Line Detection Based on Hough Transform

Hough Transform is a classical image processing technique primarily used for detecting geometric shapes in images, such as lines, circles, and ellipses. It operates through a parameter space voting mechanism, effectively handling noise and partial occlusions.

### Line Detection (VC Implementation) In line detection, Hough Transform converts lines from the Cartesian coordinate system to a polar parameter space. Each line in the image space corresponds to a point in the parameter space, while edge points in the image correspond to curves in the parameter space. By using an accumulator to count intersections, the most probable line parameters are identified. A typical VC implementation involves three key steps: edge detection (using operators like Canny), parameter space transformation (via sine-cosine calculations), and peak detection (using thresholding or local maxima search).

### Circle Detection (MATLAB Implementation) Circle detection extends the Hough Transform concept using a three-dimensional parameter space (center coordinates x, y, and radius r). MATLAB's optimized functions like `imfindcircles` leverage gradient information to narrow the computational scope, significantly improving efficiency. The core algorithm involves voting for possible circle centers based on edge point orientations, followed by radius validation through accumulator analysis.

### Ellipse Detection (MATLAB Implementation) Ellipse detection is more complex, requiring a five-dimensional parameter space (center coordinates, major/minor axes, and rotation angle). MATLAB typically employs Randomized Hough Transform (RHT) or least-squares fitting to reduce computational load. The implementation relies on edge point sampling and parameter optimization techniques, making it suitable for detecting elliptical objects in natural scenes.

The general principle of Hough Transform involves shape parameterization and statistical voting, but computational costs grow exponentially with parameter dimensions. Practical applications often combine edge preprocessing (e.g., smoothing and thinning) with optimization algorithms (like probabilistic voting) to balance accuracy and performance.