[Insight-developers] BUG in BinaryBallStructuringElement

[Ho Cheung]

Dirk,

As a counterpoint, I do not agree that there is a bug but rather just an ambiguity in the way we have defined whether or not a pixel is to be included.

If you take a protractor and plotted a unit circle, then superimpose a grid on it (this this case, 3x3), and then shaded in the nearest pixels to the circle, it would look like the “original” example. The same applies to the radius 5 circle.

Technically, if you look at the parametric definition of a circle, then yes, those pixels would not be included, as their physical space points fall outside the circle. 

However, I believe (anecdotal) in graphics rendering, it is common practice to include those pixels which are nearest to the actual physical space point.

Regards,

Ho Cheung
(775) 388-2368

On Oct 16, 2013, at 1:05 PM, Padfield, Dirk R (GE Global Research) <padfield at research.ge.com> wrote:

> Hi All,
> 
> I am writing to ask your advice about a bug I found in BinaryBallStructuringElement.
> 
> For a while, I have been bothered by the fact that the BinaryBallStructuringElement return balls that are larger than the specified radius.  For example, when given a radius of 1, it returns the structuring element:
> 1    1    1
> 1    1    1
> 1    1    1
> 
> But this structuring element has a radius that is more than 1!  If it truly had a radius of 1, it would be a cross shape in this case.
> 
> When choosing a larger radius, the problem is more obvious.  Setting radius = 5 (leading to a structuring element size of 11x11) results in:
> 0    0    0    1    1    1    1    1    0    0    0
> 0    0    1    1    1    1    1    1    1    0    0
> 0    1    1    1    1    1    1    1    1    1    0
> 1    1    1    1    1    1    1    1    1    1    1
> 1    1    1    1    1    1    1    1    1    1    1
> 1    1    1    1    1    1    1    1    1    1    1
> 1    1    1    1    1    1    1    1    1    1    1
> 1    1    1    1    1    1    1    1    1    1    1
> 0    1    1    1    1    1    1    1    1    1    0
> 0    0    1    1    1    1    1    1    1    0    0
> 0    0    0    1    1    1    1    1    0    0    0
> 
> This is clearly not an ellipse/circle with radius 5 because the interior ellipse/circle is touching each image border at five points rather than just one.  As it turns out, the code is actually defining a radius that is "X + 0.5", where X is the radius that is requested!
> 
> The problem is in the specification of the ellipse axes on lines 70-76 of itkBinaryBallStructuringElement.hxx:
>  // Define and set the axes lengths for the ellipsoid
>  typename EllipsoidType::InputType axes;
>  for ( i = 0; i < VDimension; i++ )
>    {
>    axes[i] = this->GetSize(i);
>    }
>  spatialFunction->SetAxes(axes);
> 
> In this case, "this->GetSize()" is equal to radius*2+1.  But, an ellipse/circle with radius X should have axes length 2X, not 2X+1!  In the implementation, the center of the ellipse is properly accounted for by setting it to "this->GetRadius+1", but the size of the ellipse is not correct!
> 
> To correct this, we can make a simple change either
>    axes[i] = this->GetSize(i) - 1;
> or
>    axes[i] = this->GetRadius(i) * 2;
> 
> The second is probably more intuitive.
> 
> With this fix, we get for radius=1:
> 0    1    0
> 1    1    1
> 0    1    0
> 
> and for radius=5:
> 0    0    0    0    0    1    0    0    0    0    0
> 0    0    1    1    1    1    1    1    1    0    0
> 0    1    1    1    1    1    1    1    1    1    0
> 0    1    1    1    1    1    1    1    1    1    0
> 0    1    1    1    1    1    1    1    1    1    0
> 1    1    1    1    1    1    1    1    1    1    1
> 0    1    1    1    1    1    1    1    1    1    0
> 0    1    1    1    1    1    1    1    1    1    0
> 0    1    1    1    1    1    1    1    1    1    0
> 0    0    1    1    1    1    1    1    1    0    0
> 0    0    0    0    0    1    0    0    0    0    0
> 
> This is a true circle with radius 5!
> 
> My questions are:
> 1) Is anyone else bothered by this bug?  I imagine that many users expect the corrected version and don't realize they are getting the incorrect one.
> 2) Do others agree with this fix?
> 3) Can we make this fix given the number of filters/applications that will change slightly as a result of this fix?
> 
> Many thanks,
> Dirk
> 
> 
> 
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