Sobel Edge Detection Algorithm
The Sobel edge detection algorithm is a widely used method in image processing to identify edges or boundaries in an image.
It works by calculating the image intensity gradient at each pixel, which highlights regions of significant intensity change (i.e., edges).
The Sobel operator is particularly effective for detecting edges in both the horizontal and vertical directions.
The operator uses two 3*3 kernels which are convolved with the original image to calculate approximations of the derivatives – one for horizontal changes and one for vertical
Gx is given as: (Horizontal Kernel)
Gradient represents change in
color or intensity
Gy is given as: (Vertical Kernel)
Magnitude of the gradient at each pixel:
Edges represent significant changes in intensity (color or brightness) between adjacent pixels. The magnitude of the gradient is a measure of how strong that change is at a given pixel.
While gradient angle describes the direction of the edge or direction of intensity variation.
The horizontal gradient (Gx) and the vertical gradient (Gy) give the rate of change (or slope) in the intensity in the x and y directions, respectively.
However, having the individual gradients (Gx and Gy) doesn’t give a complete picture of the overall edge strength.
The magnitude combines both gradients to represent the total rate of change, i.e., the overall strength of the edge at that pixel
- Pixels with a high gradient magnitude indicate strong edges, meaning a significant change in intensity.
- Pixels with a low magnitude represent flat areas or regions where there is little to no change in intensity.
- This is useful for identifying boundaries between objects or regions in an image.
Gradient Angle
The gradient angle (or edge direction) is the angle of the gradient vector at a specific pixel in an image, representing the direction of the most significant change in intensity at that point.
- An angle of 0° or 180° indicates a horizontal edge.
- An angle of 90° or 270° indicates a vertical edge.
- Angles in between (like 45°, 135°) indicate diagonal edges.
| Gradient Angle | Edge Orientation | Direction of Change |
| 0 | Horizontal | Left to right |
| 180 | Horizontal | Right to left |
| 90 | Vertical | Top to bottom |
| 270 | Vertical | Bottom to top |
* For any other degree, the edge is diagonal
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