How to remove convexity defects in a Sudoku square?

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I was doing a fun project: Solving a Sudoku from an input image using OpenCV (as in Google goggles etc). And I have completed the task, but at the end I found a little problem for which I came here.

I did the programming using Python API of OpenCV 2.3.1.

Below is what I did :

1. Read the image
2. Find the contours
3. Select the one with maximum area, ( and also somewhat equivalent to square).

4. Find the corner points.

   e.g. given below:

   (Notice here that the green line correctly coincides with the true boundary of the Sudoku, so the Sudoku can be correctly warped. Check next image)

5. warp the image to a perfect square

   eg image:

6. Perform OCR ( for which I used the method I have given in Simple Digit Recognition OCR in OpenCV-Python )

And the method worked well.

Problem:

Check out this image.

Performing the step 4 on this image gives the result below:

The red line drawn is the original contour which is the true outline of sudoku boundary.

The green line drawn is approximated contour which will be the outline of warped image.

Which of course, there is difference between green line and red line at the top edge of sudoku. So while warping, I am not getting the original boundary of the Sudoku.

My Question :

How can I warp the image on the correct boundary of the Sudoku, i.e. the red line OR how can I remove the difference between red line and green line? Is there any method for this in OpenCV?

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