blob: e2bb25ca02ca2ff4f6cff4dc88358e5d38a6c22d [file] [log] [blame]
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% CCCC OOO M M PPPP AAA RRRR EEEEE %
% C O O MM MM P P A A R R E %
% C O O M M M PPPP AAAAA RRRR EEE %
% C O O M M P A A R R E %
% CCCC OOO M M P A A R R EEEEE %
% %
% %
% MagickCore Image Comparison Methods %
% %
% Software Design %
% John Cristy %
% December 2003 %
% %
% %
% Copyright 1999-2013 ImageMagick Studio LLC, a non-profit organization %
% dedicated to making software imaging solutions freely available. %
% %
% You may not use this file except in compliance with the License. You may %
% obtain a copy of the License at %
% %
% http://www.imagemagick.org/script/license.php %
% %
% Unless required by applicable law or agreed to in writing, software %
% distributed under the License is distributed on an "AS IS" BASIS, %
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
% See the License for the specific language governing permissions and %
% limitations under the License. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
*/
/*
Include declarations.
*/
#include "MagickCore/studio.h"
#include "MagickCore/artifact.h"
#include "MagickCore/cache-view.h"
#include "MagickCore/client.h"
#include "MagickCore/color.h"
#include "MagickCore/color-private.h"
#include "MagickCore/colorspace.h"
#include "MagickCore/colorspace-private.h"
#include "MagickCore/compare.h"
#include "MagickCore/composite-private.h"
#include "MagickCore/constitute.h"
#include "MagickCore/exception-private.h"
#include "MagickCore/geometry.h"
#include "MagickCore/image-private.h"
#include "MagickCore/list.h"
#include "MagickCore/log.h"
#include "MagickCore/memory_.h"
#include "MagickCore/monitor.h"
#include "MagickCore/monitor-private.h"
#include "MagickCore/option.h"
#include "MagickCore/pixel-accessor.h"
#include "MagickCore/resource_.h"
#include "MagickCore/string_.h"
#include "MagickCore/statistic.h"
#include "MagickCore/thread-private.h"
#include "MagickCore/transform.h"
#include "MagickCore/utility.h"
#include "MagickCore/version.h"
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% C o m p a r e I m a g e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% CompareImages() compares one or more pixel channels of an image to a
% reconstructed image and returns the difference image.
%
% The format of the CompareImages method is:
%
% Image *CompareImages(const Image *image,const Image *reconstruct_image,
% const MetricType metric,double *distortion,ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o image: the image.
%
% o reconstruct_image: the reconstruct image.
%
% o metric: the metric.
%
% o distortion: the computed distortion between the images.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport Image *CompareImages(Image *image,const Image *reconstruct_image,
const MetricType metric,double *distortion,ExceptionInfo *exception)
{
CacheView
*highlight_view,
*image_view,
*reconstruct_view;
const char
*artifact;
Image
*difference_image,
*highlight_image;
MagickBooleanType
status;
PixelInfo
highlight,
lowlight;
ssize_t
y;
assert(image != (Image *) NULL);
assert(image->signature == MagickSignature);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
assert(reconstruct_image != (const Image *) NULL);
assert(reconstruct_image->signature == MagickSignature);
assert(distortion != (double *) NULL);
*distortion=0.0;
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
if ((reconstruct_image->columns != image->columns) ||
(reconstruct_image->rows != image->rows))
ThrowImageException(ImageError,"ImageSizeDiffers");
status=GetImageDistortion(image,reconstruct_image,metric,distortion,
exception);
if (status == MagickFalse)
return((Image *) NULL);
difference_image=CloneImage(image,0,0,MagickTrue,exception);
if (difference_image == (Image *) NULL)
return((Image *) NULL);
(void) SetImageAlphaChannel(difference_image,OpaqueAlphaChannel,exception);
highlight_image=CloneImage(image,image->columns,image->rows,MagickTrue,
exception);
if (highlight_image == (Image *) NULL)
{
difference_image=DestroyImage(difference_image);
return((Image *) NULL);
}
status=SetImageStorageClass(highlight_image,DirectClass,exception);
if (status == MagickFalse)
{
difference_image=DestroyImage(difference_image);
highlight_image=DestroyImage(highlight_image);
return((Image *) NULL);
}
(void) SetImageAlphaChannel(highlight_image,OpaqueAlphaChannel,exception);
(void) QueryColorCompliance("#f1001e33",AllCompliance,&highlight,exception);
artifact=GetImageArtifact(image,"highlight-color");
if (artifact != (const char *) NULL)
(void) QueryColorCompliance(artifact,AllCompliance,&highlight,exception);
(void) QueryColorCompliance("#ffffff33",AllCompliance,&lowlight,exception);
artifact=GetImageArtifact(image,"lowlight-color");
if (artifact != (const char *) NULL)
(void) QueryColorCompliance(artifact,AllCompliance,&lowlight,exception);
/*
Generate difference image.
