Practical Example of Hough and Radon Transforms for Clock Shape Drawing

In this article, we present a practical implementation of Hough and Radon transforms for drawing clock-shaped graphics. We begin by examining the Hough transform, an image processing technique primarily used for line detection in digital images. The algorithm works by converting each pixel into parameter space (typically polar coordinates) and identifying collinear points through accumulator array voting. Key implementation steps include edge detection preprocessing using operators like Canny, followed by theta-rho parameter space mapping where peak values correspond to detected lines. Next, we explore the Radon transform, a powerful technique for detecting both lines and curves in images. This method computes line integrals across the image at various angles, generating a sinogram representation where bright spots indicate prominent features. Implementation typically involves projecting image intensities along specified orientations using interpolation methods, with the resulting transform highlighting linear structures through intensity variations. Finally, we demonstrate how to integrate both techniques to construct clock-shaped graphics. The process involves: 1) Using Hough transform to identify clock hands and major markers through line parameter extraction 2) Applying Radon transform for circular component detection and curvature analysis 3) Combining results through coordinate transformation and geometric rendering. We detail critical steps including angle calculation using inverse trigonometric functions, line positioning via parameter space back-projection, and shape assembly through matrix operations. This implementation showcases practical applications of these transforms in computer vision, utilizing MATLAB's image processing toolbox functions like hough(), houghpeaks(), radon(), and iradon() for efficient computation. Through this example, you'll learn to apply Hough and Radon transforms in real-world scenarios while understanding their mathematical foundations and optimization considerations for complex shape detection.