Why does translation with imwarp + affine2d-object enlarges the object?

Hey everybody,

i searched the forum for an answer but couldnt find one, so i hope oyu can help me here.

I have some troubles with image translation which i need to center objects in a binary image with its centroid to the image center. After i thought i am already done i found some bug for which i dont find a solution.

When ever i try to translate an object in a binary image by any given delta_x/y the object after translation has increased its area.

Here is some example i wrote for the questions to point out the problem:

 %create binary T shape
 shape = zeros(40,40);
 shape(10,10:30) = 1;
 shape(11:30,20) = 1;
 shape = im2bw(shape);

 disp(['Area before: ',num2str(sum(sum(shape)))]);

 %create Reference2D object
 Rout = imref2d(size(shape));

 %create affine2d object for translation
 delta_x = -5;
 delta_y = 8;
 tform = affine2d([1 0 0; 0 1 0; delta_x delta_y 1]);

 %execute translation
 output = imwarp(shape,tform,'outputView',Rout);
 disp(['Area after: ',num2str(sum(sum(output)))]);

The Output then is:

Area before: 41
Area after: 84

The syntax of the affine2d-object should be right, regarding to this page: http://de.mathworks.com/help/images/performing-general-2-d-spatial-transformations.html

I tried it with a couple of objects and i am facing always the same problem. Even with:

shape = zeros(40,40);
shape(10:30,10:30) = 1;
shape = im2bw(shape);

i got the following output:

Area before: 441
Area after: 484

So its not a problem of "slim" objects with parts of width = 1;

I would be very happy if anybody could help me out, as it is essential for me to maintain objects size...

Thanks in advance, Frederik

[Frederik Kratzert]

btw: using circshift(shape,[delta_x,delta_y]) does work properly...anyway i would be interested in a answer/solution, because i find imwarp somehow easier to use if the image has to be enlarged because the translation would the object cause to be outside of the image..

Answer 1

[David Young]

The reason for the enlargement is the interpolation rule that imwarp uses - 'linear' by default. Because the image is binary, some pixels close to the boundary of the translated shape are given interpolated values that are rounded to be 1 rather than 0. If you use 'nearest' interpolation, you will not get the increase.

output = imwarp(shape,tform,'nearest','outputView',Rout);

[Frederik Kratzert]

thank you very much, this solves the problem perfectly!

Answer 2

[Image Analyst]

That transform enlarges the object. Use imshow() to show it:

%create binary T shape
shape = zeros(40,40);
shape(10,10:30) = 1;
shape(11:30,20) = 1;
shape = im2bw(shape);
subplot(1,2,1);
imshow(shape);
axis on;

disp(['Area before: ',num2str(sum(sum(shape)))]);

%create Reference2D object
Rout = imref2d(size(shape));

%create affine2d object for translation
delta_x = -5;
delta_y = 8;
tform = affine2d([1 0 0; 0 1 0; delta_x delta_y 1]);

%execute translation
output = imwarp(shape,tform,'outputView',Rout);
subplot(1,2,2);
imshow(output);
axis on;
disp(['Area after: ',num2str(sum(sum(output)))]);

[Frederik Kratzert]

Hey Image Analyst,

thanks for your answer but i think you understood me wrong or i expressed my question not the way i wanted.

I know, that the the code enlarges the object, the question is "why"!

Because the affine2d object should only apply a translation and no scaling as the corresponding entries in the tform matrix are 1's.

Referring again to this link: http://de.mathworks.com/help/images/performing-general-2-d-spatial-transformations.html

So what i want is a translation without enlargment as circshift does.

Any suggestions or comments on the problem?