# Automated Sudoku Solver. Marty Otzenberger EGGN 510 December 4, 2012

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1 Automated Sudoku Solver Marty Otzenberger EGGN 510 December 4, 2012

2 Outline Goal Problem Elements Initial Testing Test Images Approaches Final Algorithm Results/Statistics Conclusions Problems/Limits Future Work/Improvements References Questions

3 Goal From an image of a Sudoku puzzle, extract and solve the puzzle, and display the solution over the top of the puzzle.

4 Problem Elements Extract the puzzle from the image. Identify the numbers in each cell. Correlate the numbers to their respective cell position. Solve the puzzle. Display the solution over the image.

5 Initial Testing Began by using an ideal digitally fabricated image to reduce complexity. Chose the Wikipedia image for Sudoku. Used a Hough Transform to extract the lines in the puzzle, and segmented the image based on the rho values. Parameters very sensitive to capture only one Hough line per puzzle line. Used averages if multiple existed close together

6 Initial Testing cont. Cropped image between each set of rho values, and performed Normalized Cross Correlation on each sub image. I saved the max score for a cross correlation of each sub image with all 9 template digits, and then used the max of those peak scores to identify the digit. Used the total number of black pixels in a square as a threshold for determining if it was empty. Cropped the template images out of the puzzle. Processed sub images in order to preserve location information.

7 Initial Testing cont. Solved the puzzle using a MATLAB script I found which recursively solves for possible values for every blank cell in the puzzle[1]. Used Hough line rho values to re project the solution onto the image using MATLAB text. [1] G.M. Boynton, MATLAB Sudoku Solver, MATLAB Central File Exchange, 2005, Accessed: 12/2/2012, matlab sudoku solver

8 Test Images Want to expand code to handle real images of puzzles taken from a variety of angles. Took a series of 25 test images of 25 different puzzles to test with. All images taken from the same Sudoku book to keep digits in a common font. Intentionally took some extreme images to test the robustness of my algorithm.

9 Test Images cont.

10 Approaches Initially tried to again use Hough Transforms, but had difficulty. Curvature in the lines caused finding a single line difficult without human intervention on every image. Even extraction of the puzzle boundary was difficult using Hough. Found connected components helpful to extract puzzle region by looking for objects of the right size. Still had difficulty finding lines. Could have caused problems if the images were at different zoom levels.

11 Final Algorithm Use MATLAB cpselect tool to manually identify the corners of the puzzle, and project them onto a template image of a square.

12 Final Algorithm cont. Used a projective transform which preserves quadrilaterals through scaling, rotation, and translation. This made the puzzle the same size and shape in every image. Also reduced the size of the images to speed up processing. Next used regionprops to find connected components and extract the puzzle by looking at the component s width, and height. Absolute pixel changes every time because MATLAB does not crop the image when transforming. Used the bounding box of the puzzle to crop the image.

13 Final Algorithm cont. After cropping the image to extract the puzzle, I again looked at the connected components to extract the numbers. I then cropped out the region around the centroid of each number to ensure it was larger than my template image and used the same normalized crosscorrelation strategy as before.

14 Final Algorithm cont. Used the absolute pixel value of the digit centroid to identify its row and column within the puzzle. Possible because the projective transform made the puzzle the same size in every image. From here I used the same solver to solve the puzzle, and used absolute pixel locations to display the solution on top of the puzzle.

15 Results/Statistics 18 of my 25 test images processed successful. 3 failed due to shadows on the puzzle. 2 failed due to discontinuous borders on the puzzle preventing regionprops from finding it. 1 failed due to noise connected to the border of the puzzle. 1 failed due to distortion leading to incorrect numeric classification. This is a 72% success rate.

16 Results/Statistics cont.

17 Results/Statistics cont.

18 Conclusions Pleasantly surprised by the performance of the algorithm. Handled off angle images of the puzzles very well. Most issues due noise/thresholding.

19 Problems/Limits Current algorithm requires user interaction. Difficulty handling shadows on the puzzle. Can only process puzzles using the same font set. Cannot handle distortion in the puzzle. This will probably be difficult to fix, particularly without changing away from cross correlation.

20 Future Work/Improvements Automate corner detection to find projection. Should be able to make process fully automated. Look at better thresholding algorithm. Try to eliminate some of the shadow and noise issues. Use mean centroid value of digits to align solutions. Sometimes the solutions don t line up well with the grid because of distortion in the projected image. Project the solution onto original image. Re project the solutions back to the orientation of the original image and show them on the original. Implement camera calibration. Could help improve cross correlation reliability.

21 Questions?

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