In this paper we deal with camera motion smoothing. We focus our attention on the case of video cameras mounted on a tripod. In such case, for each time t of the video sequence, camera motion configuration is provided by parameters : (1) P(t) (PAN) which represents the tripod vertical axis rotation, (2) T(t) (TILT) which represents the tripod horizontal axis rotation and (3) Z(t) (CAMERA ZOOM) the camera lens zoom setting. From these 3 parameter functions we can easily deduce (using tripod information), for each time t the camera calibration, that is, the camera intrinsic and extrinsic parameters which determine the position of the camera in the 3D space and the way 3D objects are projected in the camera projection plane (the CCD in the case of digital cameras).
Human being visual system is very sensitive to motion, and small perturbations over time of P(t), T(t) and Z(t) values produce small oscillations in the camera motion disturbing the observer. To remove such perturbations is a critical issue in applications like the inclusion of artificial graphic objects in real video sequence scenarios. To illustrate this phenomenon, we show the next real video sequence where a CTIM logo have been included. Each frame of this video sequence has been calibrated in an independent way using standard techniques. We have also added to P(t), T(t) and Z(t) a uniformly distributed noise up to 1% of their magnitude to illustrate how small perturbations can be very relevant perceptually for a human being. We can also observe that in frame number 5 (in the first second of the video sequence) and in frame 199 (in second 8 of the video sequence) the standard calibration method fails and we can observe a strong displacement of CTIM logo at these frames.
In this paper we propose to smooth P(t), T(t) and Z(t) functions by minimizing the following energy:
where is the time interval, are weights to balance the different components of the energy and is an standard calibration function which forces, for each time , that the projection of points be close to primitives detected in the image. In fact, when no time regularization is used, P(t), T(t) and Z(t) are usually estimated by minimizing independently for each time So, by using the proposed variational model, we introduce a time regularity condition in the video camera calibration procedure. In the next video we show the result obtained in the above video sequence after regularization using the proposed model. We can observe that oscillations are strongly reduced and the singularities of frames 5 and 199 are removed.
Next we present some graphics comparing original and smoothed P(t), T(t) and Z(t) functions for the above videos.
