Determining Circle Parameters (Center Coordinates and Radius) in Images Using Hough Transform

The Hough Transform algorithm provides an effective solution for extracting circle parameters from images, including center coordinates and radius measurements. As a fundamental image processing technique, Hough Transform enables robust detection of geometric shapes like lines and circles while precisely determining their mathematical parameters. For circle detection, the algorithm operates by accumulating votes in a 3D parameter space (x-center, y-center, radius) where each edge pixel in the image contributes to potential circle candidates. Implementation typically involves these key steps: First, apply edge detection (using methods like Canny) to identify circle boundaries. Then, for each edge point, calculate possible circle centers at different radii using the circle equation (x-a)² + (y-b)² = r². The algorithm accumulates these possibilities in an accumulator array, where peak values correspond to the most probable circle parameters. In MATLAB, this can be implemented using the imfindcircles function which employs the Circular Hough Transform variant, requiring parameters like sensitivity threshold and edge gradient threshold for optimal detection. The function returns center coordinates and radii for detected circles, with options to specify radius range for improved computational efficiency. This methodology enables accurate localization and analysis of circular objects in images, making it invaluable for computer vision applications such as industrial inspection, medical imaging, and autonomous navigation systems where precise circle detection is critical. The parameter space accumulation approach makes Hough Transform particularly resilient to noise and partial occlusions in real-world images.