*/
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
highlight_view=AcquireAuthenticCacheView(highlight_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,highlight_image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
MagickBooleanType
sync;
register const Quantum
*restrict p,
*restrict q;
register Quantum
*restrict r;
register ssize_t
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
r=QueueCacheViewAuthenticPixels(highlight_view,0,y,highlight_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL) ||
(r == (Quantum *) NULL))
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
MagickStatusType
difference;
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
SetPixelInfoPixel(highlight_image,&lowlight,r);
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
r+=GetPixelChannels(highlight_image);
continue;
}
difference=MagickFalse;
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=p[i]-(double) GetPixelChannel(reconstruct_image,channel,q);
if (fabs((double) distance) >= MagickEpsilon)
difference=MagickTrue;
}
if (difference == MagickFalse)
SetPixelInfoPixel(highlight_image,&lowlight,r);
else
SetPixelInfoPixel(highlight_image,&highlight,r);
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
r+=GetPixelChannels(highlight_image);
}
sync=SyncCacheViewAuthenticPixels(highlight_view,exception);
if (sync == MagickFalse)
status=MagickFalse;
}
highlight_view=DestroyCacheView(highlight_view);
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
(void) CompositeImage(difference_image,highlight_image,image->compose,
MagickTrue,0,0,exception);
highlight_image=DestroyImage(highlight_image);
if (status == MagickFalse)
difference_image=DestroyImage(difference_image);
return(difference_image);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G e t I m a g e D i s t o r t i o n %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetImageDistortion() compares one or more pixel channels of an image to a
% reconstructed image and returns the specified distortion metric.
%
% The format of the GetImageDistortion method is:
%
% MagickBooleanType GetImageDistortion(const Image *image,
% const Image *reconstruct_image,const MetricType metric,
% double *distortion,ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o image: the image.
%
% o reconstruct_image: the reconstruct image.
%
% o metric: the metric.
%
% o distortion: the computed distortion between the images.
%
% o exception: return any errors or warnings in this structure.
%
*/
static MagickBooleanType GetAbsoluteDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
ssize_t
y;
/*
Compute the absolute difference in pixels between two images.
