[Insight-developers] BUG in BinaryBallStructuringElement

Miller, James V (GE Global Research) millerjv at ge.com
Thu Oct 17 15:45:53 EDT 2013 

Our current element does not build the ball by alternating the application of crosses and boxes.  Perhaps we should have an element that does it that way.  For speed, I think old school morphology would not build a large structuring element but apply small elements in a particular sequence to the image (dilate with triangle, dilate with rotated triangle, ...).

I like the idea of introducing a new structuring element that implements Dirk's design.  I'd also be happy with a mode on the current element to switch between the behaviors as long as the default was the current behavior.



-----Original Message-----
From: insight-developers-bounces at itk.org [mailto:insight-developers-bounces at itk.org] On Behalf Of Bradley Lowekamp
Sent: Thursday, October 17, 2013 1:44 PM
To: Padfield, Dirk R (GE Global Research)
Cc: Richard Beare; Johnson, Hans J; insight-developers at itk.org
Subject: Re: [Insight-developers] BUG in BinaryBallStructuringElement

Dirk,

First, I have been using the FlatStructuringElement class as opposed to the BinaryBallStructuring element. Does the resulting shape differ? I think they should be consistent.

Please, please do not  change the shape of the current structuring elements.

Many optimized usage and implementation of morphology rely on a specific decomposition of the binary ball structuring element. To create a ball, you are alternate between a 1-cross and a 1-box. I believe your change is simple switching for the cross be for the box. Which would make such decomposition optimization inconsistent.

I would suggest you create a new structuring element class to meet you needs. I think this would make a easier transition of we wish to deprecate the current version in favor of yours interpretation of correctness.

I would like to hear from Richard Beare and/or Gaetan on this issue. They are the resident morphology experts in our community.


Brad

On Oct 17, 2013, at 1:14 PM, "Padfield, Dirk R (GE Global Research)" <padfield at research.ge.com> wrote:

> Hi Ho,
> 
> Thanks for looking into this more closely.  Your agreement that this is a bug is encouraging!
> 
> Now, what to do...This is the perennial battle between backward compatibility and future correctness!
> 
> Hans' suggestion to add a member function to enable the correct behavior makes sense.  But I am concerned that it adds additional complexity and that these methods will be ignored if not set as default.
> 
> Hans, what do you think about the idea of adding such a method and then marking the old method as deprecated and setting an ITK_FUTURE_LEGACY_REMOVE flag?
> 
> Thanks,
> Dirk
> 
> ________________________________
> From: Ho Cheung [hocheung20 at gmail.com]
> Sent: Thursday, October 17, 2013 12:22 PM
> To: Padfield, Dirk R (GE Global Research)
> Subject: Re: [Insight-developers] BUG in BinaryBallStructuringElement
> 
> I totally agree that the corrected version is more accurate.
> 
> Upon examining the code more closely and further thought, it also does seem to be an oversight by the original author.
> 
> Furthermore, my suggestion that it was simply a discretization problem turns out to be a non-sequiter. It turns out that the additional pixel on the axes length was approximating the "rounding discretization process" for the radius sizes I was looking at.
> 
> I do share the same concerns about backwards compatibility as Hans and Wes, but definitely I'll change my opinion of this to being an actual bug.
> 
> Regards,
> 
> Ho Cheung
> (775) 388-2368
> 
> On Oct 17, 2013, at 8:09 AM, Padfield, Dirk R (GE Global Research) <padfield at research.ge.com<mailto:padfield at research.ge.com>> wrote:
> 
> Hi Ho,
> 
> Thanks for your feedback and insight!  I agree that discretizing continuous functions is always a tricky thing.  Luckily, we have the spatial objects to help with this since they define their own inside-outside tests.  The Ellipse spatial object is used in the BinaryBallStructuringElement implementation, but the problem is that the spatial object itself is used incorrectly.  By definition, the axes should be "radius*2" rather than "radius*2+1".  Defining the axes of an ellipse/circle to be "radius*2+1" is simply an error.
> 
> We can also attack this question by considering the area of the continuous function versus the discretized version by counting the number of "on" pixels in the kernel as follows:
> 
> For radius=1, the true area is pi = 3.14 Using the old version, we get 
> 9 Using the correction, we get 5
> 
> For radius=5, the true area is 25*pi = 78.5 Using the old version, we 
> get 97 (24% error) Using the correction, we get 81 (3% error)
> 
> For radius=11, the true area is 121*pi = 380 Using the old version, we 
> get 421 (11% error) Using the correction, we get 377 (1% error)
> 
> For radius=21, the true area is 21*21*pi = 1385 Using the old version, 
> we get 1457 (5% error) Using the correction, we get 1373 (1% error)
> 
> As expected, as the radius increases, the discretized version better approximates the continuous function.  We can also see that the corrected version is always more accurate than the old version.
> 
> What do you think?
> 
> Thanks,
> Dirk
> 
> 
> ________________________________
> From: Ho Cheung [hocheung20 at gmail.com<mailto:hocheung20 at gmail.com>]
> Sent: Wednesday, October 16, 2013 6:26 PM
> To: Padfield, Dirk R (GE Global Research)
> Cc: ITK
> Subject: Re: [Insight-developers] BUG in BinaryBallStructuringElement
> 
> 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<mailto:padfield at research.ge.com><mailto: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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