized by the underlying long-range and local crystalline order. Deformations and defects are structural hallmarks of plasticity, ice formation, and crystal growth mechanisms. Partitioning topological networks into constituent crystal building blocks, which is the basis of topological identification criteria, is an intuitive approach for classification in both bulk and confinement. However, techniques reliant on the convex hull for assigning orientations of component units fail for non-convex blocks. Here, we propose a new framework, called Topological Unit Matching (TUM), which exploits information from topological criteria for an efficient shape-matching procedure. TUM is a general family of algorithms, capable of quantifying deformations and unambiguously determining grains of bulk and confined ice polymorphs. We show that TUM significantly improves the identification of quasi-one-dimensional ice by including deformed prism blocks. We demonstrate the efficacy of TUM by analyzing supercooled water nanoparticles, amorphous ice, and phase transitions in an ice nanotube. We also illustrate the superiority of TUM in resolving topological defect structures with minimal parameterization.
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