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segment.c
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% SSSSS EEEEE GGGG M M EEEEE N N TTTTT %
% SS E G MM MM E NN N T %
% SSS EEE G GGG M M M EEE N N N T %
% SS E G G M M E N NN T %
% SSSSS EEEEE GGGG M M EEEEE N N T %
% %
% %
% MagickCore Methods to Segment an Image with Thresholding Fuzzy c-Means %
% %
% Software Design %
% Cristy %
% April 1993 %
% %
% %
% Copyright @ 1999 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 %
% %
% https://imagemagick.org/license/ %
% %
% 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. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Segment segments an image by analyzing the histograms of the color
% components and identifying units that are homogeneous with the fuzzy
% c-means technique. The scale-space filter analyzes the histograms of
% the three color components of the image and identifies a set of
% classes. The extents of each class is used to coarsely segment the
% image with thresholding. The color associated with each class is
% determined by the mean color of all pixels within the extents of a
% particular class. Finally, any unclassified pixels are assigned to
% the closest class with the fuzzy c-means technique.
%
% The fuzzy c-Means algorithm can be summarized as follows:
%
% o Build a histogram, one for each color component of the image.
%
% o For each histogram, successively apply the scale-space filter and
% build an interval tree of zero crossings in the second derivative
% at each scale. Analyze this scale-space ''fingerprint'' to
% determine which peaks and valleys in the histogram are most
% predominant.
%
% o The fingerprint defines intervals on the axis of the histogram.
% Each interval contains either a minima or a maxima in the original
% signal. If each color component lies within the maxima interval,
% that pixel is considered ''classified'' and is assigned an unique
% class number.
%
% o Any pixel that fails to be classified in the above thresholding
% pass is classified using the fuzzy c-Means technique. It is
% assigned to one of the classes discovered in the histogram analysis
% phase.
%
% The fuzzy c-Means technique attempts to cluster a pixel by finding
% the local minima of the generalized within group sum of squared error
% objective function. A pixel is assigned to the closest class of
% which the fuzzy membership has a maximum value.
%
% Segment is strongly based on software written by Andy Gallo,
% University of Delaware.
%
% The following reference was used in creating this program:
%
% Young Won Lim, Sang Uk Lee, "On The Color Image Segmentation
% Algorithm Based on the Thresholding and the Fuzzy c-Means
% Techniques", Pattern Recognition, Volume 23, Number 9, pages
% 935-952, 1990.
%
%
*/
␌
#include "MagickCore/studio.h"
#include "MagickCore/cache.h"
#include "MagickCore/color.h"
#include "MagickCore/colormap.h"
#include "MagickCore/colorspace.h"
#include "MagickCore/colorspace-private.h"
#include "MagickCore/exception.h"
#include "MagickCore/exception-private.h"
#include "MagickCore/image.h"
#include "MagickCore/image-private.h"
#include "MagickCore/memory_.h"
#include "MagickCore/memory-private.h"
#include "MagickCore/monitor.h"
#include "MagickCore/monitor-private.h"
#include "MagickCore/pixel-accessor.h"
#include "MagickCore/quantize.h"
#include "MagickCore/quantum.h"
#include "MagickCore/quantum-private.h"
#include "MagickCore/resource_.h"
#include "MagickCore/segment.h"
#include "MagickCore/string_.h"
#include "MagickCore/thread-private.h"
␌
/*
Define declarations.
*/
#define MaxDimension 3
#define DeltaTau 0.5f
#if defined(FastClassify)
#define WeightingExponent 2.0
#define SegmentPower(ratio) (ratio)
#else
#define WeightingExponent 2.5
#define SegmentPower(ratio) pow(ratio,(double) (1.0/(weighting_exponent-1.0)));
#endif
#define Tau 5.2f
␌
/*
Typedef declarations.
*/
typedef struct _ExtentPacket
{
double
center;
ssize_t
index,
left,
right;
} ExtentPacket;
typedef struct _Cluster
{
struct _Cluster
*next;
ExtentPacket
red,
green,
blue;
ssize_t
count,
id;
} Cluster;
typedef struct _IntervalTree
{
double
tau;
ssize_t
left,
right;
double
mean_stability,
stability;
struct _IntervalTree
*sibling,
*child;
} IntervalTree;
typedef struct _ZeroCrossing
{
double
tau,
histogram[256];
short
crossings[256];
} ZeroCrossing;
␌
/*
Constant declarations.
*/
static const int
Blue = 2,
Green = 1,
Red = 0,
SafeMargin = 3,
TreeLength = 600;
␌
/*
Method prototypes.
*/
static double
OptimalTau(const ssize_t *,const double,const double,const double,
const double,short *);
static ssize_t
DefineRegion(const short *,ExtentPacket *);
static void
FreeNodes(IntervalTree *),
InitializeHistogram(const Image *,ssize_t **,ExceptionInfo *),
ScaleSpace(const ssize_t *,const double,double *),
ZeroCrossHistogram(double *,const double,short *);
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ C l a s s i f y %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Classify() defines one or more classes. Each pixel is thresholded to
% determine which class it belongs to. If the class is not identified it is
% assigned to the closest class based on the fuzzy c-Means technique.
%
% The format of the Classify method is:
%
% MagickBooleanType Classify(Image *image,short **extrema,
% const double cluster_threshold,const double weighting_exponent,
% const MagickBooleanType verbose,ExceptionInfo *exception)
%
% A description of each parameter follows.
%
% o image: the image.
