Contour Tracking and Hough Transforms
Date: October 3, 2024
Lecture Duration: 2.5 hours
Topic Overview: In this lecture, we explore how to transition from pixel-level features to structural shapes. We cover edge detection techniques, contour analysis for shape representation, and the Hough Transform for robust mathematical shape detection (lines and circles).
1. Edge Detection and Image Gradients
Before we can find shapes, we need to find boundaries. We discussed how edges correspond to rapid changes in image intensity.
- Image Gradients: We used the Sobel Operator to compute the gradient magnitude and direction, highlighting vertical and horizontal edges.
- Canny Edge Detection: We explored the Canny algorithm, a multi-stage process (smoothing, gradients, non-maximum suppression, and hysteresis thresholding) that produces clean, continuous, one-pixel-wide edges.
2. Contours and Shape Analysis
Once edges are identified, we can connect them into continuous curves called Contours. This allows us to perform object tracking and shape analysis.
- Finding Contours: We implemented contour extraction on binary images to isolate objects from the background.
- Shape Bounding: We calculated various structural bounds for detected contours, including:
- Bounding Rectangles: Axis-aligned bounding boxes (AABB) and rotated bounding boxes.
- Minimum Enclosing Circles: Finding the smallest circle that completely covers an object.
- Polygonal Approximations: Simplifying complex contours into polygons with fewer vertices.
3. The Hough Transform
How do we detect shapes when edges are noisy, broken, or partially occluded? We introduced the Hough Transform, a powerful voting-based technique for mathematical shape detection.
- Hough Line Transform: We learned how to map spatial points \((x, y)\) into the parameter space \((\rho, \theta)\). A line in image space becomes a point in Hough space, allowing us to find lines by detecting intersections (votes) in the parameter space.
- Hough Circle Transform: We extended the concept to detect circles by voting in a 3D parameter space \((x_c, y_c, r)\) representing the center coordinates and radius.
Interactive Demonstration
Below is the complete Jupyter Notebook used in class. It contains Python implementations for Edge Detection, Contour Tracking, and the Hough Transform.