*/
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
channel_distortion[MaxPixelChannels+1];
register const Quantum
*restrict p,
*restrict q;
register ssize_t
i,
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
continue;
}
(void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
for (x=0; x < (ssize_t) image->columns; x++)
{
MagickBooleanType
difference;
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
difference=MagickFalse;
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
if (p[i] != GetPixelChannel(reconstruct_image,channel,q))
difference=MagickTrue;
}
if (difference != MagickFalse)
{
channel_distortion[i]++;
channel_distortion[CompositePixelChannel]++;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_GetAbsoluteError)
#endif
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]+=channel_distortion[i];
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
return(status);
}
static size_t GetImageChannels(const Image *image)
{
register ssize_t
i;
size_t
channels;
channels=0;
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
PixelChannel
channel;
PixelTrait
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
if ((traits & UpdatePixelTrait) != 0)
channels++;
}
return(channels);
}
static MagickBooleanType GetFuzzDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
register ssize_t
i;
ssize_t
y;
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
channel_distortion[MaxPixelChannels+1];
register const Quantum
*restrict p,
*restrict q;
register ssize_t
i,
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
{
status=MagickFalse;
continue;
}
(void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=QuantumScale*(p[i]-(double) GetPixelChannel(reconstruct_image,
channel,q));
distance*=distance;
channel_distortion[i]+=distance;
channel_distortion[CompositePixelChannel]+=distance;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_GetFuzzDistortion)
#endif
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]+=channel_distortion[i];
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]/=((double) image->columns*image->rows);
distortion[CompositePixelChannel]/=(double) GetImageChannels(image);
distortion[CompositePixelChannel]=sqrt(distortion[CompositePixelChannel]);
return(status);
}
static MagickBooleanType GetMeanAbsoluteDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
register ssize_t
i;
ssize_t
y;
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
channel_distortion[MaxPixelChannels+1];
register const Quantum
*restrict p,
*restrict q;
register ssize_t
i,
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
continue;
}
(void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=QuantumScale*fabs(p[i]-(double) GetPixelChannel(
reconstruct_image,channel,q));
channel_distortion[i]+=distance;
channel_distortion[CompositePixelChannel]+=distance;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_GetMeanAbsoluteError)
#endif
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]+=channel_distortion[i];
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]/=((double) image->columns*image->rows);
distortion[CompositePixelChannel]/=(double) GetImageChannels(image);
return(status);
}
static MagickBooleanType GetMeanErrorPerPixel(Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
double
alpha,
area,
beta,
maximum_error,
mean_error;
ssize_t
y;
status=MagickTrue;
alpha=1.0;
beta=1.0;
area=0.0;
maximum_error=0.0;
mean_error=0.0;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
for (y=0; y < (ssize_t) image->rows; y++)
{
register const Quantum
*restrict p,
*restrict q;
register ssize_t
x;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
break;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=fabs((double) (alpha*p[i]-beta*GetPixelChannel(
reconstruct_image,channel,q)));
distortion[i]+=distance;
distortion[CompositePixelChannel]+=distance;
mean_error+=distance*distance;
if (distance > maximum_error)
maximum_error=distance;
area++;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
image->error.mean_error_per_pixel=distortion[CompositePixelChannel]/area;
image->error.normalized_mean_error=QuantumScale*QuantumScale*mean_error/area;
image->error.normalized_maximum_error=QuantumScale*maximum_error;
return(status);
}
static MagickBooleanType GetMeanSquaredDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
register ssize_t
i;
ssize_t
y;
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
channel_distortion[MaxPixelChannels+1];
register const Quantum
*restrict p,
*restrict q;
register ssize_t
i,
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
continue;
}
(void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=QuantumScale*(p[i]-(double) GetPixelChannel(
reconstruct_image,channel,q));
distance*=distance;
channel_distortion[i]+=distance;
channel_distortion[CompositePixelChannel]+=distance;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_GetMeanSquaredError)
#endif
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]+=channel_distortion[i];
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]/=((double) image->columns*image->rows);
distortion[CompositePixelChannel]/=GetImageChannels(image);
return(status);
}
static MagickBooleanType GetNormalizedCrossCorrelationDistortion(
const Image *image,const Image *reconstruct_image,double *distortion,
ExceptionInfo *exception)
{
#define SimilarityImageTag "Similarity/Image"
CacheView
*image_view,
*reconstruct_view;
ChannelStatistics
*image_statistics,
*reconstruct_statistics;
MagickBooleanType
status;
MagickOffsetType
progress;
double
area;
register ssize_t
i;
ssize_t
y;
/*
Normalize to account for variation due to lighting and exposure condition.
*/
image_statistics=GetImageStatistics(image,exception);
reconstruct_statistics=GetImageStatistics(reconstruct_image,exception);
status=MagickTrue;
progress=0;
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]=0.0;
area=1.0/((double) image->columns*image->rows-1);
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
for (y=0; y < (ssize_t) image->rows; y++)
{
register const Quantum
*restrict p,
*restrict q;
register ssize_t
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distortion[i]+=area*QuantumScale*(p[i]-image_statistics[i].mean)*
(GetPixelChannel(reconstruct_image,channel,q)-
reconstruct_statistics[channel].mean);
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
if (image->progress_monitor != (MagickProgressMonitor) NULL)
{
MagickBooleanType
proceed;
proceed=SetImageProgress(image,SimilarityImageTag,progress++,
image->rows);
if (proceed == MagickFalse)
status=MagickFalse;
}
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
/*
Divide by the standard deviation.