%
% o extrema: Specifies a pointer to an array of integers. They
% represent the peaks and valleys of the histogram for each color
% component.
%
% o cluster_threshold: This double represents the minimum number of
% pixels contained in a hexahedra before it can be considered valid
% (expressed as a percentage).
%
% o weighting_exponent: Specifies the membership weighting exponent.
%
% o verbose: A value greater than zero prints detailed information about
% the identified classes.
%
% o exception: return any errors or warnings in this structure.
%
*/
static MagickBooleanType Classify(Image *image,short **extrema,
const double cluster_threshold,const double weighting_exponent,
const MagickBooleanType verbose,ExceptionInfo *exception)
{
#define SegmentImageTag "Segment/Image"
#define ThrowClassifyException(severity,tag,label) \
{\
for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster) \
{ \
next_cluster=cluster->next; \
cluster=(Cluster *) RelinquishMagickMemory(cluster); \
} \
if (squares != (double *) NULL) \
{ \
squares-=255; \
free_squares=squares; \
free_squares=(double *) RelinquishMagickMemory(free_squares); \
} \
ThrowBinaryException(severity,tag,label); \
}
CacheView
*image_view;
Cluster
*cluster,
*head,
*last_cluster,
*next_cluster;
double
*free_squares;
ExtentPacket
blue,
green,
red;
MagickOffsetType
progress;
MagickStatusType
status;
ssize_t
i;
double
*squares;
size_t
number_clusters;
ssize_t
count,
y;
/*
Form clusters.
*/
cluster=(Cluster *) NULL;
head=(Cluster *) NULL;
squares=(double *) NULL;
(void) memset(&red,0,sizeof(red));
(void) memset(&green,0,sizeof(green));
(void) memset(&blue,0,sizeof(blue));
while (DefineRegion(extrema[Red],&red) != 0)
{
green.index=0;
while (DefineRegion(extrema[Green],&green) != 0)
{
blue.index=0;
while (DefineRegion(extrema[Blue],&blue) != 0)
{
/*
Allocate a new class.
*/
if (head != (Cluster *) NULL)
{
cluster->next=(Cluster *) AcquireQuantumMemory(1,
sizeof(*cluster->next));
cluster=cluster->next;
}
else
{
cluster=(Cluster *) AcquireQuantumMemory(1,sizeof(*cluster));
head=cluster;
}
if (cluster == (Cluster *) NULL)
ThrowClassifyException(ResourceLimitError,"MemoryAllocationFailed",
image->filename);
/*
Initialize a new class.
*/
(void) memset(cluster,0,sizeof(*cluster));
cluster->red=red;
cluster->green=green;
cluster->blue=blue;
}
}
}
if (head == (Cluster *) NULL)
{
/*
No classes were identified-- create one.
*/
cluster=(Cluster *) AcquireQuantumMemory(1,sizeof(*cluster));
if (cluster == (Cluster *) NULL)
ThrowClassifyException(ResourceLimitError,"MemoryAllocationFailed",
image->filename);
/*
Initialize a new class.
*/
(void) memset(cluster,0,sizeof(*cluster));
cluster->red=red;
cluster->green=green;
cluster->blue=blue;
head=cluster;
}
/*
Count the pixels for each cluster.
*/
status=MagickTrue;
count=0;
progress=0;
image_view=AcquireVirtualCacheView(image,exception);
for (y=0; y < (ssize_t) image->rows; y++)
{
const Quantum
*p;
ssize_t
x;
p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
if (p == (const Quantum *) NULL)
break;
for (x=0; x < (ssize_t) image->columns; x++)
{
PixelInfo
pixel;
pixel.red=(double) ScaleQuantumToChar(GetPixelRed(image,p));
pixel.green=(double) ScaleQuantumToChar(GetPixelGreen(image,p));
pixel.blue=(double) ScaleQuantumToChar(GetPixelBlue(image,p));
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
if ((pixel.red >= (double) (cluster->red.left-SafeMargin)) &&
(pixel.red <= (double) (cluster->red.right+SafeMargin)) &&
(pixel.green >= (double) (cluster->green.left-SafeMargin)) &&
(pixel.green <= (double) (cluster->green.right+SafeMargin)) &&
(pixel.blue >= (double) (cluster->blue.left-SafeMargin)) &&
(pixel.blue <= (double) (cluster->blue.right+SafeMargin)))
{
/*
Count this pixel.
*/
count++;
cluster->red.center+=pixel.red;
cluster->green.center+=pixel.green;
cluster->blue.center+=pixel.blue;
cluster->count++;
break;
}
p+=(ptrdiff_t) GetPixelChannels(image);
}
if (image->progress_monitor != (MagickProgressMonitor) NULL)
{
MagickBooleanType
proceed;
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp atomic
#endif
progress++;
proceed=SetImageProgress(image,SegmentImageTag,progress,2*image->rows);
if (proceed == MagickFalse)
status=MagickFalse;
}
}
image_view=DestroyCacheView(image_view);
/*
Remove clusters that do not meet minimum cluster threshold.
*/
count=0;
last_cluster=head;
next_cluster=head;
for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
{
next_cluster=cluster->next;
if ((cluster->count > 0) &&
(cluster->count >= (count*cluster_threshold/100.0)))
{
/*
Initialize cluster.
*/
cluster->id=count;
cluster->red.center/=cluster->count;
cluster->green.center/=cluster->count;
cluster->blue.center/=cluster->count;
count++;
last_cluster=cluster;
continue;
}
/*
Delete cluster.
