[Insight-users] RE: Wondering if it is a bug in Danielsson distance map filter

Thu, 15 Apr 2004 17:59:37 -0700

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Hi Luis,
The pixel type is unsigned char for everything.
Radhika

-----Original Message-----
From: Luis Ibanez [mailto:luis.ibanez at kitware.com] 
Sent: Thursday, April 15, 2004 4:39 PM
To: Radhika Sivaramakrishna
Cc: ITK
Subject: Re: Wondering if it is a bug in Danielsson distance map filter

Hi Radhika,

Thanks for posting this detailed report.

This looks like a bug...

Just a question... what is the pixel type that you
use as output for the ShiftScale image ?

I'm wondering that if it is a float pixel type, we
may be dealing with a pixel that has a float value
very close to zero in the image passed as input
to the Danielsson filter.

Please let us know,

   Thanks

-----------------------------
Radhika Sivaramakrishna wrote:

> Hi Luis,
> I am observing a strange behavior in the Danielsson map filter and I am 
> wondering if it is a bug. I have been experimenting with this for a few 
> days now and I have found this behavior even on 3D images. I have 
> attached an image (Mask_2D.img) that I ran the distance map filter on. I 
> inverted this mask before running the filter. I ran it with and without 
> setting UseImageSpacing. When I do not
> 
> set UseImageSpacing, I observe some strange behavior. It sets 1 in 
> places where it should not. Could you explain what is happening? My 
> pixel type is unsigned char. Here is a very small portion of the code 
> that just runs the shiftscale and Danielsson Filter. In the attached 
> results you will clearly see an extra 1 in location (8,18) which should 
> not be. I don't know if I am using this incorrectly or something else is 
> happening.
> 
> Thanks
> Radhika
> 
> typedef itk::Image<PixelType,2> ImageType2D;
> typedef itk::ImageFileWriter< ImageType2D >  WriterType2D;     
> typedef itk::ShiftScaleImageFilter <ImageType2D, ImageType2D> 
> ShiftScaleFilterType2D;
> typedef itk::DanielssonDistanceMapImageFilter <ImageType2D, ImageType2D> 
> EDMFilterType2D;       EDMFilterType2D::Pointer edmfilter2D = 
> EDMFilterType2D::New();
> 
> ShiftScaleFilterType2D::Pointer ssfilter2D =
ShiftScaleFilterType2D::New();
>        
> ssfilter2D->SetShift(shift);
> ssfilter2D->SetScale(scale);
> edmfilter2D->SetInputIsBinary(true);
> //      edmfilter2D->SetUseImageSpacing(true);
> ssfilter2D->SetInput(mask);
> edmfilter2D->SetInput(ssfilter2D->GetOutput());
> edmfilter2D->Update();
> 
> -----Original Message-----
> From: Luis Ibanez [mailto:luis.ibanez at kitware.com]
> Sent: Wednesday, April 14, 2004 1:13 PM
> To: Radhika Sivaramakrishna
> Cc: ITK
> Subject: Re: [Insight-users] More questions on Daniellson distance map 
> filter
> 
> 
> Hi Radhika,
> 
> The DanielssonDistanceMap takes into account diagonal distances
> regardless of whether the UseImageSpacing flag is enabled or not.
> 
> What changes when the flag is enabled is that the components
> of the pixel spacing are taken into account. Therefore the
> distances are reported in physical units (e.g. millimeters)
> instead of pixels.  As a consequence, enabling the flag also
> takes care of taking pixel anisotropy into account.
> 
> The distances are computed as Euclidean distances, not as
> Manhattan distances (city-block), but are limited in precision
> to one-pixel. That is, there is no sub-pixel accuracy in the
> distance values.  An easy way to verify the Euclidean-ness of
> the resulting DistanceMap is to create a dataset with a single
> pixel on in the middle and pass it as input to the Danielsson
> DistanceMap filter.
> 
> Using the DanielssonDistanceMap plugin for VolView would
> be a very easy way of experimenting with the distances.
> 
> 
> Please let us know if you have further questions.
> 
> 
>    Thanks
> 
> 
>      Luis
> 
> 
> 
> -----------------------------
> Radhika Sivaramakrishna wrote:
> 
