Text skew detection and correction in image

clc;clear all; close all;
a=imread('eq2.jpg');
figure;
imshow(a)
if size(a,3)==3
    a=rgb2gray(a);
end
b=im2bw(a);
ar=imrotate_white(b,30);
figure
imshow(ar);

br=~(ar);
figure
imshow(br)

[r c]=size(b);
X=[];
for i=1:r
    for j=1:c
        if br(i,j)==1;
            X=[X; i j];
        end
    end
end
size(X);
[coeff, score, latent]=pca(X);
figure;
biplot(coeff(:,1:2),'Scores',score(:,1:2),'VarLabels',{'v_1','v_2'});

r=sqrt((coeff(1,1))^2+(coeff(1,2))^2);
th=real(double(vpa(acos(coeff(1,1)/r)*180/pi)))
syms x
th=real(double(vpa(solve(x==th-90))))

rotatedImage=imrotate(br,-th);
figure
imshow(rotatedImage)




function rotated_image = imrotate_white(image, rot_angle_degree)
    RA = imref2d(size(image));    
    tform = affine2d([cosd(rot_angle_degree)    -sind(rot_angle_degree)     0; ...
                      sind(rot_angle_degree)     cosd(rot_angle_degree)     0; ...
                      0                          0                          1]);
      Rout = images.spatialref.internal.applyGeometricTransformToSpatialRef(RA,tform);
      Rout.ImageSize = RA.ImageSize;
      xTrans = mean(Rout.XWorldLimits) - mean(RA.XWorldLimits);
      yTrans = mean(Rout.YWorldLimits) - mean(RA.YWorldLimits);
      Rout.XWorldLimits = RA.XWorldLimits+xTrans;
      Rout.YWorldLimits = RA.YWorldLimits+yTrans;
      rotated_image = imwarp(image, tform, 'OutputView', Rout, 'interp', 'cubic', 'fillvalues', 255);
end

The output is

Rotate orgin image angle= 30

The answer is angle = 25.1508 !!!!

The angle must be 30 .

How do I solve this problem?

This problem appears to me in the rational equations only, but in the linear equations the angle is shown with high accuracy.

Answer 1

[cr]

In general, pattern maching is used. See estimateGeometricTransform()

But the result may not be exactly the angle it's rotated to.

[Yahya]

Not useful :( ,thanks for answering

[Image Analyst]

@Yahya Then why did you accept the answer?

In general, for an arbitrary, random set of blobs, there is no way to determine what is the "correct" skew and orientation angle.