Explain first order edge detection operators i) Roberts operator ii) Prewitt operator iii) Sobel operator

10 b] Explain first order edge detection operators

i) Roberts operator

ii) Prewitt operator

iii) Sobel operator

First-Order Edge Detection Operators

First-order edge detection operators are used to detect edges in an image by identifying areas where the intensity of pixels changes significantly. These operators calculate the gradient of the image intensity at each pixel, which highlights the edges. Here’s an explanation of three common first-order edge detection operators:

i) Roberts Operator

The Roberts operator is a simple, first-order edge detection method that calculates the gradient using a pair of 2×2 convolution masks. It detects edges by approximating the gradient of the image intensity at each pixel. The operator uses two kernels:

• ( G_x) detects changes in the vertical direction, and ( G_y ) detects changes in the horizontal direction.
• The magnitude of the gradient is calculated as

• It’s sensitive to noise due to its small kernel size and is best suited for detecting diagonal edges.

ii) Prewitt Operator

The Prewitt operator is another first-order edge detection method that uses larger convolution kernels (3×3) to calculate the gradient, making it more robust to noise than the Roberts operator. The Prewitt operator uses two kernels:

• ( G_x ) detects horizontal edges, and ( G_y ) detects vertical edges.
• The gradient magnitude is calculated similarly as

• Prewitt operator is effective for detecting edges in images with more uniform noise levels and provides a better edge response for edges aligned with the horizontal and vertical directions.

iii) Sobel Operator

The Sobel operator is an extension of the Prewitt operator, with an added emphasis on the central pixels of the convolution kernel. It also uses 3×3 kernels, but the weights are adjusted to give more importance to the center pixel:

• ( G_x ) detects vertical edges, and ( G_y ) detects horizontal edges.
• The gradient magnitude is calculated as

• The Sobel operator is widely used due to its effectiveness in reducing noise and its ability to highlight edges with a higher degree of precision, particularly for images with significant noise or uneven lighting.

These operators are foundational in image processing for edge detection and are often used as the first step in more complex image analysis tasks.