Fixing Convexity Defects in Sudoku Squares

• Introduction
• Step-by-Step Guide
• Code Example
• Additional Notes
• Summary
• Conclusion
• References

This article provides a step-by-step guide on how to detect and fill the grid lines of a Sudoku puzzle in an image using OpenCV in Python. The process involves loading the image, converting it to grayscale, applying thresholding to obtain a binary image, finding contours, identifying the largest contour as the Sudoku grid, approximating the contour to a polygon, and filling its convexity defects to complete the grid lines.

1. Import necessary libraries:

import cv2

2. Load the image:

image = cv2.imread('sudoku_image.jpg')

3. Convert the image to grayscale:

gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)

4. Apply thresholding to create a binary image:

thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY)[1]

5. Find contours in the binary image:

contours, _ = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

6. Find the contour with the largest area (assumed to be the Sudoku grid):

largest_contour = max(contours, key=cv2.contourArea)

7. Approximate the contour to a polygon:

epsilon = 0.1 * cv2.arcLength(largest_contour, True)
approx = cv2.approxPolyDP(largest_contour, epsilon, True)

8. Check if the polygon has 4 sides (indicating a square):

if len(approx) == 4:
    # Proceed with convexity defect analysis

9. Find convexity defects of the contour:

hull = cv2.convexHull(approx, returnPoints=False)
defects = cv2.convexityDefects(approx, hull)

10. Iterate through the defects and draw lines to fill the convexity defects:

for i in range(defects.shape[0]):
    s, e, f, d = defects[i, 0]
    start = tuple(approx[s][0])
    end = tuple(approx[e][0])
    far = tuple(approx[f][0])
    cv2.line(image, start, end, (0, 255, 0), 2)

11. Display the image with filled convexity defects:

cv2.imshow('Sudoku Grid', image)
cv2.waitKey(0)

This Python code uses OpenCV to detect and fill in the gaps in a Sudoku grid from an image. It first identifies the grid as the largest square shape in the image. Then, it analyzes the grid's outline and fills any inward indentations, resulting in a more complete and defined grid for further processing.

import cv2

# Load the image
image = cv2.imread('sudoku_image.jpg')

# Convert the image to grayscale
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)

# Apply thresholding to create a binary image
thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY)[1]

# Find contours in the binary image
contours, _ = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

# Find the contour with the largest area (assumed to be the Sudoku grid)
largest_contour = max(contours, key=cv2.contourArea)

# Approximate the contour to a polygon
epsilon = 0.1 * cv2.arcLength(largest_contour, True)
approx = cv2.approxPolyDP(largest_contour, epsilon, True)

# Check if the polygon has 4 sides (indicating a square)
if len(approx) == 4:
    # Find convexity defects of the contour
    hull = cv2.convexHull(approx, returnPoints=False)
    defects = cv2.convexityDefects(approx, hull)

    # Iterate through the defects and draw lines to fill the convexity defects
    for i in range(defects.shape[0]):
        s, e, f, d = defects[i, 0]
        start = tuple(approx[s][0])
        end = tuple(approx[e][0])
        far = tuple(approx[f][0])
        cv2.line(image, start, end, (0, 255, 0), 2)

# Display the image with filled convexity defects
cv2.imshow('Sudoku Grid', image)
cv2.waitKey(0)

Explanation:

1. Import cv2: This line imports the OpenCV library.
2. Load the image: This line loads the image from the specified file path.
3. Convert to grayscale: This line converts the color image to grayscale.
4. Apply thresholding: This line applies binary thresholding to the grayscale image, creating a black and white image where pixels above the threshold are white and below are black.
5. Find contours: This line finds the outlines of the objects in the binary image.
6. Find largest contour: This line finds the contour with the largest area, which is assumed to be the Sudoku grid.
7. Approximate contour: This line approximates the contour to a polygon, simplifying its shape.
8. Check for square: This line checks if the approximated polygon has 4 sides, indicating a square.
9. Find convexity defects: This line finds the convexity defects of the contour, which are the inward indentations.
10. Fill convexity defects: This loop iterates through the defects and draws lines between the start and end points of each defect, effectively filling the indentations.
11. Display the image: This line displays the image with the filled convexity defects.

