Derives explicit geometry-dependent radii R_m < S_m that sharply separate smeary from non-smeary rotationally symmetric and general absolutely continuous measures on S^m, with constructions showing the thresholds are tight for m ≥ 4.
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A literature survey that compiles ten years of 3D scene completion research, builds a taxonomy of representation paradigms, and outlines a future research agenda.
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Sharp Support Thresholds for Smeariness of Absolutely Continuous Measures on Spheres
Derives explicit geometry-dependent radii R_m < S_m that sharply separate smeary from non-smeary rotationally symmetric and general absolutely continuous measures on S^m, with constructions showing the thresholds are tight for m ≥ 4.