Circle Detection with Unknown Radius Using Hough Transform

The Hough transform enables detection of circular objects with unknown radii. As a fundamental image processing technique, Hough transform converts each pixel in the image into a curve in parameter space to identify circular patterns. In implementation, each edge pixel maps to a conical surface in the 3D Hough space (parameterized by center coordinates x,y and radius r), where circles manifest as intersecting surface clusters. The detection algorithm typically involves edge detection preprocessing using operators like Canny, followed by accumulator array voting where peaks correspond to potential circle centers and radii. Key MATLAB functions include imfindcircles which employs Circular Hough Transform (CHT) with gradient information, or custom implementations using hough and houghpeaks functions for parameter space analysis. While Hough transform excels at detecting circles of arbitrary sizes and positions, it demonstrates sensitivity to noise and interference from other shapes. Practical applications require preprocessing steps such as Gaussian filtering for noise reduction, contrast enhancement, and morphological operations to improve detection accuracy. Computational optimization techniques include using gradient direction to reduce parameter space sampling and employing the Hough gradient method for improved efficiency.