Practical 3: Negation, Subtraction & Inversion

Run this practical in Google Colab

1. Aim

Objective

To implement and analyze fundamental intensity transformation operations: image negation, image subtraction, and intensity inversion.

2. Description / Theory

Theory: Intensity transformations are point operations that modify pixel values individually. Negation reverses the intensity scale: \(s = (L-1) - r\), useful for enhancing detail in dark regions. Image subtraction \(g = |f_1 - f_2|\) reveals differences between two images, widely used in medical imaging (Digital Subtraction Angiography).

3. Code



# ----------------------------------------------------------------------

# Install dependencies (uncomment for Google Colab)
# !pip install opencv-python-headless matplotlib numpy

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

# === AUTO-DOWNLOAD DATASET (works in Google Colab and locally) ===
import os, urllib.request, zipfile

# Choose which chapter to download (CH01-CH12)
CHAPTER = "CH02"  # Chapter 2: Digital Image Fundamentals
DATASET_PATH = f"datasets/{CHAPTER}/"
DOWNLOAD_BASE = "https://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_book_images"

if not os.path.exists(DATASET_PATH) or not any(f.endswith('.tif') for f in os.listdir(DATASET_PATH)):
    zip_name = f"DIP3E_{CHAPTER}_Original_Images.zip"
    url = f"{DOWNLOAD_BASE}/{zip_name}"
    print(f"Downloading {CHAPTER} dataset from imageprocessingplace.com...")
    urllib.request.urlretrieve(url, "chapter.zip")
    os.makedirs(DATASET_PATH, exist_ok=True)
    with zipfile.ZipFile("chapter.zip", "r") as z:
        for f in z.namelist():
            if f.lower().endswith(".tif"):
                fname = os.path.basename(f)
                if fname:
                    with z.open(f) as src, open(os.path.join(DATASET_PATH, fname), "wb") as dst:
                        dst.write(src.read())
    os.remove("chapter.zip")
    print(f"Downloaded {len([f for f in os.listdir(DATASET_PATH) if f.endswith('.tif')])} images")
else:
    print(f"Dataset ready: {len([f for f in os.listdir(DATASET_PATH) if f.endswith('.tif')])} images")

# List all available images
images = sorted([f for f in os.listdir(DATASET_PATH) if f.endswith('.tif')])
print(f"\nAvailable images ({len(images)}):")
for i, name in enumerate(images, 1):
    print(f"  {i}. {name}")

# === SELECT YOUR IMAGE HERE ===
selected_image = "Fig0232(a)(partial_body_scan).tif"  # Change to any image

# Load the image
img_color = cv2.imread(os.path.join(DATASET_PATH, selected_image))
img_gray = cv2.cvtColor(img_color, cv2.COLOR_BGR2GRAY)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 5))
ax1.imshow(cv2.cvtColor(img_color, cv2.COLOR_BGR2RGB))
ax1.set_title("Original (Color)")
ax1.axis('off')

ax2.imshow(img_gray, cmap='gray')
ax2.set_title("Grayscale")
ax2.axis('off')

plt.suptitle("Grayscale Conversion", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()
print(f"Color shape: {img_color.shape}, Grayscale shape: {img_gray.shape}")

# === SELECT IMAGE FOR NEGATION ===
negation_image = "Fig0232(a)(partial_body_scan).tif"  # Change to any image

img = cv2.imread(os.path.join(DATASET_PATH, negation_image), cv2.IMREAD_GRAYSCALE)

# Compute negative: s = 255 - r
negative = 255 - img

fig, axes = plt.subplots(2, 2, figsize=(12, 10))

# Original image
axes[0, 0].imshow(img, cmap='gray')
axes[0, 0].set_title("Original Image")
axes[0, 0].axis('off')

# Negative image
axes[0, 1].imshow(negative, cmap='gray')
axes[0, 1].set_title("Negative (s = 255 - r)")
axes[0, 1].axis('off')

# Original histogram
axes[1, 0].hist(img.ravel(), bins=256, range=(0, 256), color='black', alpha=0.7)
axes[1, 0].set_title("Original Histogram")
axes[1, 0].set_xlabel("Intensity")
axes[1, 0].set_ylabel("Frequency")

# Negative histogram
axes[1, 1].hist(negative.ravel(), bins=256, range=(0, 256), color='black', alpha=0.7)
axes[1, 1].set_title("Negative Histogram")
axes[1, 1].set_xlabel("Intensity")
axes[1, 1].set_ylabel("Frequency")

plt.suptitle(f"Image Negation: {negation_image}", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

# === ANGIOGRAPHY IMAGE PAIR (change to any two images) ===
mask_file = "Fig0228(a)(angiography_mask_image).tif"
live_file = "Fig0228(b)(angiography_live_ image).tif"

mask = cv2.imread(os.path.join(DATASET_PATH, mask_file), cv2.IMREAD_GRAYSCALE)
live = cv2.imread(os.path.join(DATASET_PATH, live_file), cv2.IMREAD_GRAYSCALE)