*/
distortion[CompositePixelChannel]=0.0;
for (i=0; i < MaxPixelChannels; i++)
{
double
gamma;
PixelChannel
channel;
channel=GetPixelChannelChannel(image,i);
gamma=image_statistics[i].standard_deviation*
reconstruct_statistics[channel].standard_deviation;
gamma=PerceptibleReciprocal(gamma);
distortion[i]=QuantumRange*gamma*distortion[i];
distortion[CompositePixelChannel]+=distortion[i]*distortion[i];
}
distortion[CompositePixelChannel]=sqrt(distortion[CompositePixelChannel]/
GetImageChannels(image));
/*
Free resources.
*/
reconstruct_statistics=(ChannelStatistics *) RelinquishMagickMemory(
reconstruct_statistics);
image_statistics=(ChannelStatistics *) RelinquishMagickMemory(
image_statistics);
return(status);
}
static MagickBooleanType GetPeakAbsoluteDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
ssize_t
y;
status=MagickTrue;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
double
channel_distortion[MaxPixelChannels+1];
register const Quantum
*restrict p,
*restrict q;
register ssize_t
i,
x;
if (status == MagickFalse)
continue;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (const Quantum *) NULL))
{
status=MagickFalse;
continue;
}
(void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=QuantumScale*fabs(p[i]-(double) GetPixelChannel(
reconstruct_image,channel,q));
if (distance > channel_distortion[i])
channel_distortion[i]=distance;
if (distance > channel_distortion[CompositePixelChannel])
channel_distortion[CompositePixelChannel]=distance;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_GetPeakAbsoluteError)
#endif
for (i=0; i <= MaxPixelChannels; i++)
if (channel_distortion[i] > distortion[i])
distortion[i]=channel_distortion[i];
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
return(status);
}
static MagickBooleanType GetPeakSignalToNoiseRatio(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
MagickBooleanType
status;
register ssize_t
i;
status=GetMeanSquaredDistortion(image,reconstruct_image,distortion,exception);
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]=20.0*log10((double) 1.0/sqrt(distortion[i]));
return(status);
}
static MagickBooleanType GetRootMeanSquaredDistortion(const Image *image,
const Image *reconstruct_image,double *distortion,ExceptionInfo *exception)
{
MagickBooleanType
status;
register ssize_t
i;
status=GetMeanSquaredDistortion(image,reconstruct_image,distortion,exception);
for (i=0; i <= MaxPixelChannels; i++)
distortion[i]=sqrt(distortion[i]);
return(status);
}
MagickExport MagickBooleanType GetImageDistortion(Image *image,
const Image *reconstruct_image,const MetricType metric,double *distortion,
ExceptionInfo *exception)
{
double
*channel_distortion;
MagickBooleanType
status;
size_t
length;
assert(image != (Image *) NULL);
assert(image->signature == MagickSignature);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
assert(reconstruct_image != (const Image *) NULL);
assert(reconstruct_image->signature == MagickSignature);
assert(distortion != (double *) NULL);
*distortion=0.0;
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
if ((reconstruct_image->columns != image->columns) ||
(reconstruct_image->rows != image->rows))
ThrowBinaryException(ImageError,"ImageSizeDiffers",image->filename);
/*
Get image distortion.
