Classical Vision Concepts Edges Corners

Why this matters

Edges and corners are the backbone of many classical computer vision pipelines. As a Computer Vision Engineer, you will often need to detect document borders, lane lines, object outlines, and stable keypoints for tracking and 3D tasks. Even in deep-learning workflows, clean edge maps and reliable corners help with pre/post-processing, debugging, and speed-sensitive applications on embedded devices.

• Document scanning: find page edges, rectify perspective, crop neatly.
• AR/SLAM: detect and track corners/keypoints across frames.
• Robotics: follow lane edges, detect obstacles, localize within a map.
• Quality inspection: find scratches, cracks, and outline deviations.

Who this is for

• Beginners in computer vision who know basic image concepts (grayscale, pixels).
• Engineers moving from deep learning to classic vision for speed/interpretability.
• Students preparing for interviews or a first CV project portfolio.

Prerequisites

• Basics: images as matrices, grayscale vs color, pixel intensity (0–255).
• Math: very light calculus/linear algebra intuition (gradients, matrices).
• Tools: any environment that can display images (Python, MATLAB, or your preferred tool). Hand calculations are fine for small patches.

Concepts explained simply

Edges

An edge is where image intensity changes quickly. Think of it as a cliff in brightness. We estimate change using gradients (partial derivatives along x and y). Strong gradients indicate edges.

• Gradient operators: Sobel, Prewitt (compute approximate derivatives).
• Canny edge detector: a robust pipeline with Gaussian smoothing, gradient magnitude/direction, non-maximum suppression (thin edges), and hysteresis thresholding (link edges).
• Noise handling: blur first (Gaussian) so random speckles don’t look like edges.

Corners

A corner is where intensity changes in at least two directions. Imagine standing at a city block corner: moving north or east both change the view sharply, unlike along a flat edge where only one direction changes.

• Harris corner detector: uses the structure tensor (second moment matrix) to measure how gradients vary in a neighborhood. Large response in two directions = corner.
• Shi–Tomasi (Good Features to Track): similar idea but uses the minimum eigenvalue of the structure tensor.
• FAST: very fast corner test using a circle of pixels; great for real-time.

Worked examples

1) Clean document edges with Canny

Goal: detect the 4 page borders.

• Apply Gaussian blur (sigma ~1–2) to reduce noise.
• Use Canny with a high threshold that keeps clear borders and a low threshold about half of high to connect faint segments.
• Find the largest 4-sided contour and warp to a rectangle.

2) Lane hints: edges + Hough

Goal: extract lane markings under moderate noise.

• Focus on the lower half of the frame (region of interest).
• Canny edges with a bit more smoothing (sigma 1.5–2.0) to handle texture.
• Use Hough lines on the edge map to get lane lines.

3) Stable corners for AR markers (Harris vs FAST)

Goal: track marker corners across frames.

• Harris/ Shi–Tomasi for accuracy when you can afford computation.
• FAST for mobile/embedded where speed matters.
• Apply non-maximum suppression and a minimum distance between keypoints to avoid clusters.

Learning path

1. Gradients and filtering: Sobel/Prewitt, Gaussian smoothing.
2. Edges: Canny pipeline, non-maximum suppression, hysteresis.
3. Corners: Harris, Shi–Tomasi, FAST; non-maximum suppression and thresholding.
4. Geometric use: Hough transform, contour finding, homography from corners.
5. Descriptors next: SIFT/ORB (beyond this lesson), matching, RANSAC.
6. Integrate with DL: use classic features for pre/post-processing and debugging.

Exercises (hands-on)

Everyone can do the exercises. The quick test is available to everyone; sign in to save your progress.

Exercise 1: Canny by hand (concept + tuning)

Pick any photo from your device. Follow the steps below and record your chosen parameters and observations.

1. Decide a Gaussian sigma (start with 1.0; try 1.5 if noisy).
2. Pick high/low thresholds (e.g., high=100, low=50 in 0–255 scale). Adjust until edges are thin and connected.
3. Describe what changes when you raise/lower high or low thresholds.

Exercise 2: Compute gradients on a 3x3 patch

Using Sobel kernels, compute Gx, Gy, magnitude, direction at the center pixel for this patch:

Patch (center at value 2):
[1 1 1]
[1 2 3]
[1 3 4]
Sobel Gx = [-1 0 1; -2 0 2; -1 0 1]
Sobel Gy = [-1 -2 -1; 0 0 0; 1 2 1]

Report Gx, Gy, |G|, and direction in degrees.

Self-check checklist

• I can explain why smoothing is applied before edge detection.
• I can tune Canny thresholds to trade off between missing edges and noise.
• I can distinguish edge-like vs corner-like regions using gradient reasoning.
• I know when to choose Harris, Shi–Tomasi, or FAST.
• I apply non-maximum suppression to keep only the best responses.

Common mistakes and how to self-check

• No smoothing before Canny: noisy textures blow up the edge map. Fix: add Gaussian blur; verify with side-by-side inspection.
• Thresholds too low: many false edges. Fix: raise high threshold or sigma.
• Thresholds too high: missing important boundaries. Fix: lower high threshold or reduce sigma.
• Ignoring scale: small features vanish at large sigma. Fix: try multi-scale (different sigmas) and merge results.
• Too many corner clusters: no non-maximum suppression or min distance. Fix: enforce spacing between keypoints.
• Using Harris on tight real-time budgets: may drop frames. Fix: use FAST or tune grid-based detection.

Practical projects

• Auto document scanner: detect page edges with Canny, find contour, compute homography, and warp to a flat scan.
• Lane line demo: ROI + Canny + Hough lines on a short driving clip.
• Keypoint tracker: detect corners (FAST or Shi–Tomasi) and track with optical flow across 50 frames; visualize trajectories.

Mini challenge

For each scenario, pick the tool and a brief tuning note:

• Faint pencil sketch on textured paper.
• High-contrast QR code for fast mobile detection.
• Shaky camera video of a building facade you want to track.

Next steps

• Explore descriptors (ORB/SIFT) to make corners matchable across images.
• Add RANSAC to robustly estimate homographies/fundamental matrices.
• Combine classic features with neural nets for hybrid, production-ready pipelines.