Circle Detection in Images Using Hough Transform

The Hough transform is a classic image processing algorithm used for detecting geometric shapes in images, such as lines, circles, and ellipses. For circle detection, the process typically involves two main steps: edge extraction and Hough transform detection.

### 1. Edge Extraction First, edge detection is performed on the original image using methods like the Canny edge detection algorithm. This algorithm effectively extracts contour information while minimizing background noise interference. The output is a binary image where edge pixels are marked white against a black background. In code implementation, the Canny function typically requires parameters for low/high thresholds and aperture size for gradient calculation.

### 2. Hough Transform for Circle Detection The Hough transform maps image features to parameter space to identify potential circles. A circle is defined by three parameters: center coordinates (x, y) and radius r. The core algorithm operates as follows: - Iterate through all edge pixels and compute possible center positions for each candidate radius r - Accumulate votes in the 3D parameter space (x, y, r) - Select parameter combinations with high vote counts as detected circles In practical implementations like OpenCV's HoughCircles function, gradient information is often used to reduce computational complexity by constraining center candidates along edge normal directions.

To improve efficiency, constraints can be applied to the radius range or gradient-based optimizations employed. While Hough transform demonstrates robustness against noise and occlusion, its performance depends critically on parameter settings such as minimum/maximum radius and detection thresholds.

### Enhancement Approaches Optimization methods: Multi-scale Hough transforms can detect circles of varying sizes by scaling the input image or parameter ranges. Application scenarios: Suitable for industrial inspection (component positioning), traffic sign recognition, and medical image analysis. Advanced algorithms: Compared to standard Hough transform, probabilistic Hough transform (PHT) or deep learning-based circle detection methods can achieve higher accuracy and faster processing through sampling techniques or convolutional neural networks.