Despite the intrinsically stochastic nature of damage, sensory organs recapitulate normal architecture during repair to maintain function. Here we present a quantitative approach that combines live cell-lineage tracing and multifactorial classification by machine learning to reveal how cell identity and localization are coordinated during organ regeneration. We use the superficial neuromasts in larval zebrafish, which contain three cell classes organized in radial symmetry and a single planar-polarity axis. Visualization of cell-fate transitions at high temporal resolution shows that neuromasts regenerate isotropically to recover geometric order, proportions and polarity with exceptional accuracy. We identify mediolateral position within the growing tissue as the best predictor of cell-fate acquisition. We propose a self-regulatory mechanism that guides the regenerative process to identical outcome with minimal extrinsic information. The integrated approach that we have developed is simple and broadly applicable, and should help define predictive signatures of cellular behavior during the construction of complex tissues.