*/
length=MaxPixelChannels+1;
channel_distortion=(double *) AcquireQuantumMemory(length,
sizeof(*channel_distortion));
if (channel_distortion == (double *) NULL)
ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
(void) ResetMagickMemory(channel_distortion,0,length*
sizeof(*channel_distortion));
switch (metric)
{
case AbsoluteErrorMetric:
{
status=GetAbsoluteDistortion(image,reconstruct_image,channel_distortion,
exception);
break;
}
case FuzzErrorMetric:
{
status=GetFuzzDistortion(image,reconstruct_image,channel_distortion,
exception);
break;
}
case MeanAbsoluteErrorMetric:
{
status=GetMeanAbsoluteDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case MeanErrorPerPixelMetric:
{
status=GetMeanErrorPerPixel(image,reconstruct_image,channel_distortion,
exception);
break;
}
case MeanSquaredErrorMetric:
{
status=GetMeanSquaredDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case NormalizedCrossCorrelationErrorMetric:
default:
{
status=GetNormalizedCrossCorrelationDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case PeakAbsoluteErrorMetric:
{
status=GetPeakAbsoluteDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case PeakSignalToNoiseRatioMetric:
{
status=GetPeakSignalToNoiseRatio(image,reconstruct_image,
channel_distortion,exception);
break;
}
case RootMeanSquaredErrorMetric:
{
status=GetRootMeanSquaredDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
}
*distortion=channel_distortion[CompositePixelChannel];
channel_distortion=(double *) RelinquishMagickMemory(channel_distortion);
return(status);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G e t I m a g e D i s t o r t i o n s %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetImageDistortions() compares the pixel channels of an image to a
% reconstructed image and returns the specified distortion metric for each
% channel.
%
% The format of the GetImageDistortions method is:
%
% double *GetImageDistortions(const Image *image,
% const Image *reconstruct_image,const MetricType metric,
% ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o image: the image.
%
% o reconstruct_image: the reconstruct image.
%
% o metric: the metric.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport double *GetImageDistortions(Image *image,
const Image *reconstruct_image,const MetricType metric,
ExceptionInfo *exception)
{
double
*channel_distortion;
MagickBooleanType
status;
size_t
length;
assert(image != (Image *) NULL);
assert(image->signature == MagickSignature);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
assert(reconstruct_image != (const Image *) NULL);
assert(reconstruct_image->signature == MagickSignature);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
if ((reconstruct_image->columns != image->columns) ||
(reconstruct_image->rows != image->rows))
{
(void) ThrowMagickException(exception,GetMagickModule(),ImageError,
"ImageSizeDiffers","'%s'",image->filename);
return((double *) NULL);
}
/*
Get image distortion.
*/
length=MaxPixelChannels+1UL;
channel_distortion=(double *) AcquireQuantumMemory(length,
sizeof(*channel_distortion));
if (channel_distortion == (double *) NULL)
ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
(void) ResetMagickMemory(channel_distortion,0,length*
sizeof(*channel_distortion));
status=MagickTrue;
switch (metric)
{
case AbsoluteErrorMetric:
{
status=GetAbsoluteDistortion(image,reconstruct_image,channel_distortion,
exception);
break;
}
case FuzzErrorMetric:
{
status=GetFuzzDistortion(image,reconstruct_image,channel_distortion,
exception);
break;
}
case MeanAbsoluteErrorMetric:
{
status=GetMeanAbsoluteDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case MeanErrorPerPixelMetric:
{
status=GetMeanErrorPerPixel(image,reconstruct_image,channel_distortion,
exception);
break;
}
case MeanSquaredErrorMetric:
{
status=GetMeanSquaredDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case NormalizedCrossCorrelationErrorMetric:
default:
{
status=GetNormalizedCrossCorrelationDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case PeakAbsoluteErrorMetric:
{
status=GetPeakAbsoluteDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
case PeakSignalToNoiseRatioMetric:
{
status=GetPeakSignalToNoiseRatio(image,reconstruct_image,
channel_distortion,exception);
break;
}
case RootMeanSquaredErrorMetric:
{
status=GetRootMeanSquaredDistortion(image,reconstruct_image,
channel_distortion,exception);
break;
}
}
if (status == MagickFalse)
{
channel_distortion=(double *) RelinquishMagickMemory(channel_distortion);
return((double *) NULL);
}
return(channel_distortion);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% I s I m a g e s E q u a l %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% IsImagesEqual() measures the difference between colors at each pixel
% location of two images. A value other than 0 means the colors match
% exactly. Otherwise an error measure is computed by summing over all
% pixels in an image the distance squared in RGB space between each image
% pixel and its corresponding pixel in the reconstruct image. The error
% measure is assigned to these image members:
%
% o mean_error_per_pixel: The mean error for any single pixel in
% the image.