*/
if (cluster == head)
head=next_cluster;
else
last_cluster->next=next_cluster;
cluster=(Cluster *) RelinquishMagickMemory(cluster);
}
number_clusters=(size_t) count;
if (verbose != MagickFalse)
{
/*
Print cluster statistics.
*/
(void) FormatLocaleFile(stdout,"Fuzzy C-means Statistics\n");
(void) FormatLocaleFile(stdout,"===================\n\n");
(void) FormatLocaleFile(stdout,"\tCluster Threshold = %g\n",(double)
cluster_threshold);
(void) FormatLocaleFile(stdout,"\tWeighting Exponent = %g\n",(double)
weighting_exponent);
(void) FormatLocaleFile(stdout,"\tTotal Number of Clusters = %.20g\n\n",
(double) number_clusters);
/*
Print the total number of points per cluster.
*/
(void) FormatLocaleFile(stdout,"\n\nNumber of Vectors Per Cluster\n");
(void) FormatLocaleFile(stdout,"=============================\n\n");
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
(void) FormatLocaleFile(stdout,"Cluster #%.20g = %.20g\n",(double)
cluster->id,(double) cluster->count);
/*
Print the cluster extents.
*/
(void) FormatLocaleFile(stdout,
"\n\n\nCluster Extents: (Vector Size: %d)\n",MaxDimension);
(void) FormatLocaleFile(stdout,"================");
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
{
(void) FormatLocaleFile(stdout,"\n\nCluster #%.20g\n\n",(double)
cluster->id);
(void) FormatLocaleFile(stdout,
"%.20g-%.20g %.20g-%.20g %.20g-%.20g\n",(double)
cluster->red.left,(double) cluster->red.right,(double)
cluster->green.left,(double) cluster->green.right,(double)
cluster->blue.left,(double) cluster->blue.right);
}
/*
Print the cluster center values.
*/
(void) FormatLocaleFile(stdout,
"\n\n\nCluster Center Values: (Vector Size: %d)\n",MaxDimension);
(void) FormatLocaleFile(stdout,"=====================");
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
{
(void) FormatLocaleFile(stdout,"\n\nCluster #%.20g\n\n",(double)
cluster->id);
(void) FormatLocaleFile(stdout,"%g %g %g\n",(double)
cluster->red.center,(double) cluster->green.center,(double)
cluster->blue.center);
}
(void) FormatLocaleFile(stdout,"\n");
}
if (number_clusters > 256)
ThrowClassifyException(ImageError,"TooManyClusters",image->filename);
/*
Speed up distance calculations.
*/
squares=(double *) AcquireQuantumMemory(513UL,sizeof(*squares));
if (squares == (double *) NULL)
ThrowClassifyException(ResourceLimitError,"MemoryAllocationFailed",
image->filename);
squares+=255;
for (i=(-255); i <= 255; i++)
squares[i]=(double) i*(double) i;
/*
Allocate image colormap.
*/
if (AcquireImageColormap(image,number_clusters,exception) == MagickFalse)
ThrowClassifyException(ResourceLimitError,"MemoryAllocationFailed",
image->filename);
i=0;
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
{
image->colormap[i].red=(double) ScaleCharToQuantum((unsigned char)
(cluster->red.center+0.5));
image->colormap[i].green=(double) ScaleCharToQuantum((unsigned char)
(cluster->green.center+0.5));
image->colormap[i].blue=(double) ScaleCharToQuantum((unsigned char)
(cluster->blue.center+0.5));
i++;
}
/*
Do course grain classes.
*/
image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static) shared(progress,status) \
magick_number_threads(image,image,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
Cluster
*c;
const PixelInfo
*magick_restrict p;
ssize_t
x;
Quantum
*magick_restrict q;
if (status == MagickFalse)
continue;
q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
if (q == (Quantum *) NULL)
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
PixelInfo
pixel;
SetPixelIndex(image,(Quantum) 0,q);
pixel.red=(double) ScaleQuantumToChar(GetPixelRed(image,q));
pixel.green=(double) ScaleQuantumToChar(GetPixelGreen(image,q));
pixel.blue=(double) ScaleQuantumToChar(GetPixelBlue(image,q));
for (c=head; c != (Cluster *) NULL; c=c->next)
{
if ((pixel.red >= (double) (c->red.left-SafeMargin)) &&
(pixel.red <= (double) (c->red.right+SafeMargin)) &&
(pixel.green >= (double) (c->green.left-SafeMargin)) &&
(pixel.green <= (double) (c->green.right+SafeMargin)) &&
(pixel.blue >= (double) (c->blue.left-SafeMargin)) &&
(pixel.blue <= (double) (c->blue.right+SafeMargin)))
{
/*
Classify this pixel.
*/
SetPixelIndex(image,(Quantum) c->id,q);
break;
}
}
if (c == (Cluster *) NULL)
{
double
distance_squared,
local_minima,
numerator,
ratio,
sum;
ssize_t
j,
k;
/*
Compute fuzzy membership.