>  > Hi Luis,
>  > Thanks for your explanation. I have a doubt: when the UseImageSpacing
is
>  > enabled, does this (1) take into account diagonal distances and (2)
>  > nonisotropic voxels also? I thought it did both. If I want to just make
>  > sure that diagonal distances are taken into account (ie I don't want to
>  > do city block distances or chessboard distances), but do not want to
>  > take non-isotropy into account, what should I do?
>  >
>  > Hope my question is clear.
>  > Thanks
>  > Radhika
>  >
>  >
>  >
>  > -----Original Message-----
>  > From: Luis Ibanez [mailto:luis.ibanez at kitware.com]
>  > Sent: Monday, April 12, 2004 6:46 PM
>  > To: Radhika Sivaramakrishna
>  > Cc: ITK
>  > Subject: Re: [Insight-users] More questions on Daniellson distance map
>  > filter
>  >
>  >
>  >
>  > Hi Radhika,
>  >
>  > When you enable the "UseImageSpacing" flag, the values
>  > of pixel spacing are used in the last stage of distance
>  > computation. The spacing is used to multiply the distance
>  > components when their squares are summed up.
>  >
>  > The resulting distance is then casted to the type of the
>  > output image pixel type. This is done in the file:
>  >
>  >      Insight/Code/BasicFilters/
>  >        itkDanielssonDistanceMapImageFilter.txx:
>  >
>  > in line 299:
>  >
>  >     dt.Set(
>  >       static_cast<
>  >          typename
>  >            OutputImageType::PixelType>(sqrt( distance )) );
>  >
>  >
>  > Note that the casting is done as a flat truncation.
>  > No effort is made for scaling the distances in the
>  > range of the pixel type.  Depending on the physical
>  > extent of your image, this may or may not be a problem.
>  >
>  >
>  >
>  > If you want to compute this distance scaling in a better
>  > way, you could setup the output pixel type as float,
>  > and then connect the output of the DanielssonDistanceMap
>  > filter to a RescaleIntensityImageFilter with output pixel
>  > type = unsigned char.  This last filter will then rescale
>  > nicely the distances into the range of intensities of the
>  > output image. Note that with this filter you can select
>  > what values to use for representing the maximum and minimum
>  > values of the distance.
>  >
>  >
>  > --
>  >
>  > You may want to take a look at the new VolView plugin
>  > for computing the Danielsson distance. The source code
>  > for this plugin is available at
>  >
>  >
>  >        InsightApplications/
>  >                 VolviewPlugins/
>  >                    vvITKDanielssonDistanceMap.cxx
>  >
>  >
>  >
>  >
>  > Please let us know if you have further questions,
>  >
>  >
>  > Thanks
>  >
>  >
>  >    Luis
>  >
>  >
>  >
>  > -------------------------------
>  >
>  > Radhika Sivaramakrishna wrote:
>  >
>  >  > Hi,
>  >  >
>  >  > I had more questions on the Danielsson distance map filter. I have 
> set
>  >  > the input and output of the filter to unsigned char.
>  >  >
>  >  > I have also put the SetUseImageSpacing flag to true. This means that
>  >  > actual distances may be computed which are more floating point
>  >  >
>  >  > numbers.  Since I am forcing the output to unsigned char, then 
> does this
>  >  > mean that the actual distances are truncated to unsigned char
>  >  >
>  >  > or are they rounded to it? Is there a better way to handle this?
>  >  >
>  >  > Thanks
>  >  >
>  >  > Radhika
>  >  >
>  >  >
>  >  >
>  >  > -----------------------------------------------------
>  >  >
>  >  > Confidentiality Notice.
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unauthorized
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> may contain confidential and privileged information. Any unauthorized 
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>  
> 

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<P><FONT SIZE=2>Hi Luis,</FONT>
<BR><FONT SIZE=2>The pixel type is unsigned char for everything.</FONT>
<BR><FONT SIZE=2>Radhika</FONT>
</P>
<BR>