%
% o normalized_mean_error: The normalized mean quantization error for
% any single pixel in the image. This distance measure is normalized to
% a range between 0 and 1. It is independent of the range of red, green,
% and blue values in the image.
%
% o normalized_maximum_error: The normalized maximum quantization
% error for any single pixel in the image. This distance measure is
% normalized to a range between 0 and 1. It is independent of the range
% of red, green, and blue values in your image.
%
% A small normalized mean square error, accessed as
% image->normalized_mean_error, suggests the images are very similar in
% spatial layout and color.
%
% The format of the IsImagesEqual method is:
%
% MagickBooleanType IsImagesEqual(Image *image,
% const Image *reconstruct_image,ExceptionInfo *exception)
%
% A description of each parameter follows.
%
% o image: the image.
%
% o reconstruct_image: the reconstruct image.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport MagickBooleanType IsImagesEqual(Image *image,
const Image *reconstruct_image,ExceptionInfo *exception)
{
CacheView
*image_view,
*reconstruct_view;
MagickBooleanType
status;
double
area,
maximum_error,
mean_error,
mean_error_per_pixel;
ssize_t
y;
assert(image != (Image *) NULL);
assert(image->signature == MagickSignature);
assert(reconstruct_image != (const Image *) NULL);
assert(reconstruct_image->signature == MagickSignature);
if ((reconstruct_image->columns != image->columns) ||
(reconstruct_image->rows != image->rows))
ThrowBinaryException(ImageError,"ImageSizeDiffers",image->filename);
area=0.0;
maximum_error=0.0;
mean_error_per_pixel=0.0;
mean_error=0.0;
image_view=AcquireVirtualCacheView(image,exception);
reconstruct_view=AcquireVirtualCacheView(reconstruct_image,exception);
for (y=0; y < (ssize_t) image->rows; y++)
{
register const Quantum
*restrict p,
*restrict q;
register ssize_t
x;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
1,exception);
if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
break;
for (x=0; x < (ssize_t) image->columns; x++)
{
register ssize_t
i;
if (GetPixelMask(image,p) != 0)
{
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
{
double
distance;
PixelChannel
channel;
PixelTrait
reconstruct_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
reconstruct_traits=GetPixelChannelTraits(reconstruct_image,channel);
if ((traits == UndefinedPixelTrait) ||
(reconstruct_traits == UndefinedPixelTrait) ||
((reconstruct_traits & UpdatePixelTrait) == 0))
continue;
distance=fabs(p[i]-(double) GetPixelChannel(reconstruct_image,
channel,q));
mean_error_per_pixel+=distance;
mean_error+=distance*distance;
if (distance > maximum_error)
maximum_error=distance;
area++;
}
p+=GetPixelChannels(image);
q+=GetPixelChannels(reconstruct_image);
}
}
reconstruct_view=DestroyCacheView(reconstruct_view);
image_view=DestroyCacheView(image_view);
image->error.mean_error_per_pixel=(double) (mean_error_per_pixel/area);
image->error.normalized_mean_error=(double) (QuantumScale*QuantumScale*
mean_error/area);
image->error.normalized_maximum_error=(double) (QuantumScale*maximum_error);
status=image->error.mean_error_per_pixel == 0.0 ? MagickTrue : MagickFalse;
return(status);
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% S i m i l a r i t y I m a g e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SimilarityImage() compares the reference image of the image and returns the
% best match offset. In addition, it returns a similarity image such that an
% exact match location is completely white and if none of the pixels match,
% black, otherwise some gray level in-between.
%
% The format of the SimilarityImageImage method is:
%
% Image *SimilarityImage(const Image *image,const Image *reference,
% const MetricType metric,RectangleInfo *offset,double *similarity,
% ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o image: the image.
%
% o reference: find an area of the image that closely resembles this image.
%
% o metric: the metric.
%
% o the best match offset of the reference image within the image.
%
% o similarity: the computed similarity between the images.
%
% o exception: return any errors or warnings in this structure.
