In the first series, synthetic images are obtained with distortion parameters , with varying at different levels (from extreme pincushion to barrel distortion). For a positive (pincushion distortion), the size of synthetic images is larger than pixels, and the distortion center is different from known parameters of . For a negative (barrel distortion), the size of synthetic images is , and the distortion center is fixed at (320, 240). The synthetic images, corrected images, and the corresponding 1-D Hough transforms are shown in Fig. 2. For the extreme case of , we only map the points for which , resulting in a circular valid region around the image center.