Re: [OctDev] imrotate

[Paul K. <pki...@us...>]

On Feb 16, 2005, at 5:08 AM, Justus Piater wrote:

>> Using a smoother function worked better:
>>
>> 	X = peaks(30);
>> 	Y = imrotate(imrotate(X,30,'bicubic'),-30,'bicubic');
>> 	norm(X(17+[1:5],17+[1:5])-Y(30+[1:5],30+[1:5]))
>> 	ans = 0.0036647
>
> I like this. I suggest to use "crop", this saves indexing adjustments
> and makes the code more transparent and robust to future changes to
> the size of the rotated image. Moreover, Fourier does not seem to
> handle negative pixel values:
>
>   X = peaks(30);
>   X -= min(min(X));
>   Y = imrotate(imrotate(X, 30, "bicubic", "crop"), -30, "bicubic", 
> "crop");
>   norm(X(10:20,10:20) - Y(10:20,10:20))
>   ans = 0.076178
>
> This can now be used with all four interpolation methods.

This still begs the question of what is a 'good' value.  How about the
following:

    x=peaks(50);
    y=x; for i=1:5, y=imrotate(y,60,'bicubic','crop'); end
    norm((x-imrotate(y,59,'bicubic','crop'))(10:40,10:40))
      ans = 2.6138
    norm((x-imrotate(y,60,'bicubic','crop'))(10:40,10:40))
      ans = 0.069348
    norm((x-imrotate(y,61,'bicubic','crop'))(10:40,10:40))
      ans = 2.6850

This should be a pretty good test of slight over- or under- rotation.

I'm sure you already know the rotation is lossy:

     y=x=peaks(50);
     for i=1:6, y=imrotate(y,60,'bicubic','crop'); end
     norm((x-y)(10:40,10:40))
       ans = 0.069348
    for i=1:6, y=imrotate(y,60,'bicubic','crop'); end
    norm((x-y)(10:40,10:40))
       ans = 0.13736


> As a complementary test of the "nearest" method, I suggest to compare
> near-90-degree rotations to exact 90-degree rotations (only the latter
> are handled by rot90, with greetings to Todd!). For odd image sizes,
> the result should be exact:
>
>   X = rand(99);
>   Y = imrotate(X,  89.9, "nearest");
>   Z = imrotate(Y, -89.9, "nearest");
>   norm(X-Z)
>   ans = 0
>   norm(Y - imrotate(X, 90, "nearest"))
>   ans = 0
>
> Also try 90.1 degrees, and likewise around 180 and 270.
>
> I think it would be useful to add these test cases to imrotate.m.
>

Send me a patch and I will add it.

Embedded tests are run automatically.  E.g., I added the following test:

%!test
%! X = rand(19);
%! Z = imrotate(imrotate(X, 89.9, "nearest"), -89.9, "nearest");
%! assert(norm(X-Z),0);

See 'help test' for more details.

Thanks,

- Paul