[Insight-developers] NumericTraits for RGBPixel

[Rupert Brooks]

Hi Brad,

I'll just point out that this < operator, as defined on RGBPixel,
defines a strict partial ordering of the set (see
http://en.wikipedia.org/wiki/Partially_ordered_set ).  I would
therefore hesitate to call it a bug.  You are correct though that it
does not define a maximum.

Whether its a useful or well documented concept is open to debate.
Myself, i have never used RGBPixel in ITK, so i have no experience
with it to offer.

At first thought - i think that if the non strict partial ordering <=
(which may or may not be defined, i didnt check) is used, then a
unique maximum can be defined as
< Type::max(), Type::max(), Type::max() >  All other elements are <=
to this one.  I think the same result could be achieved by redefining
< as meaning
"having any element less than, and no element greater than"

Check my math though, its early :-)

Cheers,
Rupert B.

On Wed, Jan 14, 2009 at 11:39 AM, Bradley Lowekamp
<blowekamp at mail.nih.gov> wrote:
> Hello,
> I see that < is in fact defined for RGBPixelType:
> /**
>  * Returns the results from a test for less than (all components must be
> less than)
>  */
> template<class T>
> bool
> RGBPixel<T>
> ::operator<(const Self & r) const
> {
>   for( unsigned int i=0; i<3; i++)
>     {
>     if((*this)[i] >= r[i])
>       {
>       return false;
>       }
>     }
>   return true;
> }
> Hrmm... this is a very "interesting" definition of the < operator. It does
> not produce a well ordered set. It is logically inconsistent. And you can
> not define a unique maximum from it. Consider the following:
> Let a = (1,0,0) and b = (0,1,0)
> as defined above:
> a < b =>false
> b < a => false
> a == b => false
> Let  c = (255, 255, 255)  and d = (255, 0, 0)
> c < d => false;
> d < c => false;
> c == d => false;
>
> By interesting, I mean I'd like to call it a bug.
> Brad
>
>
> On Jan 14, 2009, at 10:51 AM, Bradley Lowekamp wrote:
>
> Hello,
> ITK does not have max defined for any of the vector or array like classes
> either. I am pretty sure that this was done on purpose.
>
> From a theoretical point of view, a maximum is defined as the greatest
> element in a set. This essentially implies that the set can be ordered and
> have comparative operators. I don't think this is true for vector-like
> elements.
>
> Does the connected components algorithm need the max trait?
>
> Brad
> On Jan 14, 2009, at 9:18 AM, Gaëtan Lehmann wrote:
>
> Hi,
>
> I'm fixing the bug uncovered by Julien Michel in
> ConnectedComponentImageFilter with RGB images as input, and want to add a
> test for it.
> However, I can't succeed to build the modified test because
> itk::NumericTraits< RGBPixelType< unsigned char > >::max() is not defined.
> Is it done on purpose?
>
> Also, some functions defined in those numeric traits look suspicious to me,
> like
>
>  typedef _TYPENAME_ NumericTraits<T>::RealType       ElementRealType; \
>  typedef RGBPixel<ElementRealType>         RealType; \
>  static const RealType max( const Self & a ) \
>    {  \
>      RealType b(a.Size());  \
>      b.Fill( NumericTraits< T >::max() ); \
>      return b; \
>    } \
>
> Why should max( const Self & a ) return a RealType? Why b inside the
> function is filled with the size of a (which is always 3), and then filled
> with zeros?
> For the scalar types, that function simply return the value of max().
>
> Regards,
>
> Gaëtan
>
>
> --
> Gaëtan Lehmann
> Biologie du Développement et de la Reproduction
> INRA de Jouy-en-Josas (France)
> tel: +33 1 34 65 29 66    fax: 01 34 65 29 09
> http://voxel.jouy.inra.fr  http://www.mandriva.org
> http://www.itk.org  http://www.clavier-dvorak.org
>
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>
> ========================================================
> Bradley Lowekamp
> Lockheed Martin Contractor for
> Office of High Performance Computing and Communications
> National Library of Medicine
> blowekamp at mail.nih.gov
>
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>
> ========================================================
>
> Bradley Lowekamp
>
> Lockheed Martin Contractor for
>
> Office of High Performance Computing and Communications
>
> National Library of Medicine
>
> blowekamp at mail.nih.gov
>
>
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>



-- 
--------------------------------------------------------------
Rupert Brooks, Ph. D.

Attaché de recherches | Research Associate
Simulation des Matériaux Déformables | Simulation of Deformable Materials
Institut des matériaux industriels | Industrial Materials Institute
Conseil national de recherches Canada | National Research Council Canada
75, de Mortagne, Boucherville, Québec, Canada, J4B 6Y4
Gouvernement du Canada | Government of Canada