Hough Transform MATLAB Source Code Implementation

The Hough transform is a classic image processing technique primarily used for detecting geometric shapes (such as lines, circles, etc.) in images. It operates by converting image space into parameter space, making it particularly effective for images with noise or partial occlusion.

The core concept of Hough transform utilizes a parameter space accumulation voting mechanism. For line detection, each edge point in the image corresponds to a sinusoidal curve in the parameter space (ρ, θ), while intersections of multiple curves represent lines in the original image.

In MATLAB implementation, Hough transform typically involves the following steps: Edge Detection: Extract image edges using Canny or Sobel operators through functions like edge() with specified method parameters. Parameter Space Quantization: Define discrete value ranges for ρ and θ using appropriate bin sizes and angular resolutions. Accumulator Construction: Count voting results in parameter space by incrementing accumulator cells corresponding to calculated (ρ, θ) pairs. Peak Detection: Identify local maxima in the accumulator array using techniques like thresholding or non-maximum suppression, which correspond to detected lines in the image.

While MATLAB provides built-in functions (such as hough() and houghpeaks()), manual implementation offers better understanding of algorithmic details. Typical optimizations include using gradient direction to reduce θ calculation range through directional filtering, or employing non-maximum suppression to improve detection accuracy by eliminating spurious peaks.

The Hough transform can be extended for circle detection (using three-dimensional parameter space with parameters a, b, r) or other shape recognition, though computational complexity increases significantly with higher parameter dimensions, requiring efficient memory management and sampling strategies.