<P><FONT SIZE=2>-----Original Message-----</FONT>
<BR><FONT SIZE=2>From: Luis Ibanez [<A HREF="mailto:luis.ibanez at kitware.com">mailto:luis.ibanez at kitware.com</A>] </FONT>
<BR><FONT SIZE=2>Sent: Thursday, April 15, 2004 4:39 PM</FONT>
<BR><FONT SIZE=2>To: Radhika Sivaramakrishna</FONT>
<BR><FONT SIZE=2>Cc: ITK</FONT>
<BR><FONT SIZE=2>Subject: Re: Wondering if it is a bug in Danielsson distance map filter</FONT>
</P>
<BR>
<BR>

<P><FONT SIZE=2>Hi Radhika,</FONT>
</P>

<P><FONT SIZE=2>Thanks for posting this detailed report.</FONT>
</P>

<P><FONT SIZE=2>This looks like a bug...</FONT>
</P>

Just a question... what is the pixel type that you
 use as output for the ShiftScale image ?

<P><FONT SIZE=2>I'm wondering that if it is a float pixel type, we</FONT>
<BR><FONT SIZE=2>may be dealing with a pixel that has a float value</FONT>
<BR><FONT SIZE=2>very close to zero in the image passed as input</FONT>
<BR><FONT SIZE=2>to the Danielsson filter.</FONT>
</P>
<BR>

<P><FONT SIZE=2>Please let us know,</FONT>
</P>
<BR>
<BR>

<P><FONT SIZE=2>&nbsp;&nbsp; Thanks</FONT>
</P>
<BR>
<BR>

<P><FONT SIZE=2>-----------------------------</FONT>
<BR><FONT SIZE=2>Radhika Sivaramakrishna wrote:</FONT>
</P>

