1. Basic Syntax

% Default Sobel edge detection with automatic thresholding
BW = edge(I, 'Sobel');

% Sobel with a user-specified sensitivity threshold
BW = edge(I, 'Sobel', thresh);

% Sobel with directional filtering ('both', 'horizontal', or 'vertical')
BW = edge(I, 'Sobel', thresh, direction);

% Return both the binary edge map and the computed threshold value
[BW, threshOut] = edge(I, 'Sobel');

2. Complete, Runnable MATLAB Script

This script uses the built-in cameraman.tif sample image to demonstrate automatic, custom threshold, and directional Sobel edge detection.

% 1. Load sample grayscale image
I = imread('cameraman.tif');

% Note: If your image is RGB, convert it first using:
% I = im2gray(I);

% 2. Standard Sobel with automatic thresholding
[BW_auto, threshAuto] = edge(I, 'Sobel');

% 3. Sobel with a custom sensitivity threshold
BW_custom = edge(I, 'Sobel', 0.15);

% 4. Detect only horizontal edges
BW_horizontal = edge(I, 'Sobel', [], 'horizontal');

% 5. Detect only vertical edges
BW_vertical = edge(I, 'Sobel', [], 'vertical');

% 6. Plot and compare the results
figure('Name', 'Sobel Edge Detection Comparison', 'Color', 'w');

subplot(2, 3, 1);
imshow(I);
title('Original Image');

subplot(2, 3, 2);
imshow(BW_auto);
title(['Auto Sobel (Thresh = ', num2str(threshAuto, '%.4f'), ')']);

subplot(2, 3, 3);
imshow(BW_custom);
title('Custom Thresh (0.15)');

subplot(2, 3, 5);
imshow(BW_horizontal);
title('Horizontal Edges');

subplot(2, 3, 6);
imshow(BW_vertical);
title('Vertical Edges');

3. Parameter Reference

4. How the Sobel Algorithm Works

The Sobel operator calculates the image gradient at each pixel by convolving the image with two 3x3 integer filters:

• Horizontal Kernel (Gx): Highlights vertical edges by computing derivatives along the horizontal axis.
• Vertical Kernel (Gy): Highlights horizontal edges by computing derivatives along the vertical axis.

Gx = [ -1   0  +1
       -2   0  +2
       -1   0  +1 ]

Gy = [ +1  +2  +1
        0   0   0
       -1  -2  -1 ]

The gradient magnitude is computed as G = sqrt(Gx.^2 + Gy.^2). Any pixel whose magnitude exceeds the threshold value is assigned a value of 1 (edge), and all other pixels are assigned 0 (background).

5. Best Practices and Edge Cases

• Pre-filtering Noisy Images: Sobel operators amplify high-frequency noise. Apply Gaussian smoothing before edge detection for cleaner boundaries:

  I_clean = imgaussfilt(I, 1.0);
  BW = edge(I_clean, 'Sobel');

• Choosing Between Sobel and Canny: Sobel is fast and computationally lightweight. For thinner, single-pixel wide, and continuous edge boundaries, consider using edge(I, 'Canny').