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

Video Motion Magnification (VMM) reveals imperceptible dynamics but often suffers from structural inconsistencies under complex geometric transformations. Existing learning-based methods generally face a trade-off between the limited global context of CNNs and the high computational cost of Transformers. In addition, current training protocols, largely dominated by simple linear motion, fail to capture the geometric and imaging complexities encountered in real-world videos. To address these issues, we propose GeoMag, a geometric-aware VMM framework built upon State Space Models to achieve globally consistent motion amplification with linear complexity. We further construct Geo-200K, a large-scale synthetic dataset that introduces rich geometric transformations together with sensor-realistic degradations, improving the diversity and realism of training signals. Extensive experiments on synthetic and real-world benchmarks show that GeoMag consistently outperforms prior methods in visual fidelity and computational efficiency, while producing fewer artifacts and better structural consistency.

Uniform frame sampling can miss brief evidence in sparse-event videos when the VLM sees only K frames. We propose EARS (Evidence-Aware Retrieval via Sound and motion), a training-free, query-free front-end that ranks frames using optical-flow motion and audio energy, then applies temporal non-maximum suppression for diversity. The evidence score alone has frame-level AP 0.39; used only to select frames for the VLM, EARS with temporal diversity reaches localization AP 0.94, compared with 0.88 under Uniform sampling. In the updated matched study, at K = 1 EARS reaches XD-subset F1 0.660 versus 0.614 for centered Uniform (the paired interval includes zero); earlier backbone studies use separate protocols. On mostly-silent UCF-Crime, however, EARS slightly trails Uniform. A single configuration is used across both benchmarks; the new controls do not repeat the original held-out search. EARS therefore targets low-budget videos whose salient evidence aligns with motion or audio; on dense narratives or stealthy events, uniform or semantic selection remains preferable, and cheap modality statistics cannot reliably route between them. Code: https://github.com/mikeslin-ir/EARS

Motion blur arises from the temporal integration of a continuous sharp signal over a finite exposure window, yet existing learning-based methods sidestep this physical model and predict only the sharp signal itself: most single-image deblurring methods recover a single frame at the exposure center, while blur-to-video methods predict a fixed set of frames. We introduce PickMoment, a continuous-time reformulation that directly learns the interval-mean blur over arbitrary sub-intervals of the exposure with a single deterministic model. Drawing an analogy to MeanFlow's average-velocity formulation, we train the model with three supervisions derived from the blur integral: an empirical reconstruction loss from available subframes, an additivity loss that enforces self-consistency across overlapping sub-intervals, and a sharp-frame loss anchored at the zero-interval limit. A single trained model unifies single-image deblurring, blur-to-video generation, and continuous-time pick-a-moment recovery as different queries to the same network, with no separate training for each task. Our PickMoment achieves state-of-the-art performance among generative-based deblurring methods on GoPro and HIDE while competitive against restoration-based methods on RealBlur, and the highest per-frame fidelity on GoPro-7 blur-to-video, all in a single forward pass without iterative sampling.