*/
local_minima=0.0;
for (j=0; j < (ssize_t) image->colors; j++)
{
sum=0.0;
p=image->colormap+j;
distance_squared=
squares[(ssize_t) (pixel.red-ScaleQuantumToChar((const Quantum) p->red))]+
squares[(ssize_t) (pixel.green-ScaleQuantumToChar((const Quantum) p->green))]+
squares[(ssize_t) (pixel.blue-ScaleQuantumToChar((const Quantum) p->blue))];
numerator=distance_squared;
for (k=0; k < (ssize_t) image->colors; k++)
{
p=image->colormap+k;
distance_squared=
squares[(ssize_t) (pixel.red-ScaleQuantumToChar((const Quantum) p->red))]+
squares[(ssize_t) (pixel.green-ScaleQuantumToChar((const Quantum) p->green))]+
squares[(ssize_t) (pixel.blue-ScaleQuantumToChar((const Quantum) p->blue))];
ratio=numerator/distance_squared;
sum+=SegmentPower(ratio);
}
if ((sum != 0.0) && ((1.0/sum) > local_minima))
{
/*
Classify this pixel.
*/
local_minima=1.0/sum;
SetPixelIndex(image,(Quantum) j,q);
}
}
}
q+=(ptrdiff_t) GetPixelChannels(image);
}
if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
status=MagickFalse;
if (image->progress_monitor != (MagickProgressMonitor) NULL)
{
MagickBooleanType
proceed;
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp atomic
#endif
progress++;
proceed=SetImageProgress(image,SegmentImageTag,progress,2*image->rows);
if (proceed == MagickFalse)
status=MagickFalse;
}
}
image_view=DestroyCacheView(image_view);
status&=(MagickStatusType) SyncImage(image,exception);
/*
Relinquish resources.
*/
for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
{
next_cluster=cluster->next;
cluster=(Cluster *) RelinquishMagickMemory(cluster);
}
squares-=255;
free_squares=squares;
free_squares=(double *) RelinquishMagickMemory(free_squares);
return(MagickTrue);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ C o n s o l i d a t e C r o s s i n g s %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ConsolidateCrossings() guarantees that an even number of zero crossings
% always lie between two crossings.
%
% The format of the ConsolidateCrossings method is:
%
% ConsolidateCrossings(ZeroCrossing *zero_crossing,
% const size_t number_crossings)
%
% A description of each parameter follows.
%
% o zero_crossing: Specifies an array of structures of type ZeroCrossing.
%
% o number_crossings: This size_t specifies the number of elements
% in the zero_crossing array.
%
*/
static void ConsolidateCrossings(ZeroCrossing *zero_crossing,
const size_t number_crossings)
{
ssize_t
i,
j,
k,
l;
ssize_t
center,
correct,
count,
left,
right;
/*
Consolidate zero crossings.
*/
for (i=(ssize_t) number_crossings-1; i >= 0; i--)
for (j=0; j <= 255; j++)
{
if (zero_crossing[i].crossings[j] == 0)
continue;
/*
Find the entry that is closest to j and still preserves the
property that there are an even number of crossings between
intervals.
*/
for (k=j-1; k > 0; k--)
if (zero_crossing[i+1].crossings[k] != 0)
break;
left=MagickMax(k,0);
center=j;
for (k=j+1; k < 255; k++)
if (zero_crossing[i+1].crossings[k] != 0)
break;
right=MagickMin(k,255);
/*
K is the zero crossing just left of j.
*/
for (k=j-1; k > 0; k--)
if (zero_crossing[i].crossings[k] != 0)
break;
if (k < 0)
k=0;
/*
Check center for an even number of crossings between k and j.
*/
correct=(-1);
if (zero_crossing[i+1].crossings[j] != 0)
{
count=0;
for (l=k+1; l < center; l++)
if (zero_crossing[i+1].crossings[l] != 0)
count++;
if (((count % 2) == 0) && (center != k))
correct=center;
}
/*
Check left for an even number of crossings between k and j.
*/
if (correct == -1)
{
count=0;
for (l=k+1; l < left; l++)
if (zero_crossing[i+1].crossings[l] != 0)
count++;
if (((count % 2) == 0) && (left != k))
correct=left;
}
/*
Check right for an even number of crossings between k and j.
*/
if (correct == -1)
{
count=0;
for (l=k+1; l < right; l++)
if (zero_crossing[i+1].crossings[l] != 0)
count++;
if (((count % 2) == 0) && (right != k))
correct=right;
}
l=(ssize_t) zero_crossing[i].crossings[j];
zero_crossing[i].crossings[j]=0;
if (correct != -1)
zero_crossing[i].crossings[correct]=(short) l;
}
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ D e f i n e R e g i o n %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DefineRegion() defines the left and right boundaries of a peak region.
%
% The format of the DefineRegion method is:
%
% ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
%
% A description of each parameter follows.
%
% o extrema: Specifies a pointer to an array of integers. They
% represent the peaks and valleys of the histogram for each color
% component.
%
% o extents: This pointer to an ExtentPacket represent the extends
% of a particular peak or valley of a color component.
%
*/
static ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
{
/*
Initialize to default values.
*/
extents->left=0;
extents->center=0.0;
extents->right=255;
/*
Find the left side (maxima).
*/
for ( ; extents->index <= 255; extents->index++)
if (extrema[extents->index] > 0)
break;
if (extents->index > 255)
return(MagickFalse); /* no left side - no region exists */
extents->left=extents->index;
/*
Find the right side (minima).
*/
for ( ; extents->index <= 255; extents->index++)
if (extrema[extents->index] < 0)
break;
extents->right=extents->index-1;
return(MagickTrue);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ D e r i v a t i v e H i s t o g r a m %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DerivativeHistogram() determines the derivative of the histogram using
% central differencing.
%
% The format of the DerivativeHistogram method is:
%
% DerivativeHistogram(const double *histogram,
% double *derivative)
%
% A description of each parameter follows.
