# ROBUST VEHICLE TRACKING IN VIDEO IMAGES BEING TAKEN FROM A HELICOPTER

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3 if both sides of the equation are divided by a one obtains: I xu + I yv + I t + a 1 a I(x1, y1, t1) + b a The parameters a 1 a = gt (8) and b are changed to k1 and k2 respectively. a I xu + I yv + I t + k 1I(x 1, y 1, t 1) + k 2 = g t (9) Non-linear least square approach (Teunissen 03) similar to the OFCE is used to solve the above equation by determining 4 parameter values u, v, a, and b compared to the above. Just the coefficient matrix, A = I x I y I 1 ], and parameter matrix, x = û ˆv k 1 k 2 ] T, are changed RESULT REDUNDANCY EXPLOITATION Figure 1. Displacement of each inside-car pixel in between two consecutive frames: the first and the second row show two consecutive images; the displacement result for each pixel is presented by an arrow Firstly, the optical flow parameters are calculated in the most coarse resolution. Then they are again calculated in a finer resolution using the scaled results of the previous level. This process is continued until the original scale is reached. When the displacements between pixels in the different successive frames are large, the chance of getting wrong results is increasing. Using the results from a coarser scale improves the results in the following step and reduces the chance of errors. The following algorithm describes the tracking process which is used in our implementation. for frame = 1 to Nframes do for scale = coarse to fine do repeat for feature type in {points, corner, boundary, region} do until the observation error is less than a threshold end end The result of each pixel is independent to the results of the other pixels. With this approach, a wrong result can not infect the other results. 4.1 LINEAR BRIGHTNESS MODEL Using a linear model is suggested in the case of changing brightness. Consequently the linear brightness model is substituted for the OFCE. This is translated mathematically as follows: I(x 1, y 1, t 1) = ai(x 2, y 2, t 2) + b (6) I(x 1, y 1, t 1) = a(i(x 1, y 1, t 1) + ai xu + ai yv + ag t + b) (7) None of the above-described methods can give the correct results independently in the case of changing brightness and shape. Therefore in this paper we try to provide the correct results as much as possible for each vehicle. According to the Equation 9 and OFCE, only a few pixels are required to solve these equation. These pixels should have the same displacement. In the conventional method the neighboring pixels in the specific window area are used to solve the equation OFCE. Here we have used another pixel as well. In the ideal case the results should be the same using different pixels. But because of unavoidable errors occurring in brightness and shape variations the results are in general not the same. Therefore we should decide whether a solution is correct or incorrect. Finally we get a correct value for the displacement using the redundancy in the results. The objective of this section is to describe how to provide the different results obtained using different methods, area based matching and optical flow, as well as using different pixels. 5.1 FEATURE SELECTION Extraction of car features is required to prepare the redundant exploitation of results. These features are car pixel, region, boundary, and corner. Displacement of each pixel inside the car is calculated using optical flow. The OFCE is provided by the optical flow elements. The 3 3 neighboring pixels are participating in the OFCE to calculate the displacement of the central pixel. The car region is extracted using a reference image (Hoogendoorn et al. 03). The first frame is reduced from the reference image being made median of whole frames. The car region is obtained by a threshold and using morphological operations. However the whole vehicle can not be detected by this method. It is highly dependent on the reference image and the selected threshold. Instability of the helicopter and variable weather conditions change the brightness of the road surface and the road lines, even in successive frames. Due to the brightness changing of fixed objects and similarity between dark car and the road surface brightness, a small threshold inserts a lot of errors and while a big threshold causes the dark cars to get lost. In this paper the dark cars are detected manually. The fully automatic detection of vehicles is suggested for the future. The car boundary is extracted from the region by a morphological operation. The extracted car-regions are eroded by structural

5 Figure 2. Problems: similar brightness (top left); similar texture (top right); ambiguity in edges (down) Figure 3. Brightness variations: The position of the specific pixel is shown by red circle (the first image); the brightness variation of this pixel in successive frames is represented as a graph with x-direction is position and y-direction is the brightness (the second image); pixel position, similar for the white car (the third image); brightness variation, similar for white car (the forth image) Figure 4. Missing of point tracking: pixel tracking is lost in the third frame Figure 5. Feature extraction: Image frame (top left); vehicle region extraction (top right); vehicle boundary extraction (down left); corner point extraction (down right) Hoogendoorn, S. P., Zuylen, H. J. V., Schreuder, M., Gorte, B. G. H., and Vosselman, G., 03. Traffic data collection form aerial imagery.

6 Figure 6. Tracking: the tracking using ZNCC, optical flow assuming constant brightness model, optical flow assuming linear brightness model, optical flow using the boundary pixels, and optical flow using the region pixels is represented respectively in five different rows IFAC/IFORS. Jahne, B., 01. Digital image processing. 6th revised and extended edition. Lucas, B. and Kanade, T. An iterative image registration technique with an application to stereo vision. IJCAI81, Partsinevelos, P., Agouris, P., and Stefanidis, A., 05. Reconstructing spatiotemporal trajectories from sparse data. Journal of ISPRS (1), Smith, S. M., Asset-2: Real-time motion segmentation and object tracking. Real-Time Imaging 4(1), 21. Smith, S. M. and Brady, J. M., Asset-2: Real-time motion segmentation and shape tracking. IEEE Transactions on pattern analysis and machine intelligence 17(8), Teunissen, P. J. G., 03. Adjustment theory, and introduction.

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