Canny Edge Detection is one of the most popular and effective edge detection algorithms used in computer vision.

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Introduction

Canny Edge Detection, developed by John F. Canny in 1986, is a multi-stage algorithm designed to detect a wide range of edges in images robustly and accurately.

Its goals were to:

• Detect true edges (good detection)
• Locate edges precisely (good localization)
• Avoid multiple responses to a single edge (minimal response)

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Step-by-Step Process of the Canny Algorithm

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1. Noise Reduction with Gaussian Filter

• Why? Edges are susceptible to noise, which can cause false detections.
• How? Smooth the image by convolving it with a Gaussian kernel:

$$G(x, y) = \frac{1}{2\pi \sigma^2} e^{-\frac{x^2 + y^2}{2\sigma^2}}$$

• $\sigma$ controls the amount of smoothing (larger $\sigma$ means more blur).
• The smoothed image $I_s$ is:

$$I_s = G * I$$

where $*$ is convolution.

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2. Compute Intensity Gradients (Using Sobel Filters)

• Calculate gradients in the horizontal and vertical directions:

$$G_x = I_s * K_x, \quad G_y = I_s * K_y$$

where $K_x, K_y$ are Sobel kernels.

• Compute gradient magnitude $G$ and gradient direction $\theta$:

$$G = \sqrt{G_x^2 + G_y^2}$$

$$\theta = \arctan\left(\frac{G_y}{G_x}\right)$$

• The magnitude $G$ indicates edge strength, and $\theta$ shows edge orientation.

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3. Non-Maximum Suppression (NMS)

• Goal: Thin out edges to 1-pixel wide by suppressing non-maximum pixels along the gradient direction.

• For each pixel:

  • Compare gradient magnitude $G(x,y)$ with neighbors along the gradient direction.
  • If $G(x,y)$ is not greater than neighbors, suppress it (set to zero).

This step preserves only the local maxima (potential edge pixels).

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4. Double Thresholding

• Use two thresholds: high and low.
• Categorize pixels:

Category	Condition	Interpretation
Strong edge	$G(x,y) \geq T_\text{high}$	Definitely edge
Weak edge	$T_\text{low} \leq G(x,y) < T_\text{high}$	Potential edge, needs validation
Non-edge	$G(x,y) < T_\text{low}$	Suppress

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5. Edge Tracking by Hysteresis

• Final edges include all strong edges.
• Also include weak edges connected to strong edges (connected by 8-neighborhood).
• Discard weak edges not connected to strong edges (likely noise).

This step helps reduce false edges while preserving meaningful contours.

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Summary Diagram of the Pipeline

1. Smooth image with Gaussian
2. Compute gradient magnitude and direction
3. Apply Non-Maximum Suppression
4. Double Thresholding
5. Edge Tracking by Hysteresis

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Important Parameters and Their Effects

Parameter	Effect
Gaussian $\sigma$	Controls smoothing; higher means smoother image, fewer edges detected, but less noise
High threshold $T_\text{high}$	Controls strong edge sensitivity; higher means fewer strong edges
Low threshold $T_\text{low}$	Controls inclusion of weak edges; lower means more edges included (including noise)

• Typically, $T_\text{low}$ is about half of $T_\text{high}$.

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Practical Usage in OpenCV

edges = cv2.Canny(image, threshold1=low_threshold, threshold2=high_threshold)

• threshold1 = low threshold
• threshold2 = high threshold
• Input image should be grayscale

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Why Is Canny Edge Detection Effective?

• Combines noise reduction, precise localization, and robust edge selection.
• Avoids detecting false edges caused by noise.
• Produces thin edges, suitable for downstream tasks like shape detection.

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Visualization Example

• After applying Canny, edges appear as thin white lines on a black background.
• Changing thresholds changes edge density and continuity.

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Would you like me to provide code examples and visualizations for Canny edge detection? Or maybe a comparison with simpler edge detectors like Sobel?