发表机构
University of Oviedo（奥维耶多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出FrAM算法，用分数阶Grünwald–Letnikov导数和单演信号局部幅度加权替代传统欧拉放大的恒定增益，可在保持放大效果的同时降低平坦区噪声，且因果版本计算成本大幅降低。
AI 中文摘要
欧拉视频放大技术通过对逐像素强度轨迹进行带通滤波并应用统一增益来增强亚像素运动，但该增益忽略了局部结构，导致传感器噪声与信号一同被放大，尤其在单演相位不可靠的无纹理区域更为明显。本文提出FrAM（分数阶自适应运动放大，Fractional-order Adaptive Motion Magnification），该流程先离线开发后转化为因果流，它将恒定时间增益替换为分数阶的Grünwald–Letnikov导数，实现对高频强调的连续控制，并将统一空间增益替换为基于单演信号局部幅度的逐像素权重。在被分为纹理区与平坦区的受控合成序列上，FrAM与欧拉基线的放大效果相当，同时保持平坦区时间噪声处于输入水平，该降噪效果在输入噪声水平的八倍范围内均成立；真实视频实验显示其在所有案例中均提升了空间选择性并降低了背景噪声，因果重构使每帧计算成本降低两个数量级，在640×480分辨率下达到69fps。
英文摘要
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.
Comments11 pages, 6 figures, 8 tables
