✨ Sharpening & Gradient Operators

Enhance image detail by emphasising high-frequency components (edges, fine transitions). Sharpening and gradient filters are fundamental for feature detection and image enhancement.

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1. What Is Sharpening?

Sharpening makes images look crisper by boosting edges, details and light-dark transitions. It’s the opposite of blurring—amplifying high-frequency content.

How It Works

Apply a kernel that amplifies the centre pixel while subtracting its neighbours, highlighting intensity changes (edges).

Common 3×3 Sharpening Kernel

K = [ [ 0, -1,  0],
      [-1,  5, -1],
      [ 0, -1,  0] ]

• Centre weight: 5 boosts the pixel

• Surround weights: –1 subtract the neighbours

Python Example: Image Sharpening

import cv2
import numpy as np
import matplotlib.pyplot as plt

# Load and convert to RGB
img = cv2.imread("bird.jpg")
img_rgb = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# Define sharpening kernel
kernel_sharp = np.array([[ 0, -1,  0],
                         [-1,  5, -1],
                         [ 0, -1,  0]], dtype=np.float32)

# Apply filter
sharpened = cv2.filter2D(img_rgb, -1, kernel_sharp)

# Display without axes
plt.figure(figsize=(12, 5))

plt.subplot(1, 2, 1)
plt.imshow(img_rgb)
plt.title("Original")
plt.axis("off")

plt.subplot(1, 2, 2)
plt.imshow(sharpened)
plt.title("Sharpened")
plt.axis("off")

plt.tight_layout()
plt.show()

2. Gradient Operators

Gradient operators detect directional intensity changes and are often used before sharpening or as part of edge detection.

Common Gradient Operators

Operator	Kernel Example	Detects
Sobel X	[-1, 0, 1]	Vertical edges
Sobel Y	[-1, -2, -1]	Horizontal edges
Laplacian	2nd derivative	All-direction edges

Laplacian Example in Code

import cv2
import matplotlib.pyplot as plt

# Convert to grayscale
img_gray = cv2.cvtColor(img_rgb, cv2.COLOR_RGB2GRAY)

# Apply Laplacian operator
lap = cv2.Laplacian(img_gray, cv2.CV_64F)
lap = cv2.convertScaleAbs(lap)

# Display without axes
plt.figure(figsize=(6, 4))
plt.imshow(lap, cmap="gray")
plt.title("Laplacian (2nd Derivative)")
plt.axis("off")
plt.show()

🔍 Sharpening vs Gradient Operators

Technique	Purpose	Output
Sharpening	Enhance detail and contrast	Crisper, more defined image
Sobel / Laplacian	Detect edges or texture transitions	Edge maps

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✅ Summary

Tool	Function	Code
Sharpening	Highlight detail	cv2.filter2D()
Sobel Operator	First derivative (edges)	cv2.Sobel()
Laplacian	Second derivative (edges)	cv2.Laplacian()