%
% o histogram: Specifies an array of doubles representing the number
% of pixels for each intensity of a particular color component.
%
% o derivative: This array of doubles is initialized by
% DerivativeHistogram to the derivative of the histogram using central
% differencing.
%
*/
static void DerivativeHistogram(const double *histogram,
double *derivative)
{
ssize_t
i,
n;
/*
Compute endpoints using second order polynomial interpolation.
*/
n=255;
derivative[0]=(-1.5*histogram[0]+2.0*histogram[1]-0.5*histogram[2]);
derivative[n]=(0.5*histogram[n-2]-2.0*histogram[n-1]+1.5*histogram[n]);
/*
Compute derivative using central differencing.
*/
for (i=1; i < n; i++)
derivative[i]=(histogram[i+1]-histogram[i-1])/2.0;
return;
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ G e t I m a g e D y n a m i c T h r e s h o l d %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GetImageDynamicThreshold() returns the dynamic threshold for an image.
%
% The format of the GetImageDynamicThreshold method is:
%
% MagickBooleanType GetImageDynamicThreshold(const Image *image,
% const double cluster_threshold,const double smooth_threshold,
% PixelInfo *pixel,ExceptionInfo *exception)
%
% A description of each parameter follows.
%
% o image: the image.
%
% o cluster_threshold: This double represents the minimum number of
% pixels contained in a hexahedra before it can be considered valid
% (expressed as a percentage).
%
% o smooth_threshold: the smoothing threshold eliminates noise in the second
% derivative of the histogram. As the value is increased, you can expect a
% smoother second derivative.
%
% o pixel: return the dynamic threshold here.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport MagickBooleanType GetImageDynamicThreshold(const Image *image,
const double cluster_threshold,const double smooth_threshold,
PixelInfo *pixel,ExceptionInfo *exception)
{
Cluster
*background,
*cluster,
*object,
*head,
*last_cluster,
*next_cluster;
ExtentPacket
blue,
green,
red;
MagickBooleanType
proceed;
double
threshold;
const Quantum
*p;
ssize_t
i,
x;
short
*extrema[MaxDimension];
ssize_t
count,
*histogram[MaxDimension],
y;
/*
Allocate histogram and extrema.
*/
assert(image != (Image *) NULL);
assert(image->signature == MagickCoreSignature);
if (IsEventLogging() != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
GetPixelInfo(image,pixel);
for (i=0; i < MaxDimension; i++)
{
histogram[i]=(ssize_t *) AcquireQuantumMemory(256UL,sizeof(**histogram));
extrema[i]=(short *) AcquireQuantumMemory(256UL,sizeof(**histogram));
if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
{
for (i-- ; i >= 0; i--)
{
extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
}
(void) ThrowMagickException(exception,GetMagickModule(),
ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
return(MagickFalse);
}
}
/*
Initialize histogram.
*/
InitializeHistogram(image,histogram,exception);
(void) OptimalTau(histogram[Red],Tau,0.2f,DeltaTau,
(smooth_threshold == 0.0 ? 1.0 : smooth_threshold),extrema[Red]);
(void) OptimalTau(histogram[Green],Tau,0.2f,DeltaTau,
(smooth_threshold == 0.0 ? 1.0 : smooth_threshold),extrema[Green]);
(void) OptimalTau(histogram[Blue],Tau,0.2f,DeltaTau,
(smooth_threshold == 0.0 ? 1.0 : smooth_threshold),extrema[Blue]);
/*
Form clusters.
*/
cluster=(Cluster *) NULL;
head=(Cluster *) NULL;
(void) memset(&red,0,sizeof(red));
(void) memset(&green,0,sizeof(green));
(void) memset(&blue,0,sizeof(blue));
while (DefineRegion(extrema[Red],&red) != 0)
{
green.index=0;
while (DefineRegion(extrema[Green],&green) != 0)
{
blue.index=0;
while (DefineRegion(extrema[Blue],&blue) != 0)
{
/*
Allocate a new class.
*/
if (head != (Cluster *) NULL)
{
cluster->next=(Cluster *) AcquireQuantumMemory(1,
sizeof(*cluster->next));
cluster=cluster->next;
}
else
{
cluster=(Cluster *) AcquireQuantumMemory(1,sizeof(*cluster));
head=cluster;
}
if (cluster == (Cluster *) NULL)
{
(void) ThrowMagickException(exception,GetMagickModule(),
ResourceLimitError,"MemoryAllocationFailed","`%s'",
image->filename);
return(MagickFalse);
}
/*
Initialize a new class.
*/
cluster->count=0;
cluster->red=red;
cluster->green=green;
cluster->blue=blue;
cluster->next=(Cluster *) NULL;
}
}
}
if (head == (Cluster *) NULL)
{
/*
No classes were identified-- create one.
*/
cluster=(Cluster *) AcquireQuantumMemory(1,sizeof(*cluster));
if (cluster == (Cluster *) NULL)
{
(void) ThrowMagickException(exception,GetMagickModule(),
ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
return(MagickFalse);
}
/*
Initialize a new class.
*/
cluster->count=0;
cluster->red=red;
cluster->green=green;
cluster->blue=blue;
cluster->next=(Cluster *) NULL;
head=cluster;
}
/*
Count the pixels for each cluster.
