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OPENCV – PYTHON | Canny Edge Detection EXPLAINED | Coding SOBEL, LAPLACIAN and CANNY Filters

Sobel and Laplacian filters are fundamental tools in image processing, particularly for edge detection tasks. These filters help identify significant changes in intensity or color within an image, highlighting edges and boundaries. In this section, we’ll delve into the concepts behind Sobel and Laplacian filters, elucidating their mathematical foundations, providing code examples for implementation in Python using OpenCV, and exploring their diverse applications.

Flow of Article:

  1. Understanding the Sobel Filter
  2. Coding the Sobel Filter
  3. Understanding the Laplacian Filter 
  4. Coding the Laplacian filter
  5. Understanding the Canny Edge Detection
  6. Coding Canny edge detection

 

Video Explanation:

 

Sobel Filter:

The Sobel filter is a discrete differentiation operator used for edge detection in digital images. It computes the gradient magnitude of an image by convolving it with a pair of 3×3 kernels—one for horizontal changes and the other for vertical changes. The resulting gradient approximates the rate of change of intensity in the image, effectively highlighting edges in the horizontal and vertical directions.

 

Mathematical Explanation:

Let’s denote the image as I(x,y), and the Sobel operators for horizontal and vertical changes as Gx and Gy respectively. The gradient magnitude is calculated as:

Code for OpenCV Implementation:

import cv2
import numpy as np

# Read the input image
img = cv2.imread(‘image.jpg’, cv2.IMREAD_GRAYSCALE)

# Apply Sobel filter for horizontal changes
sobel_x = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=3)

# Apply Sobel filter for vertical changes
sobel_y = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=3)

# Compute gradient magnitude
gradient_magnitude = np.sqrt(sobel_x**2 + sobel_y**2)

# Display the results
cv2.imshow(‘Original Image’, img)
cv2.imshow(‘Sobel Filter – Horizontal’, np.uint8(np.abs(sobel_x)))
cv2.imshow(‘Sobel Filter – Vertical’, np.uint8(np.abs(sobel_y)))
cv2.imshow(‘Gradient Magnitude’, np.uint8(gradient_magnitude))
cv2.waitKey(0)
cv2.destroyAllWindows()

Uses:

  • Sobel filters are widely used in edge detection, line detection, and feature extraction tasks.
  • They are employed in computer vision applications such as object detection, optical character recognition (OCR), and autonomous navigation systems.

 

Laplacian Filter

The Laplacian filter, also known as the Laplacian of Gaussian (LoG) operator, is a second-order derivative operator used for edge detection. It highlights regions of rapid intensity change in an image by detecting zero-crossings in the second derivative of the image intensity. The Laplacian filter is more sensitive to noise compared to the Sobel filter but provides sharper edge localization.

Mathematical Explanation:

The Laplacian operator ∇2 is defined as the divergence of the gradient of the image intensity function I(x,y). Mathematically, it is expressed as:

Code for OpenCV Implementation:

import cv2

# Read the input image
img = cv2.imread(‘image.jpg’, cv2.IMREAD_GRAYSCALE)

# Apply Laplacian filter
laplacian = cv2.Laplacian(img, cv2.CV_64F)

# Display the results
cv2.imshow(‘Original Image’, img)
cv2.imshow(‘Laplacian Filter’, np.uint8(np.abs(laplacian)))
cv2.waitKey(0)
cv2.destroyAllWindows()

Uses:

  • Laplacian filters are effective in edge detection tasks where sharp and precise edge localization is required.
  • They find applications in medical imaging, image segmentation, and feature enhancement in digital photography.

Understanding Canny Edge Detection:

The Canny edge detection algorithm comprises multiple steps, including Gaussian smoothing, gradient calculation, non-maximum suppression, and hysteresis thresholding. It aims to identify edges in an image by locating areas of rapid intensity change while minimizing noise and false detections. The resulting edge map provides a clear delineation of object boundaries and contours within the image.

Mathematical Explanation:

The Canny edge detection algorithm involves the following steps:

  1. Gaussian Smoothing: The image is convolved with a Gaussian kernel to reduce noise and blur the image slightly.
  2. Gradient Calculation: The gradients (magnitude and direction) of the smoothed image are calculated using Sobel operators.
  3. Non-Maximum Suppression: Only the local maxima in the gradient magnitude along the edge directions are retained.
  4. Hysteresis Thresholding: Two thresholds (high and low) are applied to determine strong and weak edges, with weak edges being considered as part of an edge if they are connected to strong edges.

Implementing Canny Edge Detection in OpenCV:

import cv2
import numpy as np

# Read the input image
img = cv2.imread(‘image.jpg’, cv2.IMREAD_GRAYSCALE)

# Apply Gaussian blur
blurred_img = cv2.GaussianBlur(img, (5, 5), 0)

# Apply Canny edge detection
canny_edges = cv2.Canny(blurred_img, 50, 150)

# Display the results
cv2.imshow(‘Original Image’, img)
cv2.imshow(‘Canny Edge Detection’, canny_edges)
cv2.waitKey(0)
cv2.destroyAllWindows()

Uses:

  • Canny edge detection is widely used in computer vision tasks such as object detection, shape recognition, and image segmentation.
  • It is employed in autonomous vehicles, robotics, medical imaging, and quality inspection systems for detecting edges and contours in real-time environments.

 

Conclusion

In conclusion, Sobel, Laplacian, and Canny edge detection operators stand as indispensable tools in the field of image processing, offering robust solutions for edge detection tasks with varying levels of complexity and precision.

Sobel filters provide a straightforward approach to edge detection by computing gradients along horizontal and vertical directions, enabling the detection of edges with distinct orientations. This technique finds widespread applications in tasks such as object detection, feature extraction, and gradient-based image analysis. For more information and detailed usage, one can refer to the [OpenCV documentation].

Laplacian filters, on the other hand, offer a more advanced approach to edge detection by detecting zero-crossings in the second derivative of image intensity. While more sensitive to noise, Laplacian filters excel in precise edge localization, making them suitable for applications requiring high edge detection accuracy. For detailed implementation guidelines and usage, interested readers can consult the [OpenCV documentation].

Lastly, the Canny edge detection algorithm represents a sophisticated technique that combines multiple steps, including Gaussian smoothing, gradient calculation, non-maximum suppression, and hysteresis thresholding, to accurately identify edges in an image while minimizing false detections. Widely regarded for its effectiveness and versatility, the Canny algorithm serves as a cornerstone in computer vision applications, including object recognition, shape detection, and image segmentation. For comprehensive details on implementation and usage, individuals can refer to the [OpenCV documentation].

In summary, Sobel, Laplacian, and Canny edge detection operators offer a diverse range of capabilities, catering to the varying needs and requirements of edge detection tasks in image processing. By understanding and leveraging these operators effectively, practitioners can enhance the accuracy, efficiency, and reliability of edge detection algorithms, thereby advancing research and innovation across numerous domains in computer vision and image analysis.

Aryan Verma, Infoaryan.com, Sobel filters, laplacian filters, aryan verma, Aryan verma blog, infoaryan, computer vision, image processing, computer vision, opencv computer vision, opencv tutorials, computer vision, image processing,