&gt; Hi Luis,
 &gt; I am observing a strange behavior in the Danielsson map filter and I am 
 &gt; wondering if it is a bug. I have been experimenting with this for a few 
 &gt; days now and I have found this behavior even on 3D images. I have 
 &gt; attached an image (Mask_2D.img) that I ran the distance map filter on. I 
 &gt; inverted this mask before running the filter. I ran it with and without 
 &gt; setting UseImageSpacing. When I do not
 &gt; 
 &gt; set UseImageSpacing, I observe some strange behavior. It sets 1 in 
 &gt; places where it should not. Could you explain what is happening? My 
 &gt; pixel type is unsigned char. Here is a very small portion of the code 
 &gt; that just runs the shiftscale and Danielsson Filter. In the attached 
 &gt; results you will clearly see an extra 1 in location (8,18) which should 
 &gt; not be. I don't know if I am using this incorrectly or something else is 
 &gt; happening.
 &gt; 
 &gt; Thanks
 &gt; Radhika
 &gt; 
 &gt; typedef itk::Image&lt;PixelType,2&gt; ImageType2D;
 &gt; typedef itk::ImageFileWriter&lt; ImageType2D &gt;&nbsp; WriterType2D;&nbsp;&nbsp;&nbsp;&nbsp; 
 &gt; typedef itk::ShiftScaleImageFilter &lt;ImageType2D, ImageType2D&gt; 
 &gt; ShiftScaleFilterType2D;
 &gt; typedef itk::DanielssonDistanceMapImageFilter &lt;ImageType2D, ImageType2D&gt; 
 &gt; EDMFilterType2D;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; EDMFilterType2D::Pointer edmfilter2D = 
 &gt; EDMFilterType2D::New();
 &gt; 
 &gt; ShiftScaleFilterType2D::Pointer ssfilter2D = ShiftScaleFilterType2D::New();
 &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
 &gt; ssfilter2D-&gt;SetShift(shift);
 &gt; ssfilter2D-&gt;SetScale(scale);
 &gt; edmfilter2D-&gt;SetInputIsBinary(true);
 &gt; //&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; edmfilter2D-&gt;SetUseImageSpacing(true);
 &gt; ssfilter2D-&gt;SetInput(mask);
 &gt; edmfilter2D-&gt;SetInput(ssfilter2D-&gt;GetOutput());
 &gt; edmfilter2D-&gt;Update();
 &gt; 
 &gt; -----Original Message-----
 &gt; From: Luis Ibanez [<A HREF="mailto:luis.ibanez at kitware.com">mailto:luis.ibanez at kitware.com</A>]
 &gt; Sent: Wednesday, April 14, 2004 1:13 PM
 &gt; To: Radhika Sivaramakrishna
 &gt; Cc: ITK
 &gt; Subject: Re: [Insight-users] More questions on Daniellson distance map 
 &gt; filter
 &gt; 
 &gt; 
 &gt; Hi Radhika,
 &gt; 
 &gt; The DanielssonDistanceMap takes into account diagonal distances
 &gt; regardless of whether the UseImageSpacing flag is enabled or not.
 &gt; 
 &gt; What changes when the flag is enabled is that the components
 &gt; of the pixel spacing are taken into account. Therefore the
 &gt; distances are reported in physical units (e.g. millimeters)
 &gt; instead of pixels.&nbsp; As a consequence, enabling the flag also
 &gt; takes care of taking pixel anisotropy into account.
 &gt; 
 &gt; The distances are computed as Euclidean distances, not as
 &gt; Manhattan distances (city-block), but are limited in precision
 &gt; to one-pixel. That is, there is no sub-pixel accuracy in the
 &gt; distance values.&nbsp; An easy way to verify the Euclidean-ness of
 &gt; the resulting DistanceMap is to create a dataset with a single
 &gt; pixel on in the middle and pass it as input to the Danielsson
 &gt; DistanceMap filter.
 &gt; 
 &gt; Using the DanielssonDistanceMap plugin for VolView would
 &gt; be a very easy way of experimenting with the distances.
 &gt; 
 &gt; 
 &gt; Please let us know if you have further questions.
 &gt; 
 &gt; 
 &gt;&nbsp;&nbsp;&nbsp; Thanks
 &gt; 
 &gt; 
 &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Luis
 &gt; 
 &gt; 
 &gt; 
 &gt; -----------------------------
 &gt; Radhika Sivaramakrishna wrote:
 &gt; 
 &gt;&nbsp; &gt; Hi Luis,
 &gt;&nbsp; &gt; Thanks for your explanation. I have a doubt: when the UseImageSpacing is
 &gt;&nbsp; &gt; enabled, does this (1) take into account diagonal distances and (2)
 &gt;&nbsp; &gt; nonisotropic voxels also? I thought it did both. If I want to just make
 &gt;&nbsp; &gt; sure that diagonal distances are taken into account (ie I don't want to
 &gt;&nbsp; &gt; do city block distances or chessboard distances), but do not want to
 &gt;&nbsp; &gt; take non-isotropy into account, what should I do?
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Hope my question is clear.
 &gt;&nbsp; &gt; Thanks
 &gt;&nbsp; &gt; Radhika
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; -----Original Message-----
 &gt;&nbsp; &gt; From: Luis Ibanez [<A HREF="mailto:luis.ibanez at kitware.com">mailto:luis.ibanez at kitware.com</A>]
 &gt;&nbsp; &gt; Sent: Monday, April 12, 2004 6:46 PM
 &gt;&nbsp; &gt; To: Radhika Sivaramakrishna
 &gt;&nbsp; &gt; Cc: ITK
 &gt;&nbsp; &gt; Subject: Re: [Insight-users] More questions on Daniellson distance map
 &gt;&nbsp; &gt; filter
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Hi Radhika,
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; When you enable the &quot;UseImageSpacing&quot; flag, the values
 &gt;&nbsp; &gt; of pixel spacing are used in the last stage of distance
 &gt;&nbsp; &gt; computation. The spacing is used to multiply the distance
 &gt;&nbsp; &gt; components when their squares are summed up.
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; The resulting distance is then casted to the type of the
 &gt;&nbsp; &gt; output image pixel type. This is done in the file:
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Insight/Code/BasicFilters/
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; itkDanielssonDistanceMapImageFilter.txx:
