## Materials and Methods
### Data Description: the SURIVSHNO 2019 Challenge Video and Its Critical Issues
In videos, because of the limited frame rate (N.B., limited with respect to the rotating speed of the object), a rotating object like a fan or a wheel looks like turning in reverse or too slowly. A similar effect is probably experienced by any human beings in the form of an optical illusion called \"wagon-wheel effect\" which may occur even under truly continuous illumination because of the human visual perception. Sampling at 30 fps, in accordance with the Nyquist sampling theorem, allows to correctly picture phenomena which are bandlimited to half the sampling rate (i.e., 15 Hz, the Nyquist frequency) without aliasing. In the SURIVSHNO 2019 video, the fan starts from a standstill and accelerates up to values lower than the Nyquist frequency, so that temporal aliasing does not occur. Nevertheless, by looking at the video, the optical illusion of a reverting direction of rotation occurs anyway as the brain cannot recognize the 10 equal blades of the fan, so the exceeding of 1,5 Hz causes a reversal of the perceived direction of rotation. A final issue is related to the autofocus of the camera. When taking photos, in fact, a convex lens is used in the camera to focus incoming light onto a photo-sensor array (e.g., a Complementary metal-oxide-semiconductor-CMOS-photo-sensor). In order to ensure crisp and clear images, the optical system commonly uses a control system and a motor to optimize the distance between the lens and the sensor. This can obviously lead to distortions of the image during the video. To summarize, three main issues should be tackled:  
* Spatial Aliasing related to the rolling shutter effect,
* Temporal Aliasing due to the 30-fps sampling rate given the 10 equal blades of the fan,
* Additional autofocus distortions. Nevertheless, a workaround can be found to simplify things. First, the spatial aliasing occurs when the object moves faster than a limit speed dictated by the rolling shutter clock. Being the fan is rotating around its center, the higher the distance from the center, the higher the tangential speed, so that, focusing on a part of the image very near to the center (i.e., the fan-locking screw head), the spatial aliasing effect is minimal. Figure 2: The thousandth frame of the video. The rolling shutter effect is highlighted as a deformation of the blades. Second, the temporal aliasing, in this case, is more a visualization issue rather than a real problem for the analysis. The fan speed, in fact, is always lower than 10 Hz, so that if the attention is brought to a feature that occurs just once per revolution (i.e., the 8.8 logo on the fan-locking screw head) rather than the blades (which are 10 and not distinguishable), no temporal aliasing occurs. Finally, the autofocus distortions can be accounted for, together with other perspective distortions by implementing the adaptive TM introduced in the following sections. In the SURVISHNO 2019 challenge video acquisition, in fact, the camera was almost but not perfectly aligned to the fan axis, so that, during the revolution, the center of rotation moves in a small region, while the image undergoes slight deformations.