Little Bits of Artificial Intelligence

Here’s a Python + NumPy example applying the Sobel operator to a small grayscale image matrix, without using external image libraries (like OpenCV). We’ll simulate a small image and manually apply Sobel filters.

Example: Sobel Filter in NumPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.ndimage import convolve

# Small 7x7 simulated grayscale image (brighter vertical edge in middle)
image = np.array([
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
    [10, 10, 10, 100, 100, 100, 100],
], dtype=np.float32)

# Sobel kernels
sobel_x = np.array([
    [-1, 0, 1],
    [-2, 0, 2],
    [-1, 0, 1]
], dtype=np.float32)

sobel_y = np.array([
    [-1, -2, -1],
    [ 0,  0,  0],
    [ 1,  2,  1]
], dtype=np.float32)

# Apply convolution (Sobel edge detection)
Gx = convolve(image, sobel_x)
Gy = convolve(image, sobel_y)

# Gradient magnitude
G = np.sqrt(Gx**2 + Gy**2)

# Plotting
fig, axs = plt.subplots(1, 4, figsize=(14, 4))
axs[0].imshow(image, cmap='gray')
axs[0].set_title('Original Image')
axs[1].imshow(Gx, cmap='gray')
axs[1].set_title('Sobel-X (Vertical Edges)')
axs[2].imshow(Gy, cmap='gray')
axs[2].set_title('Sobel-Y (Horizontal Edges)')
axs[3].imshow(G, cmap='gray')
axs[3].set_title('Gradient Magnitude')
for ax in axs:
    ax.axis('off')
plt.tight_layout()
plt.show()

Output Description:

• Sobel-X will clearly highlight the vertical edge where pixel values change from 10 to 100.
• Sobel-Y will be relatively dark since there’s little horizontal edge.
• Gradient Magnitude combines both.

Input image and sobel applied image

Gradient Magnitude

Here’s the visualization:

1. Original Image: A simple grayscale image with a vertical intensity change (left side dark, right side bright).
2. Sobel-X: Highlights the vertical edges clearly where intensity shifts from dark to bright.
3. Sobel-Y: Barely detects horizontal changes since the image is uniform in that direction.
4. Gradient Magnitude: Combines both to show the overall edge strength.

Next – Laplacian Pattern Detection