A new hough transform operated in a bounded cartesian coordinate parameter space

Abstract

In this paper, a new Hough transform is proposed to detect lines with geometric meanings. In the standard Hough transform, lines are parameterized by the length and orientation of the normal vector from the origin to the line. The parameter space of the standard Hough transform is presented in a polar coordinate system. Geometric measurements such as distance and angle are not suitable in polar coordinate space due to the inconsistency of the axes. To deal with this problem, a Hough transform which is carried out in a bounded Cartesian coordinate parameter space is developed. The lines are represented by their perpendicular feet with respect to a fixed point. Since the parameter space is in Cartesian coordinate space, it is intuitive to the researchers. When detecting the peaks in the parameter space, distance and angle constraints can be applied. The effectiveness of the proposed method has been illustrated by two applications, that is, lane line detection and convex polygon extraction. The results show that the proposed Cartesian coordinate Hough transform is suitable for detecting meaningful lines.

Deep Learning-Based Algorithm for Recognizing Tennis Balls

“…To detect a circle, the circle is transformed from the Cartesian coordinate system to the Hough space, i.e., a circle in the Cartesian coordinate system is transformed into a point in the Hough space, and a point of a circle in the Cartesian coordinate system is transformed into a cone in the Hough space. When using the Hough circle detection theory, the Canny edge detection is first performed on the original image to obtain the binary map, and then the Sobel operator is executed so that the domain gradient values of all pixels are calculated, and finally the circle center and radius of the circle in the image are estimated [22]. Therefore, the image sample pre-processing steps are as follows:…”