*/
count=0;
for (y=0; y < (ssize_t) image->rows; y++)
{
p=GetVirtualPixels(image,0,y,image->columns,1,exception);
if (p == (const Quantum *) NULL)
break;
for (x=0; x < (ssize_t) image->columns; x++)
{
double
b,
g,
r;
r=(double) ScaleQuantumToChar(GetPixelRed(image,p));
g=(double) ScaleQuantumToChar(GetPixelGreen(image,p));
b=(double) ScaleQuantumToChar(GetPixelBlue(image,p));
for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
if ((r >= (double) (cluster->red.left-SafeMargin)) &&
(r <= (double) (cluster->red.right+SafeMargin)) &&
(g >= (double) (cluster->green.left-SafeMargin)) &&
(g <= (double) (cluster->green.right+SafeMargin)) &&
(b >= (double) (cluster->blue.left-SafeMargin)) &&
(b <= (double) (cluster->blue.right+SafeMargin)))
{
/*
Count this pixel.
*/
count++;
cluster->red.center+=r;
cluster->green.center+=g;
cluster->blue.center+=b;
cluster->count++;
break;
}
p+=(ptrdiff_t) GetPixelChannels(image);
}
proceed=SetImageProgress(image,SegmentImageTag,(MagickOffsetType) y,
2*image->rows);
if (proceed == MagickFalse)
break;
}
/*
Remove clusters that do not meet minimum cluster threshold.
*/
count=0;
last_cluster=head;
next_cluster=head;
for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
{
next_cluster=cluster->next;
if ((cluster->count > 0) &&
(cluster->count >= (count*cluster_threshold/100.0)))
{
/*
Initialize cluster.
*/
cluster->id=count;
cluster->red.center/=cluster->count;
cluster->green.center/=cluster->count;
cluster->blue.center/=cluster->count;
count++;
last_cluster=cluster;
continue;
}
/*
Delete cluster.
*/
if (cluster == head)
head=next_cluster;
else
last_cluster->next=next_cluster;
cluster=(Cluster *) RelinquishMagickMemory(cluster);
}
object=head;
background=head;
if ((count > 1) && (head != (Cluster *) NULL) &&
(head->next != (Cluster *) NULL))
{
object=head->next;
for (cluster=object; cluster->next != (Cluster *) NULL; )
{
if (cluster->count < object->count)
object=cluster;
cluster=cluster->next;
}
background=head->next;
for (cluster=background; cluster->next != (Cluster *) NULL; )
{
if (cluster->count > background->count)
background=cluster;
cluster=cluster->next;
}
}
if (background != (Cluster *) NULL)
{
threshold=(background->red.center+object->red.center)/2.0;
pixel->red=(double) ScaleCharToQuantum((unsigned char)
(threshold+0.5));
threshold=(background->green.center+object->green.center)/2.0;
pixel->green=(double) ScaleCharToQuantum((unsigned char)
(threshold+0.5));
threshold=(background->blue.center+object->blue.center)/2.0;
pixel->blue=(double) ScaleCharToQuantum((unsigned char)
(threshold+0.5));
}
/*
Relinquish resources.
*/
for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
{
next_cluster=cluster->next;
cluster=(Cluster *) RelinquishMagickMemory(cluster);
}
for (i=0; i < MaxDimension; i++)
{
extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
}
return(MagickTrue);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ I n i t i a l i z e H i s t o g r a m %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% InitializeHistogram() computes the histogram for an image.
%
% The format of the InitializeHistogram method is:
%
% InitializeHistogram(const Image *image,ssize_t **histogram)
%
% A description of each parameter follows.
%
% o image: Specifies a pointer to an Image structure; returned from
% ReadImage.
%
% o histogram: Specifies an array of integers representing the number
% of pixels for each intensity of a particular color component.
%
*/
static void InitializeHistogram(const Image *image,ssize_t **histogram,
ExceptionInfo *exception)
{
const Quantum
*p;
ssize_t
i,
x;
ssize_t
y;
/*
Initialize histogram.
*/
for (i=0; i <= 255; i++)
{
histogram[Red][i]=0;
histogram[Green][i]=0;
histogram[Blue][i]=0;
}
for (y=0; y < (ssize_t) image->rows; y++)
{
p=GetVirtualPixels(image,0,y,image->columns,1,exception);
if (p == (const Quantum *) NULL)
break;
for (x=0; x < (ssize_t) image->columns; x++)
{
histogram[Red][(ssize_t) ScaleQuantumToChar(GetPixelRed(image,p))]++;
histogram[Green][(ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p))]++;
histogram[Blue][(ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p))]++;
p+=(ptrdiff_t) GetPixelChannels(image);
}
}
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ I n i t i a l i z e I n t e r v a l T r e e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% InitializeIntervalTree() initializes an interval tree from the lists of
% zero crossings.
%
% The format of the InitializeIntervalTree method is:
%
% InitializeIntervalTree(IntervalTree **list,ssize_t *number_nodes,
% IntervalTree *node)
%
% A description of each parameter follows.
%
% o zero_crossing: Specifies an array of structures of type ZeroCrossing.
%
% o number_crossings: This size_t specifies the number of elements
% in the zero_crossing array.