This code will identify the Sudoku grid in the image and fill any small gaps or irregularities in the grid lines, making it easier to process the grid further for digit recognition.

Assumptions:

• Single Sudoku Grid: The code assumes there's only one Sudoku grid in the image. If multiple grids exist, additional logic is needed to select the desired one.
• Clear Image: The success of this code depends on the quality of the input image. A clear image with good contrast between the grid lines and the background will yield better results.
• Square Grid: The code specifically looks for a 4-sided polygon, assuming a square Sudoku grid. It might not work accurately for distorted or non-square grids.

Possible Improvements:

• Adaptive Thresholding: Instead of using a fixed threshold value, consider using adaptive thresholding techniques like cv2.adaptiveThreshold() to handle varying illumination conditions in the image.
• Contour Filtering: Implement more robust contour filtering based on properties like aspect ratio and solidity to ensure the selected contour is indeed the Sudoku grid.
• Perspective Transformation: After detecting the grid, apply perspective transformation to obtain a top-down view of the Sudoku puzzle, which can be useful for digit recognition.
• Error Handling: Incorporate error handling mechanisms to handle cases where no contours are found or the largest contour doesn't meet the criteria of a Sudoku grid.

Applications:

• Sudoku Solver: This code can be used as a pre-processing step in a Sudoku solver application. After detecting and filling the grid, digit recognition techniques can be applied to extract the numbers and solve the puzzle.
• Document Scanning: The principles used in this code can be extended to detect and enhance grids in other types of documents, such as tables and forms.

Additional Considerations:

• Parameter Tuning: The threshold value and epsilon value used in the code might need adjustments depending on the specific image being processed.
• Computational Cost: While this code demonstrates a basic approach, consider optimizing for performance, especially if dealing with a large number of images or real-time applications.

This Python code uses OpenCV to detect and fill in the missing lines of a Sudoku grid from an image. Here's a breakdown:

1. Image Preprocessing:

• Load Image: Reads the Sudoku image (sudoku_image.jpg).
• Grayscale Conversion: Converts the image to grayscale for easier processing.
• Thresholding: Creates a binary (black and white) image by setting a threshold. Pixels above the threshold become white, and those below become black. This helps isolate the grid lines.

2. Contour Detection and Selection:

• Find Contours: Identifies outlines of objects (the grid lines in this case) in the binary image.
• Largest Contour: Assumes the contour with the largest area represents the Sudoku grid.

3. Grid Refinement:

• Polygon Approximation: Simplifies the contour by approximating it as a polygon. This helps smooth out any irregularities in the detected grid lines.
• Square Check: Verifies if the approximated polygon has 4 sides, indicating a square (a common Sudoku grid shape).

4. Convexity Defect Filling:

• Convex Hull: Calculates the smallest convex polygon that encloses the grid contour.
• Convexity Defects: Identifies any inward indentations (missing lines) in the contour compared to its convex hull.
• Line Drawing: Draws lines to connect the points of each convexity defect, effectively filling in the missing grid lines.

5. Result Display:

• Show Image: Displays the original image with the filled-in Sudoku grid.

In essence, the code:

1. Isolates the Sudoku grid in the image.
2. Identifies missing grid lines as convexity defects.
3. Fills in those missing lines to complete the grid.

This article demonstrated how to use OpenCV in Python to detect and fill the grid lines of a Sudoku puzzle from an image. By converting the image to grayscale, applying thresholding, finding contours, and analyzing convexity defects, the code successfully identifies and fills in missing or incomplete grid lines. This pre-processing step is crucial for developing applications like Sudoku solvers, as it prepares the image for digit recognition. The code, however, relies on certain assumptions about the input image and could benefit from further improvements, such as adaptive thresholding and perspective transformation, to enhance its robustness and applicability to a wider range of Sudoku images.

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