298 A. Sarrafi et al. Fig. 29.2 Three snap shots of the Lucas-Kanade point tracking on the cantilever beam Table 29.1 First four natural frequencies of the beam estimated by different computer vision algorithms Mode number Lucas-Kanade (Hz) Hungarian registration (Hz) Particle filter (Hz) 1 36.62 35.32 35.55 2 222.36 221.44 219.78 3 645.99 635.99 637.56 4 720 690.25 694.39 be extracted since the tracking pattern matches with true displacements on the beam. In summary Lucas-Kanade algorithm is computationally intensive since the motion filed needs to be calculated at each pixel. It is also sensitive to noise and external disturbances such as lighting variations, since the coefficients of aperture problem (@I @x , @I @y ,It) are extracted by means of applying 2D discrete wavelets on image intensity I(x, y, t) which causes the noise to propagates through the analysis [18, 19]. Therefore, the Lukas-Kanade is not the first choice for structural dynamics identification in comparison with other point tracking and computer vision techniques, but it is able to extract the natural frequencies with in an acceptable range of uncertainty Table 29.1. 29.4 Hungarian Registration Algorithm In previous section the point tracking was performed by estimating the optical flow in sequence of images, and the interest points were being moved with respect to the motion vectors. Unlike Lucas-Kanade point tracker Hungarian registration algorithm does not require the computation of the motion field which is a computationally intensive task. In order to apply Hungarian registration algorithm points with specific criteria are found by means of fundamental image processing algorithms, this approach is quite similar to the procedure which is followed by conventional point tracking algorithms. In this case study the black dots on the beam are considered as the specific points and by tuning the parameters computers are able to detect them at each frame. Detecting the points at each frame does not mean that the point tracking is performed since the point are not labeled yet, and further analysis should be considered to find out that which point at each frame corresponds to which point at another frame. Once the correspondence between the points are found the point tracking problem is solved completely. In order to find the correspondence between the points from one frame to another Hungarian registration algorithm [20] is employed. The underlying assumption in this analysis is that since the videos are captured with high-speed cameras at 2500 frames per second (fps) and the subjected scene is a vibrating beam the displacements of the points in between two consecutive frames are relatively small. Therefore, by minimizing the Euclidian distance between the sets of point in two consecutive frames the correspondence between the points could be found easily. In other words, two points in two consecutive frames with minimum Euclidian distance corresponds to each other and should have the same label. This procedure should be followed from the first frame of the sequence to the last frame till all the correspondence information is recovered.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==