%
*/
static void InitializeList(IntervalTree **list,ssize_t *number_nodes,
IntervalTree *node)
{
if (node == (IntervalTree *) NULL)
return;
if (node->child == (IntervalTree *) NULL)
list[(*number_nodes)++]=node;
InitializeList(list,number_nodes,node->sibling);
InitializeList(list,number_nodes,node->child);
}
static void MeanStability(IntervalTree *node)
{
IntervalTree
*child;
if (node == (IntervalTree *) NULL)
return;
node->mean_stability=0.0;
child=node->child;
if (child != (IntervalTree *) NULL)
{
ssize_t
count;
double
sum;
sum=0.0;
count=0;
for ( ; child != (IntervalTree *) NULL; child=child->sibling)
{
sum+=child->stability;
count++;
}
node->mean_stability=sum/(double) count;
}
MeanStability(node->sibling);
MeanStability(node->child);
}
static void Stability(IntervalTree *node)
{
if (node == (IntervalTree *) NULL)
return;
if (node->child == (IntervalTree *) NULL)
node->stability=0.0;
else
node->stability=node->tau-(node->child)->tau;
Stability(node->sibling);
Stability(node->child);
}
static IntervalTree *InitializeIntervalTree(const ZeroCrossing *zero_crossing,
const size_t number_crossings)
{
IntervalTree
*head,
**list,
*node,
*root;
ssize_t
i;
ssize_t
j,
k,
left,
number_nodes;
/*
Allocate interval tree.
*/
list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
sizeof(*list));
if (list == (IntervalTree **) NULL)
return((IntervalTree *) NULL);
/*
The root is the entire histogram.
*/
root=(IntervalTree *) AcquireCriticalMemory(sizeof(*root));
root->child=(IntervalTree *) NULL;
root->sibling=(IntervalTree *) NULL;
root->tau=0.0;
root->left=0;
root->right=255;
root->mean_stability=0.0;
root->stability=0.0;
(void) memset(list,0,(size_t) TreeLength*sizeof(*list));
for (i=(-1); i < (ssize_t) number_crossings; i++)
{
/*
Initialize list with all nodes with no children.
*/
number_nodes=0;
InitializeList(list,&number_nodes,root);
/*
Split list.
*/
for (j=0; j < number_nodes; j++)
{
head=list[j];
left=head->left;
node=head;
for (k=head->left+1; k < head->right; k++)
{
if (zero_crossing[i+1].crossings[k] != 0)
{
if (node == head)
{
node->child=(IntervalTree *) AcquireQuantumMemory(1,
sizeof(*node->child));
node=node->child;
}
else
{
node->sibling=(IntervalTree *) AcquireQuantumMemory(1,
sizeof(*node->sibling));
node=node->sibling;
}
if (node == (IntervalTree *) NULL)
{
list=(IntervalTree **) RelinquishMagickMemory(list);
FreeNodes(root);
return((IntervalTree *) NULL);
}
node->tau=zero_crossing[i+1].tau;
node->child=(IntervalTree *) NULL;
node->sibling=(IntervalTree *) NULL;
node->left=left;
node->right=k;
left=k;
}
}
if (left != head->left)
{
node->sibling=(IntervalTree *) AcquireQuantumMemory(1,
sizeof(*node->sibling));
node=node->sibling;
if (node == (IntervalTree *) NULL)
{
list=(IntervalTree **) RelinquishMagickMemory(list);
FreeNodes(root);
return((IntervalTree *) NULL);
}
node->tau=zero_crossing[i+1].tau;
node->child=(IntervalTree *) NULL;
node->sibling=(IntervalTree *) NULL;
node->left=left;
node->right=head->right;
}
}
}
/*
Determine the stability: difference between a nodes tau and its child.
*/
Stability(root->child);
MeanStability(root->child);
list=(IntervalTree **) RelinquishMagickMemory(list);
return(root);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ O p t i m a l T a u %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% OptimalTau() finds the optimal tau for each band of the histogram.
%
% The format of the OptimalTau method is:
%
% double OptimalTau(const ssize_t *histogram,const double max_tau,
% const double min_tau,const double delta_tau,
% const double smooth_threshold,short *extrema)
%
% A description of each parameter follows.
%
% o histogram: Specifies an array of integers representing the number
% of pixels for each intensity of a particular color component.
%
% o extrema: Specifies a pointer to an array of integers. They
% represent the peaks and valleys of the histogram for each color
% component.
%
*/
static void ActiveNodes(IntervalTree **list,ssize_t *number_nodes,
IntervalTree *node)
{
if (node == (IntervalTree *) NULL)
return;
if (node->stability >= node->mean_stability)
{
list[(*number_nodes)++]=node;
ActiveNodes(list,number_nodes,node->sibling);
}
else
{
ActiveNodes(list,number_nodes,node->sibling);
ActiveNodes(list,number_nodes,node->child);
}
}
static void FreeNodes(IntervalTree *node)
{
if (node == (IntervalTree *) NULL)
return;
FreeNodes(node->sibling);
FreeNodes(node->child);
node=(IntervalTree *) RelinquishMagickMemory(node);
}
static double OptimalTau(const ssize_t *histogram,const double max_tau,
const double min_tau,const double delta_tau,const double smooth_threshold,
short *extrema)
{
double
average_tau,
*derivative,
*second_derivative,
tau,
value;
IntervalTree
**list,
*node,
*root;
MagickBooleanType
peak;
ssize_t
i,
x;
size_t
count,
number_crossings;
ssize_t
index,
j,
k,
number_nodes;
ZeroCrossing
*zero_crossing;
/*
Allocate interval tree.
*/
list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
sizeof(*list));
if (list == (IntervalTree **) NULL)
return(0.0);
/*
Allocate zero crossing list.
