Circle Detection Using Randomized Hough Transform with MATLAB Implementation

The Randomized Hough Transform provides an effective methodology for detecting circular patterns in digital images. The algorithm initiates by randomly sampling candidate points from the image's edge map obtained through preprocessing steps like Canny edge detection. For each selected edge point, the algorithm generates hypothetical circles with varying radii within a specified detection range. Each candidate circle is evaluated by counting the number of edge points lying along its circumference using accumulator array techniques. In MATLAB implementation, the process can be streamlined using the vision.CircleDetector system object or custom code utilizing trigonometric calculations. Key implementation steps include: 1. Preprocessing: Apply edge detection (edge function with 'Canny' method) and obtain binary edge map 2. Parameter space definition: Set radius range [r_min, r_max] and voting threshold 3. Accumulator matrix: Create 3D parameter space (x-center, y-center, radius) for vote accumulation 4. Peak identification: Find parameter combinations exceeding threshold using findpeaks or regional maxima detection The built-in imfindcircles function provides optimized implementation supporting both standard and randomized Hough transform variants, accepting parameters like 'ObjectPolarity' and 'Sensitivity' for precision control. For custom implementations, trigonometric calculations involving sin/cos functions enable efficient circle perimeter point verification. The Randomized Hough Transform demonstrates particular efficiency in handling noisy images and partial occlusions through its probabilistic sampling approach. MATLAB's computational advantages ensure real-time performance even for high-resolution images, making this technique suitable for industrial inspection, medical imaging, and computer vision applications requiring robust circle detection capabilities.