Optical flow-based representation for video action detection - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 278

(9)
(10)
Shi-Tomasi algorithm uses the eigenvalues of the Harris matrix. In this context, it difers
from Harris corner detector. The algorithm assumes that minimum of two eigenvalues of Har-
ris matrix determines the cornerness ( C ) of the point. Therefore, the corner decision is done
using the eigenvalues of the matrix. Shi-Tomasi algorithm gives more accurate results com-
pared with Harris detector. The algorithm is also more stable for tracking.
For estimating optical flow, Lucas-Kanade algorithm is selected [ 27 ] . With videos having
suicient information and excluding noise, Lucas-Kanade algorithm is successful. The al-
gorithm works for the corners obtained from Shi-Tomasi algorithm. Basically, the following
function should be minimized for each detected corner point as seen in differential ap-
proaches:
(11)
With suitable δx and δy , optical flow vectors can be obtained. But, aperture problem is not
solved yet with this minimization. The solution approach for aperture problem is reflected to
the function definition ε ( δx , δy )as follows:
(12)
Summation on the x − y direction is a solution for the aperture problem. By using a window
w centering the point ( x , y ), the estimation of optical flow of the point is extended with the
neighboring points.