Implementing Hough Transform for Line Detection

This function utilizes the Hough transform technique to extract straight lines from input images. The implementation accepts image x as input and automatically generates visual output with detected lines overlaid on the original image. The Hough transform method operates by converting image points from Cartesian coordinates to parameter space (typically using rho-theta representation), where collinear points generate intersecting curves whose peaks correspond to line parameters. Key implementation steps include: 1. Edge detection preprocessing using algorithms like Canny to obtain binary edge maps 2. Hough space accumulation through voting mechanism where edge pixels vote for potential line parameters 3. Peak detection in Hough space to identify dominant lines using thresholding techniques 4. Line segment extraction and visualization using geometric transformation back to image coordinates The algorithm effectively handles various line orientations and lengths while providing robust detection under noise conditions. Through this implementation, users can efficiently analyze linear structures in images and perform subsequent processing operations on detected line features. The integrated plotting capability enables immediate visual validation of results, facilitating rapid prototyping and analysis workflows.