Detect angle of text in image with horizontal and rotate in matlab

Question

See the image below :

As you can seen in the image the written text in rotated by 90 deg angle and I want to rotate only the text to be horizontal. By what ever angle it is rotated I want to make it horizontal as in below :

I don't want the complete image to the rotated. I want that the text only is bounded and the angle by which the text is rotated is measured and then rotated by that angle to make it horizontal.

Can you suggest me a way to do so and then fit an ellipse onto the text ?

Thank you.

Answer 1

First, let's find x-y coordinates of all the dark pixels

bw = imread('http://i.imgur.com/0LxC6bd.png');
bw = min( bw, [], 3 ) < 50 ; % dark pixels - intensity lower than 50
[y x] = find( bw ); % note that find returns row-col coordinates.

Compute the covariance matrix of the text coordinates

mx = mean(x);
my = mean(y);
C = [ mean( (x-mx).^2 ),     mean( (x-mx).*(y-my) );...
      mean( (x-mx).*(y-my) ) mean( (y-my).^2 ) ];

---

You can get the orientation of the ellipse from the eigen vectors and eigen values of C:

[V D] = eig( C );
figure; imshow( bw ); hold on;
quiver( mx([1 1]), my([1 1]), (V(1,:)*D), (V(2,:)*D), .05 );  

Looking at the eigenvectors and eigen values:

V =
-0.9979   -0.0643
-0.0643    0.9979

D = 
1.0e+003 *
0.1001         0
     0    1.3652

You can see that the eigen-vectors (columns of V) are approximately the pointing to the -X direction (first column) and the Y direction (second column). Examining the eigen values (diagonal of D) you can see that the second eigen value is much larger than the first - this is the major axis of your ellipse. Now you can recover the orientation of the ellipse:

[~, mxi] = max(diag(D)); % find major axis index: largest eigen-value

Recover the angle from the corresponding eigen-vector

or = atan2( V(2,mxi), V(1,mxi) ) * 180/pi ; % convert to degrees for readability
or =
93.6869

As you can see the major axis of the ellipse is almost 90deg off the horizon. You can rotate the image back

imrotate( bw, -or );

---

Drawing an ellipse given the covariance matrix:

th = linspace(0, 2*pi, 500 );
xy = [cos(th);sin(th)];
RR = chol( C ); % cholesky decomposition
exy = xy'*RR; %//'
figure;imshow( bw ); hold on;
plot( 2*exy(:,1)+mx, 2*exy(:,2)+my, 'r', 'LineWidth', 2 );