Non-linear voting in the space variant Hough transform

Abstract. For space variant sensors the volume of world space that projects onto a single sensing element varies significantly with its spatial position in the sensing array. This includes the log-polar sensor, and central catadioptric cameras. In this paper, we consider the Hough transform for space variant sensors. We show that for real discrete images the voting equation must be modified to allow for the fact that a larger sub-space of parallel world planes can intersect with a larger sensing element than with a smaller one. We derive a voting algorithm for the space variant Hough Transform, and apply this algorithm to the log-polar sensor. We compare the standard voting algorithm with the proposed non-linear voting scheme for the space variant log-polar Hough transform. We demonstrate experimentally that for the standard Hough transform, lines that cover the majority of the sensor do not register a significantly larger vote count than shorter lines, while they are gain full support in the space variant transform. Further, in real images we show that this can lead to poor definition of peaks in the regular Hough transform, while similar peaks are well defined in the space variant Hough transform. Experiments are conducted on simulated images, and images from a true log-polar sensor.