Calibrating an Overhead Video Camera

In this section we discuss how to calibrate an overhead video camera used for tracking robots moving on a rectangular field. First, the radial distortion of the camera must be eliminated. The resulting corrected image represents a projective transformation of the field’s surface to the camera’s imaging plane. We show how to find the projective transformation, and how to recover from this information the position of the camera and the rotation of its coordinate system in relation to world’s coordinates. We discuss the numerical errors which arise in the computations and how to find an optimal solution. We also show how to track robots of different heights. 1 Overhead Camera calibration In the RoboCup small-size league, mobile robots are tracked using one or more video cameras overlooking the field from a height of three to four meters. The image registered in each camera provides pixel information from which the positions of robots and other objects in the field can be computed. The robots are marked with blobs of different colors. The geometry of the scene provides all necessary information for tracking the robots, sometimes at 60 frames per second. Tracking the robots can be done best when the image from the video camera is as undistorted as possible. However, once the video camera has been placed above the field, there is no guarantee that the symmetry axis of the optics will be pointing downwards perfectly. The camera’s coordinate system axis could be misaligned with the coordinate system of the field (which we call “world coordinates”). Also, wide angle lenses, necessary for capturing the field from only 3 or 4 meters height, introduce a significant amount of radial distortion in the image. The distance of objects to the center of the coordinate system is underestimated sometimes by as much as 30% to 40%. It is necessary to correct all these imaging artifacts before the coordinates of objects on the field can be recovered. This chapter provides all the necessary information for computing the best camera-to-field coordinates transformation (so that we can infer from pixel data where our robots are located), as well as the inverse field-to-camera transformation. We proceed as follows: – We eliminate the radial distortion, calibrating the camera before it is used, and applying a corrective transformation to the pixel’s coordinates,