Optical flow-based representation for video action detection - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 282

(16)
Equation (9) calculates the weighted distance for each angular interval of each frame.
Weight concept, here, is the weight of the frame to the segment. The weighted distances are
summed up and averaged according to the number of vectors in the segment. The resulting
value is the weighted velocity of the frames.
When this approach is analyzed, one can notice that another problem occurs. As the velocity
is weighted according to the number of vectors in the given angle interval of the frame, the
noise or errors resulting from optical flow estimation and insignificant number of vectors in
one dimension unfairly dominate the values of that feature. In order to avoid this problem,
thresholding is used as a common way of noise reduction. Therefore, a threshold function de-
pending on the frame and angle interval is proposed to be used in the weighted frame velocity
function.
(17)
The above function is based on the ratio of the optical flow vectors of the given angle interval
for the given frame. This ratio's being smaller or bigger according to the threshold value C dir-
ectly determines the result of the function. At this point, estimation of threshold becomes im-
portant. The estimation will be done during the classification phase. Thus, the weighted frame
velocity function is updated accordingly.
(18)