This thesis studies the perception and reasoning of geometric elements in architectural modeling. We build a reconstruction and generation system for more faithfully reconstructing building models from sensor data or generating realistic floorplan models with user controls. The technical challenges include understanding basic geometric primitives (e.g., points, lines, planes) and their relationships (e.g., parallelism, perpendicularity, angles between lines, distances between primitives), that are easily interpretable by humans. We investigate 1) non-learnable techniques for assembling buildings geometric primitives; 2) neural relational architectures for inferring building topology; 3) neural generative architectures for creating house layouts under user constraints; 4) incorporating more realistic user constraints for obtaining production-level performance on generating house layouts; and 5) the unsupervised discovery of structural regularities for architecture modeling.
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