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Extracting Homography Matrix to Determine 3D Position of Soccer Players

Fotouhi, Mehran | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51386 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Kasaei, Shohreh
  7. Abstract:
  8. Determination of the position of an object in the 3D world is one of the most basic preprocessing steps in the field of computer vision. It is used in many practical applications such as video surveillance, human action analysis, and human-computer interaction. For this determination, calibrated cameras are usually used for which the internal and external camera parameters are already known. But, in some real-life applications, a pre-access to the camera is not possible. This thesis studies the homography matrix extraction for determination of the position of soccer players. The pan-tilt-zoom (PTZ) cameras are used. (For a stationary camera, a Homography matrix is obtained once.) To determine the position of soccer players, the projection matrix extraction and the homography matrix extraction methods are proposed. That is because, fortunately, by mathematic relations it is possible to obtain the homography matrix from the projection matrix. In fact, the projection matrix is more suitable for the penalty area (as it has many information about the 3D world) while the homography matrix is a 2D transformation that can be obtained almost in all areas of the soccer field. In both proposed methods, at first, an initial estimation of image-to- world coordinate transformation are computed and then by using an iterative optimization procedure the obtained transformation is optimized. Two methods are proposed for estimating the initial homography matrix. The first, is based on the primary knowledge about the soccer field and the camera position. The other method is based on camera modeling. The error of optimized projection matrix is about 1.5 pixels with 0.4 standard deviation. The proposed method of projection matrix is compared with the direct linear transform (DLT) as a baseline method. The proposed method needs less information to calculate the projection matrix than similar exiting methods. The error of optimized homography matrix is less than 15 cm (in average) which is significantly superior to the existing methods. The required elapsed time for the optimization of homography matrix at each iteration step is 90 milliseconds in MATLAB software. In order to increase the processing speed, after optimization of the homography cost function, the homography matrix is obtained by tracking the homography matrix of consecutive frames. The proposed method for tracking the homography matrix is compared with the conventional Kanade–Lucas–Tomasi (KLT) method. To obtain the image-to-world coordinate transformation, two important pre-processing steps are needed; namely, extraction of soccer field mask and line mask. Their runtime in the C++ environment is about 2 and 3 ms, respectively. All proposed methods are evaluated on the IPL Azadi database produced by Sharif University of Technology
  9. Keywords:
  10. Camera Calibration ; Projection Matrix ; Homography ; Image to World Transformation ; Interframe Homography

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