Detection of vertical lines and circles in 3D space using Hough transform techniques

Curve detection is an important topic in computer vision. Amongst the many algorithms for curve detection, methods based on Hough transform (HT) techniques have been found to be very effective. The paper developes two specific HT techniques to detect straight lines vertical to the X-Y plane and circles parallel to the X-Y plane in the 3D space from a single perspective image. The projection of vertical lines remains straight lines in the image, but circles become ellipses when the image plane is assumed to be at an angle (<90°) to the vertical axis of the object. Based on the a-priori knowledge of the image formation and the properties of 3D vertical lines and circles, a series of new functions are developed to apply the HT technique. Vertical lines are detected in a one-dimensional process, while circles are directly recovered in a two-stage process by including gradient information. The advantages of both techniques include their computing efficiency and the reduced memory storage requirement. Experimental results are given to indicate the effectiveness of the methods