[Octave-bug-tracker] [bug #44100] image package: regionprops could easily deliver more properties

[H. G.]

Follow-up Comment #6, bug #44100 (project octave):

Here is a new version for the 4 "ellipse" properties in the regionprops.m
file. (They are slightly improved with respect to the last version, now they
are more accurate for very small regions.)


    case "majoraxislength" 
        if (N > 2)
          warning ("regionprops: skipping majoraxislength for Nd image");
          break
        endif
        
        for k = 1:num_labels
          [Y, X] = find (L == k);        
          
          if (numel(Y) > 1)
            % calculate (centralised) second moment of region
            C = cov ([X(:), Y(:)], 1);    % option 1 for normalisation with n
instead of n-1
            C = C + 1/12.*eye(size(C,1)); % centralised second moment of 1
pixel is 1/12
            lambda = eig (C);
            retval (k).MajorAxisLength =4 * sqrt(max(lambda));            
          else
            retval (k).MajorAxisLength = 1;
          endif
        endfor     
        
     case "minoraxislength" 
         if (N > 2)
          warning ("regionprops: skipping minoraxislength for Nd image");
          break
        endif
        
        for k = 1:num_labels
          [Y, X] = find (L == k);
          if (numel(Y) > 1)
            % see case majoraxislength for explanations
            C = cov ([X(:), Y(:)], 1);         
            C = C + 1/12.*eye(size(C,1)); 
            lambda = eig (C);            
            retval (k).MinorAxisLength =4 * sqrt(min(lambda));
          else
            retval (k).MinorAxisLength = 1;
          endif
        endfor    
        
     case "eccentricity"
         if (N > 2)
          warning ("regionprops: skipping eccentricity for Nd image");
          break
        endif
        
        for k = 1:num_labels
          [Y, X] = find (L == k);
          if (numel(Y) > 1)
            % see case majoraxislength for explanations
            C = cov ([X(:), Y(:)], 1);        
            C = C + 1/12.*eye(size(C,1)); 
            lambda = eig (C);
            major =  2 * sqrt(max(lambda));
            minor =  2 * sqrt(min(lambda));
            retval (k).Eccentricity = sqrt(1-(minor/major)^2);
          else
            retval (k).Eccentricity = 0; % a circle has 0 eccentricity
          endif
        endfor     
        
     case "orientation"
        if (N > 2)
          warning ("regionprops: skipping orientation for Nd image");
          break
        endif

        for k = 1:num_labels
          [Y, X] = find (L == k);
          if (numel (Y) > 1)
            % see case majoraxislength for explanations
            C = cov ([X(:), Y(:)], 1);
            C = C + 1/12.*eye(size(C,1)); 
            [V, lambda] = eig (C);
            [max_val, max_idx] = max (diag (lambda));
            max_vec = V(:, max_idx);
            retval (k).Orientation = -(180/pi)  * atan (max_vec (2) / max_vec
(1));      
          else
            retval (k).Orientation = 0; 
          endif
        endfor


As you can see, I've also added the Orientation feature to my code. Those 4
properties are consistent now. And I think they should be Matlab compatible as
well. (It may be worth checking the results of the tests with a real Matlab
nevertheless. I don't have access to it for the next months.)

And here are a few tests for those 4 new features:


a = eye(4);
t = regionprops(a, 'majoraxislength');
assert(t.MajorAxisLength, 6.4291,  1e-3);

b = ones(5);
t = regionprops(b, 'majoraxislength');
assert(t.MajorAxisLength, 5.7735 , 1e-3);

c = [0 0 1; 0 1 1; 1 1 0];
t = regionprops(c, 'majoraxislength');
assert(t.MajorAxisLength, 4.1633 , 1e-3);

a = eye(4);
t = regionprops(a, 'minoraxislength');
assert(t.MinorAxisLength, 1.1547 , 1e-3);

b = ones(5);
t = regionprops(b, 'minoraxislength');
assert(t.MinorAxisLength, 5.7735 , 1e-3);

c = [0 0 1; 0 1 1; 1 1 0];
t = regionprops(c, 'minoraxislength');
assert(t.MinorAxisLength, 1.8037 , 1e-3);

a = eye(4);
t = regionprops(a, 'eccentricity');
assert(t.Eccentricity, 0.98374 , 1e-3);

b = ones(5);
t = regionprops(b, 'eccentricity');
assert(t.Eccentricity, 0 , 1e-3);

c = [0 0 1; 0 1 1; 1 1 0];
t = regionprops(c, 'eccentricity');
assert(t.Eccentricity, 0.90128 , 1e-3);

a = eye(4);
t = regionprops(a, 'orientation');
assert(t.Orientation, -45 , 1e-3);

b = ones(5);
t = regionprops(b, 'orientation');
assert(t.Orientation, 0 , 1e-3);

c = [0 0 1; 0 1 1; 1 1 0];
t = regionprops(c, 'orientation');
assert(t.Orientation, 45 , 1e-3);



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