Fractional-Order Adaptive Motion Magnification: Phase-Reliability Weighting for Noise-Constrained Video Amplification

RESUMO

Eulerian video amplification boosts sub-pixel motion by band-pass filtering per-pixel intensity traces and applying a uniform gain. That gain ignores local structure, so sensor noise is amplified together with the signal, especially in textureless regions where the monogenic phase is unreliable. We propose FrAM (Fractional-order Adaptive Motion Magnification), a pipeline developed first offline and then as a causal stream. It replaces the constant temporal gain with a Grünwald--Letnikov derivative of fractional order, giving continuous control over high-frequency emphasis, and replaces the uniform spatial gain with a per-pixel weight derived from the local amplitude of the monogenic signal. On a controlled synthetic sequence split into textured and flat halves, FrAM matches the amplification of the Eulerian baseline while keeping flat-region temporal noise at the input level. The reduction holds across an eightfold range of input noise levels. Real videos show improved spatial selectivity and lower background noise in every case. The causal reformulation cuts the per-frame cost by two orders of magnitude, reaching 69\,fps at 640$\times$480.