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; in line 299:
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp; dt.Set(
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; static_cast&lt;
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; typename
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; OutputImageType::PixelType&gt;(sqrt( distance )) );
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Note that the casting is done as a flat truncation.
 &gt;&nbsp; &gt; No effort is made for scaling the distances in the
 &gt;&nbsp; &gt; range of the pixel type.&nbsp; Depending on the physical
 &gt;&nbsp; &gt; extent of your image, this may or may not be a problem.
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; If you want to compute this distance scaling in a better
 &gt;&nbsp; &gt; way, you could setup the output pixel type as float,
 &gt;&nbsp; &gt; and then connect the output of the DanielssonDistanceMap
 &gt;&nbsp; &gt; filter to a RescaleIntensityImageFilter with output pixel
 &gt;&nbsp; &gt; type = unsigned char.&nbsp; This last filter will then rescale
 &gt;&nbsp; &gt; nicely the distances into the range of intensities of the
 &gt;&nbsp; &gt; output image. Note that with this filter you can select
 &gt;&nbsp; &gt; what values to use for representing the maximum and minimum
 &gt;&nbsp; &gt; values of the distance.
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; --
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; You may want to take a look at the new VolView plugin
 &gt;&nbsp; &gt; for computing the Danielsson distance. The source code
 &gt;&nbsp; &gt; for this plugin is available at
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; InsightApplications/
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; VolviewPlugins/
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; vvITKDanielssonDistanceMap.cxx
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Please let us know if you have further questions,
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Thanks
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp;&nbsp;&nbsp; Luis
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; -------------------------------
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt; Radhika Sivaramakrishna wrote:
 &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; Hi,
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; I had more questions on the Danielsson distance map filter. I have 
 &gt; set
 &gt;&nbsp; &gt;&nbsp; &gt; the input and output of the filter to unsigned char.
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; I have also put the SetUseImageSpacing flag to true. This means that
 &gt;&nbsp; &gt;&nbsp; &gt; actual distances may be computed which are more floating point
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; numbers.&nbsp; Since I am forcing the output to unsigned char, then 
 &gt; does this
 &gt;&nbsp; &gt;&nbsp; &gt; mean that the actual distances are truncated to unsigned char
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; or are they rounded to it? Is there a better way to handle this?
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; Thanks
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; Radhika
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; -----------------------------------------------------
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; Confidentiality Notice.
 &gt;&nbsp; &gt;&nbsp; &gt;
 &gt;&nbsp; &gt;&nbsp; &gt; This email message is for the sole use of the intended 
 &gt; recipient(s) and
 &gt;&nbsp; &gt;&nbsp; &gt; may contain confidential and privileged information. Any unauthorized
 &gt;&nbsp; &gt;&nbsp; &gt; review, use, disclosure or distribution is prohibited. If you are not
 &gt;&nbsp; &gt;&nbsp; &gt; the intended recipient, please contact the sender by reply email and
 &gt;&nbsp; &gt;&nbsp; &gt; destroy all copies of the original message. If you are the intended
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 &gt;&nbsp; &gt; -----------------------------------------------------
 &gt;&nbsp; &gt; Confidentiality Notice.
 &gt;&nbsp; &gt; This email message is for the sole use of the intended recipient(s) and
 &gt;&nbsp; &gt; may contain confidential and privileged information. Any unauthorized
 &gt;&nbsp; &gt; review, use, disclosure or distribution is prohibited. If you are not
 &gt;&nbsp; &gt; the intended recipient, please contact the sender by reply email and
 &gt;&nbsp; &gt; destroy all copies of the original message. If you are the intended
 &gt;&nbsp; &gt; recipient, please be advised that the content of this message is subject
 &gt;&nbsp; &gt; to access, review and disclosure by the sender's Email System 
 &gt; Administrator.
 &gt;&nbsp; &gt;
 &gt; 
 &gt; 
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 &gt; This email message is for the sole use of the intended recipient(s) and 
 &gt; may contain confidential and privileged information. Any unauthorized 
 &gt; review, use, disclosure or distribution is prohibited. If you are not 
 &gt; the intended recipient, please contact the sender by reply email and 
 &gt; destroy all copies of the original message. If you are the intended 
 &gt; recipient, please be advised that the content of this message is subject 
 &gt; to access, review and disclosure by the sender's Email System Administrator.
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 &gt;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 
 &gt; 
 &gt;&nbsp; 
 &gt;

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