%
*/
static double GetSimilarityMetric(const Image *image,const Image *reference,
const MetricType metric,const ssize_t x_offset,const ssize_t y_offset,
ExceptionInfo *exception)
{
double
distortion;
Image
*similarity_image;
MagickBooleanType
status;
RectangleInfo
geometry;
SetGeometry(reference,&geometry);
geometry.x=x_offset;
geometry.y=y_offset;
similarity_image=CropImage(image,&geometry,exception);
if (similarity_image == (Image *) NULL)
return(0.0);
distortion=0.0;
status=GetImageDistortion(similarity_image,reference,metric,&distortion,
exception);
similarity_image=DestroyImage(similarity_image);
if (status == MagickFalse)
return(0.0);
return(distortion);
}
MagickExport Image *SimilarityImage(Image *image,const Image *reference,
const MetricType metric,RectangleInfo *offset,double *similarity_metric,
ExceptionInfo *exception)
{
#define SimilarityImageTag "Similarity/Image"
CacheView
*similarity_view;
Image
*similarity_image;
MagickBooleanType
status;
MagickOffsetType
progress;
ssize_t
y;
assert(image != (const Image *) NULL);
assert(image->signature == MagickSignature);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
assert(exception != (ExceptionInfo *) NULL);
assert(exception->signature == MagickSignature);
assert(offset != (RectangleInfo *) NULL);
SetGeometry(reference,offset);
*similarity_metric=1.0;
if ((reference->columns > image->columns) || (reference->rows > image->rows))
ThrowImageException(ImageError,"ImageSizeDiffers");
similarity_image=CloneImage(image,image->columns-reference->columns+1,
image->rows-reference->rows+1,MagickTrue,exception);
if (similarity_image == (Image *) NULL)
return((Image *) NULL);
status=SetImageStorageClass(similarity_image,DirectClass,exception);
if (status == MagickFalse)
{
similarity_image=DestroyImage(similarity_image);
return((Image *) NULL);
}
/*
Measure similarity of reference image against image.
*/
status=MagickTrue;
progress=0;
similarity_view=AcquireAuthenticCacheView(similarity_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(progress,status) \
dynamic_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) (image->rows-reference->rows+1); y++)
{
double
similarity;
register Quantum
*restrict q;
register ssize_t
x;
if (status == MagickFalse)
continue;
q=GetCacheViewAuthenticPixels(similarity_view,0,y,similarity_image->columns,
1,exception);
if (q == (Quantum *) NULL)
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) (image->columns-reference->columns+1); x++)
{
register ssize_t
i;
similarity=GetSimilarityMetric(image,reference,metric,x,y,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_SimilarityImage)
#endif
if (similarity < *similarity_metric)
{
*similarity_metric=similarity;
offset->x=x;
offset->y=y;
}
if (GetPixelMask(similarity_image,q) != 0)
{
q+=GetPixelChannels(similarity_image);
continue;
}
for (i=0; i < (ssize_t) GetPixelChannels(similarity_image); i++)
{
PixelChannel
channel;
PixelTrait
similarity_traits,
traits;
channel=GetPixelChannelChannel(image,i);
traits=GetPixelChannelTraits(image,channel);
similarity_traits=GetPixelChannelTraits(similarity_image,channel);
if ((traits == UndefinedPixelTrait) ||
(similarity_traits == UndefinedPixelTrait) ||
((similarity_traits & UpdatePixelTrait) == 0))
continue;
SetPixelChannel(similarity_image,channel,ClampToQuantum(QuantumRange-
QuantumRange*similarity),q);
}
q+=GetPixelChannels(similarity_image);
}
if (IfMagickFalse( SyncCacheViewAuthenticPixels(similarity_view,exception) ))
status=MagickFalse;
if (image->progress_monitor != (MagickProgressMonitor) NULL)
{
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp critical (MagickCore_SimilarityImage)
#endif
if (IfMagickFalse(SetImageProgress(image,SimilarityImageTag,
progress++,image->rows) ))
status=MagickFalse;
}
}
similarity_view=DestroyCacheView(similarity_view);
if (status == MagickFalse)
similarity_image=DestroyImage(similarity_image);
return(similarity_image);
}