# Ensure same size
if mask.shape != live.shape:
    live = cv2.resize(live, (mask.shape[1], mask.shape[0]))

# Compute absolute difference
difference = cv2.absdiff(live, mask)

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
axes[0].imshow(mask, cmap='gray')
axes[0].set_title("Mask Image (Before Contrast)")
axes[0].axis('off')

axes[1].imshow(live, cmap='gray')
axes[1].set_title("Live Image (After Contrast)")
axes[1].axis('off')

axes[2].imshow(difference, cmap='gray')
axes[2].set_title("Subtraction: |Live - Mask|")
axes[2].axis('off')

plt.suptitle("Digital Subtraction Angiography", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

# === DENTAL IMAGE PAIR (change to any two images) ===
dental_file = "Fig0230(a)(dental_xray).tif"
dental_mask_file = "Fig0230(b)(dental_xray_mask).tif"

dental = cv2.imread(os.path.join(DATASET_PATH, dental_file), cv2.IMREAD_GRAYSCALE)
dental_mask = cv2.imread(os.path.join(DATASET_PATH, dental_mask_file), cv2.IMREAD_GRAYSCALE)

if dental.shape != dental_mask.shape:
    dental_mask = cv2.resize(dental_mask, (dental.shape[1], dental.shape[0]))

dental_diff = cv2.absdiff(dental, dental_mask)

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
axes[0].imshow(dental, cmap='gray')
axes[0].set_title("Dental X-ray")
axes[0].axis('off')

axes[1].imshow(dental_mask, cmap='gray')
axes[1].set_title("Dental Mask")
axes[1].axis('off')

axes[2].imshow(dental_diff, cmap='gray')
axes[2].set_title("Subtraction: |Xray - Mask|")
axes[2].axis('off')

plt.suptitle("Dental X-ray Subtraction", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

# === TUNGSTEN IMAGE PAIR (change to any two images) ===
filament_file = "Fig0229(a)(tungsten_filament_shaded).tif"
shading_file = "Fig0229(b)(tungsten_sensor_shading).tif"

filament = cv2.imread(os.path.join(DATASET_PATH, filament_file), cv2.IMREAD_GRAYSCALE)
shading = cv2.imread(os.path.join(DATASET_PATH, shading_file), cv2.IMREAD_GRAYSCALE)

if filament.shape != shading.shape:
    shading = cv2.resize(shading, (filament.shape[1], filament.shape[0]))

# Shading correction via subtraction
corrected = cv2.absdiff(filament, shading)

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
axes[0].imshow(filament, cmap='gray')
axes[0].set_title("Shaded Filament")
axes[0].axis('off')

axes[1].imshow(shading, cmap='gray')
axes[1].set_title("Sensor Shading Pattern")
axes[1].axis('off')

axes[2].imshow(corrected, cmap='gray')
axes[2].set_title("Corrected: |Filament - Shading|")
axes[2].axis('off')

plt.suptitle("Shading Correction", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

# Invert the angiography subtraction result
inverted_diff = 255 - difference

fig, axes = plt.subplots(1, 3, figsize=(15, 5))
axes[0].imshow(difference, cmap='gray')
axes[0].set_title("Subtraction Result")
axes[0].axis('off')

axes[1].imshow(inverted_diff, cmap='gray')
axes[1].set_title("Inverted Subtraction (255 - diff)")
axes[1].axis('off')

# Enhanced version with contrast stretching
enhanced = cv2.normalize(difference, None, 0, 255, cv2.NORM_MINMAX)
axes[2].imshow(enhanced, cmap='gray')
axes[2].set_title("Enhanced (Contrast Stretched)")
axes[2].axis('off')

plt.suptitle("Inversion and Enhancement Pipeline", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

# Full pipeline on angiography images
fig, axes = plt.subplots(2, 3, figsize=(15, 10))

axes[0, 0].imshow(mask, cmap='gray')
axes[0, 0].set_title("1. Mask Image")
axes[0, 0].axis('off')

axes[0, 1].imshow(live, cmap='gray')
axes[0, 1].set_title("2. Live Image")
axes[0, 1].axis('off')

axes[0, 2].imshow(difference, cmap='gray')
axes[0, 2].set_title("3. |Live - Mask|")
axes[0, 2].axis('off')

axes[1, 0].imshow(255 - mask, cmap='gray')
axes[1, 0].set_title("4. Negation of Mask")
axes[1, 0].axis('off')

axes[1, 1].imshow(inverted_diff, cmap='gray')
axes[1, 1].set_title("5. Inverted Difference")
axes[1, 1].axis('off')

axes[1, 2].imshow(enhanced, cmap='gray')
axes[1, 2].set_title("6. Enhanced Result")
axes[1, 2].axis('off')

plt.suptitle("Complete Pipeline: Subtraction -> Negation -> Enhancement", fontsize=14, fontweight='bold')
plt.tight_layout()
plt.show()

Part 1: Image Negation (s = 255 - r)

Compute the negative of an image by inverting all pixel intensities.

Part 2: Image Subtraction |Img1 - Img2|

Compute the absolute difference between two images to reveal hidden structures.

Pairs

Part 3: Complete Pipeline (Subtraction → Negation → Enhancement)

Run the full pipeline on the selected image pair: subtraction, then negation of result, then contrast enhancement.

4. Output

5. Analysis / Conclusion

Analysis Questions

In the angiography example, what structures become visible after subtraction that were not visible in either original image?
Why is absolute difference used instead of simple subtraction? What would happen with signed vs unsigned arithmetic?
Compare the histogram of the original image with its negative. What mathematical relationship exists between them?