Video shutter angle estimation using optical flow and linear blur

TL;DR

This work tackles the problem of estimating the video shutter angle, or exposure fraction $\alpha$, from unconstrained motion-rich clips by jointly exploiting dense optical flow and per-pixel linear motion blur estimates. The method derives $\alpha$ as the ratio of blur to flow magnitudes, applied within reliably chosen patches, and aggregates patch- and frame-level estimates into a global value $\alpha_{\text{glob}}$ via medians. The authors validate on the Beam-Splitter Dataset, achieving an MAE of $0.039$ and demonstrating a forensic use case for detecting tampering through frame deletion or insertion, while also analyzing limitations at very low $\alpha$ due to blur estimator discretization. This approach advances physics-based video forensics and blur-aware motion reasoning by enabling robust exposure-fraction estimation in general video sequences.

Abstract

We present a method for estimating the shutter angle, a.k.a. exposure fraction - the ratio of the exposure time and the reciprocal of frame rate - of videoclips containing motion. The approach exploits the relation of the exposure fraction, optical flow, and linear motion blur. Robustness is achieved by selecting image patches where both the optical flow and blur estimates are reliable, checking their consistency. The method was evaluated on the publicly available Beam-Splitter Dataset with a range of exposure fractions from 0.015 to 0.36. The best achieved mean absolute error of estimates was 0.039. We successfully test the suitability of the method for a forensic application of detection of video tampering by frame removal or insertion

Figures (4)

• Figure 1: Histograms and box plots of $\hat{\alpha}$ estimates on clips from the BSD dataset with $\varepsilon = \{0.001\,s ,\,0.002\,s,\,0.003\,s\}$. Estimation parameters $\varphi = 5\degree$, $D = 30$. Note that only the (0, 0.2) range is displayed.
• Figure 2: Histograms and box plots of $\hat{\alpha}$ estimates on clips from the BSD dataset with $\varepsilon = \{0.008\,s ,\,0.016\,s,\,0.024\,s\}$. Estimation parameters $\varphi = 5\degree$, $D = 30$. Note that only the (0, 0.4) range is displayed.
• Figure 3: Example patch with nearly perfect agreement with the assumption expressed by \ref{['eq:alpha_estimation']}. The blur kernel and optical flow estimates are collinear, $\hat{\alpha}_{patch} = 0.26$ and $\alpha = 0.24$. The selected patch from frame $F_{38}$, video clip no. 16 from BSD-16ms subset. Estimation parameters $\varphi = 5\degree$, $D = 30$.
• Figure 4: A failure case of linear blur kernel estimates in a dark, low contrast area with no texture; $\hat{\alpha}_{patch} = 0.065$, $\alpha = 0.015$. The linear blur kernel estimator fails to accurately model the blur magnitudes, resulting in an inaccurate estimate of $\hat{\alpha}_{patch}$. Since the kernels still satisfy the orientation and magnitude constraints defined in \ref{['eq:cosine_constraint']}, \ref{['eq:blur_flow_length_constraints']}, \ref{['eq:minimum_length_constraint']}, they are considered valid. Similar situations remain challenging for both the linear blur kernel estimator and the method. Frame $F_{52}$, estimation parameters $\varphi = 5\degree$, $D = 30$. Video clip no. 74 from BSD-1ms subset.