EP02_11 — 🏆 Perspective Correction (Homography) in a Real Image

2.12.11 EP02_11 🏆 Perspective Correction (Homography) in a Real Image

In this activity, the goal is to apply perspective transformation (homography) to “rectify” a tilted object in a real photograph. You will work with an image of a newspaper, where the grid of a Sudoku puzzle is distorted due to the angle at which the photo was taken.

Your program must read input parameters from the terminal, load the image, compute the \(3 \times 3\) homography matrix, apply the geometric transformation, and display a global validation indicator.

• Read two integers L and C, representing the row and column dimensions (height and width) that the rectified output image should have.
• Read four coordinate pairs \((x, y)\) from the terminal, representing the four corners of the source quadrilateral (the distorted Sudoku in the original image).
• Automatically compute the four destination coordinate pairs using the provided dimensions \(L\) and \(C\), mapping the corners to the edges of the new image: \((0,0)\), \((C-1, 0)\), \((0, L-1)\), and \((C-1, L-1)\).
• Load the local image sudoku.png and convert it to grayscale.
• Compute the homography matrix and apply the spatial transformation to the image.
• Output: Calculate and print the sum of all pixels of the resulting image.

📌 Important:

• Input file: The image sudoku.png must be in the same folder as the script. The program must read it directly from disk (e.g., using mm.read("sudoku.png") or cv2.imread).
• Point Order: Ensure that the reading of the 4 source points and the generation of the 4 destination points strictly follow the same corner order: Top-Left (TL), Top-Right (TR), Bottom-Left (BL), and Bottom-Right (BR).
• Dimensions in OpenCV: Remember that functions such as cv2.warpPerspective expect the output image size in the format (width, height), which is equivalent to (C, L).
• Interpolation: To ensure mathematical consistency of the pixel sum with the automatic grader, use the default bilinear interpolation (flags=cv2.INTER_LINEAR).
• Credits: The image used is “Sudoku en periódico” by Héctor Rodríguez, licensed under CC BY 2.0.

2.12.11.3 Sudoku image acquisition and conversion to grayscale

Figure 2.22 shows the reading of the original image followed by its conversion to grayscale and resizing to a \(500 \times 500\) pixel matrix, preparing the data for the next step.

The perspective correction, applied at Figure 2.23 via the homography matrix, eliminates distortions caused by the camera angle and produces a frontal, regular view of the Sudoku grid.

import cv2
import numpy as np

# --- 1. Loads the saved image (sudoku.png) ---
img = mm.read("sudoku.png")                # BGR, 500×500

# --- 2. Padding to avoid cutting off vertices ---
PAD = 60
img_pad = cv2.copyMakeBorder(
    img, PAD, PAD, PAD, PAD,
    cv2.BORDER_CONSTANT, value=[255, 255, 255]
)

# --- 3. Source points (grid corners in the expanded image) ---
pts1 = np.float32([
    [100, 160],    # TL
    [390, 45],    # TR
    [200, 580],   # BL
    [570, 420],   # BR
])
#     W    H

# --- 4. Destination points (front view 500×500) ---
SIZE = 500
pts2 = np.float32([
    [0,    0],
    [SIZE, 0],
    [0,    SIZE],
    [SIZE, SIZE],
])

# --- 5. Homography and rectification ---
img_rect = mm.perspective_transform(img_pad, pts1, pts2, size=(SIZE, SIZE))

# --- 6. Display ---
mm.show(
    [img_pad, img_rect],
    titles=["Original (with padding)", "Rectified front view"],
    cols=2, figsize=(10, 6), axis=True
)

🎮 Simulator EP02_11: Sudoku Perspective 3×3 Homography · CC BY 2.0

📷 Original (Expanded) — Drag the Corners Photo: Héctor Rodríguez · CC BY 2.0

✅ Corrected (400×400) — Frontal View

↺ Reset Points ✨ Correct Perspective 🔲 Toggle Padding

Loading Sudoku image...

%%writefile EP02_11.py
# Python code

Overwriting EP02_11.py

TestSuite("EP02_11.py").run()

✔️ EP02_11.cases already exists in casos/
📋 4 case(s) loaded from casos/EP02_11.cases

🔍 Testing Python: EP02_11.py
⚠️ EP02_11.py: Empty file (fewer than 3 lines). Tests skipped.