A smoothed Monte-Carlo estimator of level-crossing density, derived via the co-area formula, serves as a grid-free auxiliary loss for INRs, matching but not beating frequency-domain baselines on natural images and winning on homogeneous textures.
Czarnecki, Simon Osindero, Max Jaderberg, Grzegorz ´Swirszcz, and Razvan Pascanu
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Level-Crossing Density as a Mesh-Free High-Frequency Auxiliary Loss for Implicit Neural Representations
A smoothed Monte-Carlo estimator of level-crossing density, derived via the co-area formula, serves as a grid-free auxiliary loss for INRs, matching but not beating frequency-domain baselines on natural images and winning on homogeneous textures.