Aliasing-Aware Conformal Sets for Motion Estimation: Distribution-Free Uncertainty at the Identifiability Boundary
Keywords:
Optical flow, motion estimation, aliasing, sampling theory, identifiability, conformal prediction, distribution-free uncertainty quantification, set-valued prediction, coverage guarantees.Abstract
Abstract—Motion estimation between two frames is fundamentally limited when the imaged surface is periodic: a block of period p produces a correlation surface that repeats every p pixels, so the true displacement is knowable only modulo p from the periodic component alone. Aperiodic surface detail can in principle resolve which alias is correct, but the resolving evidence decays with displacement and eventually falls below the sensor noise floor, past which no point estimator classical or deep can recover the true motion, because the branch is information-theoretically ambiguous. Rather than hide this ambiguity behind a single confident number, we ask a different question: can an estimator report a small, honest set of candidate motions that is guaranteed to contain the truth? We formalize the periodic-motion ambiguity as a structured alias lattice, derive an identifiability radius that separates the resolvable and unresolvable regimes, and build the Aliasing-Aware Conformal Set (AACS): a split-conformal predictor that uses a top-relative margin nonconformity score and Mondrian conditioning on an observable confidence gap. AACS inherits a distribution-free, finite-sample coverage guarantee while adapting its set size to the local difficulty of the scene---collapsing to a singleton when motion is identifiable and widening only when it must. In a controlled benchmark of 1140 image pairs synthesized from real USC-SIPI textures, AACS attains its target coverage while producing sets 37% smaller than a fixed-threshold baseline at matched coverage, recovers the block period blindly to within 0.00 px of ground truth, and cleanly exposes the identifiability boundary. We stress that these are controlled synthetic-scene experiments engineered to isolate the aliasing phenomenon, not standard optical-flow benchmark scores; we provide a full reproducibility protocol so the effect can be re-derived independently.