MATLAB Implementation of Hough Transform for Line and Shape Detection

The Hough Transform example presented here closely aligns with the implementation discussed in Chapter 10 of Gonzalez's Digital Image Processing textbook. This demonstration illustrates both the fundamental principles and practical applications of Hough Transform, accompanied by corresponding visual diagrams. Hough Transform serves as a powerful image processing technique primarily used for detecting geometric shapes such as lines, circles, and other parametric curves. In MATLAB implementation, key functions like hough(), houghpeaks(), and houghlines() form the core workflow for line detection, while approaches for circle detection typically involve customized accumulator arrays and voting mechanisms. The algorithm operates by transforming image space points into parameter space, where collinear points in the image plane generate intersecting curves in Hough space. Peak detection in this parameter space then identifies the most prominent geometric features. For line detection, the standard implementation uses the parametric representation (rho, theta), whereas circle detection requires three parameters (x-center, y-center, radius). This technique finds extensive application in computer vision and image analysis domains, including industrial inspection, medical imaging, and autonomous systems. The MATLAB code includes preprocessing steps like edge detection using Canny or Sobel operators, parameter space accumulation, thresholding for peak identification, and subsequent shape reconstruction. Practical implementation considerations cover parameter resolution selection, computational efficiency optimization through sparse matrix operations, and handling of imperfect data through probabilistic Hough variants. The visualization components demonstrate both the original image with detected features and the corresponding Hough space accumulator array for educational clarity.