Dissecting the Structure of a QR Code

QR codes may seem complex at first glance, but they actually have a logical structure. By understanding this structure, it is possible to decode them manually.

Basic Components

1. Finder Pattern: Large squares located at three corners of the QR code. These are used to determine the position and orientation of the QR code.

2. Alignment Pattern: Small squares present in QR codes of version 2 and above. These are used for correcting distortions.

3. Timing Pattern: Alternating black and white patterns. These are used to accurately determine the position of the cells.

4. Format Information: Located around the finder patterns. This includes information about the error correction level and mask pattern.

5. Version Information: Present in QR codes of version 7 and above. This indicates the version of the QR code.

6. Data Area: The area where the actual data is stored.

Decoding Format Information

Format information consists of 15 bits and includes the following information:

[Error Correction Level (2 bits)][Mask Pattern (3 bits)][Error Correction Data (10 bits)]

This data is masked with 101010000010010 using XOR. First, this mask needs to be removed.

Reading the Data

1. Mode Indicator: The first 4 bits indicate the data mode (numeric, alphanumeric, byte, kanji).

2. Character Count Indicator: The number of bits indicating the character count depends on the mode.

3. Data: The actual data is encoded here.

4. Terminator Pattern: A pattern of 0000 indicating the end of the data.

Removing the Mask Pattern

One of the eight mask patterns is applied to the data area. The mask pattern is determined by the following formulas:

(i, j) = (row number, column number)
0: (i + j) mod 2 = 0
1: i mod 2 = 0
2: j mod 3 = 0
3: (i + j) mod 3 = 0
4: ((i div 2) + (j div 3)) mod 2 = 0
5: (i * j) mod 2 + (i * j) mod 3 = 0
6: ((i * j) mod 2 + (i * j) mod 3) mod 2 = 0
7: ((i + j) mod 2 + (i * j) mod 3) mod 2 = 0

By inverting the color of the cells corresponding to the mask pattern, the original data can be restored.

Converting the Data

The data is divided into 8-bit segments and decoded according to the mode. For example, in alphanumeric mode:

11 bits encode 2 characters
(value of the 1st character * 45 + value of the 2nd character)

By converting in this way, the original data can be restored.

Implementing the Program

When decoding with a program, the following steps are taken:

1. Use an image processing library to binarize the QR code.
2. Detect the finder patterns and determine the orientation of the QR code.
3. Read the format information to determine the error correction level and mask pattern.
4. Read the data area and remove the mask.
5. Retrieve the data as a bit sequence and decode it according to the mode.

import cv2
import numpy as np

def decode_qr(image_path):
    # Load and binarize the image
    img = cv2.imread(image_path, cv2.IMREAD_GRAYSCALE)
    _, binary = cv2.threshold(img, 128, 255, cv2.THRESH_BINARY)

    # Detect the finder patterns
    # ...

    # Read the format information
    # ...

    # Read the data and remove the mask
    # ...

    # Decode the data
    # ...

    return decoded_data

# Example usage
result = decode_qr('qr_code.png')
print(result)

By implementing this, the process of manually decoding a QR code can be replicated programmatically.

Decoding QR codes is an intriguing challenge that goes beyond simply reading barcodes. It requires an understanding of data structures and encoding. Through this process, one can deepen their knowledge in various fields such as information theory, error correction, and image processing.