**Topology-based Phase Estimation for extracting ENF signal from digital video**

**Abstract** [pdf]

Using electrical network frequency (ENF) for video forensics has been intensely studied in recent years. The ENF signal found in videos has twice the electrical frequency (100 Hz or 120 Hz), whereas frame rates of common videos are relatively low (around 30 Hz). To extract ENF signal from video, state- of-the-art works exploit the rolling shutter effect. However, this method has a constraint that the region affected by the flickering light has to be large enough to contain all the information which light leaves at the pixels. As these regions are only part of the scene in many cases, it is hard to take advantage of the rolling shutter effect. In this paper, we propose a novel method to extract ENF signals by topological approach without utilizing the rolling shutter effect. Based on the fact that the topological representation of the possible outcomes is in the form of a closed-loop, we obtain the phase angles of each frame using dimensionality reduction algorithms. We convert the phase angles into the frequency values based on the prior knowledge about the nominal frequency of ENF and the frame rate of the video. We tested three different dimensionality reduction algorithms (i.e., PCA, UMAP, and t-SNE), and t-SNE shows the best performance achieving root-mean-square error (RMSE) of 0.0036 Hz.

# Estimating ENF from Changes in light

When we see the light bulb shown in a video filmed in everyday life, we can notice that the brightness of the light around the light bulb changes over time. Since the ENF which is the frequency of the power grid, affects the electrically powered light source, ENF can be estimated from these changes in light, namely the intensity of the pixels.

Therefore, in this paper, we propose **a novel method of estimating the phase angle of light through this change** and then estimate the ENF using the phase angle.

**Our intuition is that the phase angle can be estimated through the changes in light intensity in the image!!**

The possible outcomes (frame images) are in a closed set and it is deterministic to the phase angle.

There are 3 properties of this topology:

1) The phase angle of light is continuous

2) The same phase angles of this topology will result the same pixel images

3) The differences in phase angles produces different images; the larger differences in phase angles, the more differences in images.