MATLAB Implementation of Hough Transform for Line, Circle, and Ellipse Detection

The Hough transform is a powerful computer vision technique particularly effective for detecting geometric shapes like lines, circles, and ellipses in digital images. By converting image space parameters into Hough parameter space, this method can reliably identify shapes despite challenges like noise, occlusion, and various image quality issues. In MATLAB implementation, the Hough transform typically involves these key steps: - For line detection: Use the radon transform or implement voting in (ρ,θ) parameter space where ρ represents distance from origin and θ represents angle - For circle detection: Employ three-dimensional parameter space (a,b,r) for center coordinates and radius, using gradient information to reduce computational complexity - For ellipse detection: Utilize five-dimensional parameter space with more sophisticated voting mechanisms and optimization techniques Key MATLAB functions for implementation include: - hough() and houghpeaks() for line detection with peak identification in accumulator array - imfindcircles() for circle detection using circular Hough transform - Custom implementations for ellipse detection involving edge detection, parameter space quantization, and voting procedures Beyond computer vision applications, the Hough transform finds utility in signal processing, pattern recognition, and medical imaging domains. Its robust framework for shape analysis makes it an essential tool across various research and engineering disciplines, particularly when implemented with MATLAB's image processing toolbox for efficient computation and visualization.