*/
count=(size_t) ((max_tau-min_tau)/delta_tau)+2;
zero_crossing=(ZeroCrossing *) AcquireQuantumMemory((size_t) count,
sizeof(*zero_crossing));
if (zero_crossing == (ZeroCrossing *) NULL)
{
list=(IntervalTree **) RelinquishMagickMemory(list);
return(0.0);
}
for (i=0; i < (ssize_t) count; i++)
zero_crossing[i].tau=(-1.0);
/*
Initialize zero crossing list.
*/
derivative=(double *) AcquireCriticalMemory(256*sizeof(*derivative));
second_derivative=(double *) AcquireCriticalMemory(256*
sizeof(*second_derivative));
i=0;
for (tau=max_tau; tau >= min_tau; tau-=delta_tau)
{
zero_crossing[i].tau=tau;
ScaleSpace(histogram,tau,zero_crossing[i].histogram);
DerivativeHistogram(zero_crossing[i].histogram,derivative);
DerivativeHistogram(derivative,second_derivative);
ZeroCrossHistogram(second_derivative,smooth_threshold,
zero_crossing[i].crossings);
i++;
}
/*
Add an entry for the original histogram.
*/
zero_crossing[i].tau=0.0;
for (j=0; j <= 255; j++)
zero_crossing[i].histogram[j]=(double) histogram[j];
DerivativeHistogram(zero_crossing[i].histogram,derivative);
DerivativeHistogram(derivative,second_derivative);
ZeroCrossHistogram(second_derivative,smooth_threshold,
zero_crossing[i].crossings);
number_crossings=(size_t) i;
derivative=(double *) RelinquishMagickMemory(derivative);
second_derivative=(double *) RelinquishMagickMemory(second_derivative);
/*
Ensure the scale-space fingerprints form lines in scale-space, not loops.
*/
ConsolidateCrossings(zero_crossing,number_crossings);
/*
Force endpoints to be included in the interval.
*/
for (i=0; i <= (ssize_t) number_crossings; i++)
{
for (j=0; j < 255; j++)
if (zero_crossing[i].crossings[j] != 0)
break;
zero_crossing[i].crossings[0]=(-zero_crossing[i].crossings[j]);
for (j=255; j > 0; j--)
if (zero_crossing[i].crossings[j] != 0)
break;
zero_crossing[i].crossings[255]=(-zero_crossing[i].crossings[j]);
}
/*
Initialize interval tree.
*/
root=InitializeIntervalTree(zero_crossing,number_crossings);
if (root == (IntervalTree *) NULL)
{
zero_crossing=(ZeroCrossing *) RelinquishMagickMemory(zero_crossing);
list=(IntervalTree **) RelinquishMagickMemory(list);
return(0.0);
}
/*
Find active nodes: Stability is greater (or equal) to the mean stability of
its children.
*/
number_nodes=0;
ActiveNodes(list,&number_nodes,root->child);
/*
Initialize extrema.
*/
for (i=0; i <= 255; i++)
extrema[i]=0;
for (i=0; i < number_nodes; i++)
{
/*
Find this tau in zero crossings list.
*/
k=0;
node=list[i];
for (j=0; j <= (ssize_t) number_crossings; j++)
if (zero_crossing[j].tau == node->tau)
k=j;
/*
Find the value of the peak.
*/
peak=zero_crossing[k].crossings[node->right] == -1 ? MagickTrue :
MagickFalse;
index=node->left;
value=zero_crossing[k].histogram[index];
for (x=node->left; x <= node->right; x++)
{
if (peak != MagickFalse)
{
if (zero_crossing[k].histogram[x] > value)
{
value=zero_crossing[k].histogram[x];
index=x;
}
}
else
if (zero_crossing[k].histogram[x] < value)
{
value=zero_crossing[k].histogram[x];
index=x;
}
}
for (x=node->left; x <= node->right; x++)
{
if (index == 0)
index=256;
if (peak != MagickFalse)
extrema[x]=(short) index;
else
extrema[x]=(short) (-index);
}
}
/*
Determine the average tau.
*/
average_tau=0.0;
for (i=0; i < number_nodes; i++)
average_tau+=list[i]->tau;
average_tau*=MagickSafeReciprocal((double) number_nodes);
/*
Relinquish resources.
*/
FreeNodes(root);
zero_crossing=(ZeroCrossing *) RelinquishMagickMemory(zero_crossing);
list=(IntervalTree **) RelinquishMagickMemory(list);
return(average_tau);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ S c a l e S p a c e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ScaleSpace() performs a scale-space filter on the 1D histogram.
%
% The format of the ScaleSpace method is:
%
% ScaleSpace(const ssize_t *histogram,const double tau,
% double *scale_histogram)
%
% A description of each parameter follows.
%
% o histogram: Specifies an array of doubles representing the number
% of pixels for each intensity of a particular color component.
%
*/
static void ScaleSpace(const ssize_t *histogram,const double tau,
double *scale_histogram)
{
double
alpha,
beta,
*gamma,
sum;
ssize_t
u,
x;
gamma=(double *) AcquireQuantumMemory(256,sizeof(*gamma));
if (gamma == (double *) NULL)
ThrowFatalException(ResourceLimitFatalError,"UnableToAllocateGammaMap");
alpha=MagickSafeReciprocal(tau*sqrt(2.0*MagickPI));
beta=(-1.0*MagickSafeReciprocal(2.0*tau*tau));
for (x=0; x <= 255; x++)
gamma[x]=0.0;
for (x=0; x <= 255; x++)
{
gamma[x]=exp((double) beta*x*x);
if (gamma[x] < MagickEpsilon)
break;
}
for (x=0; x <= 255; x++)
{
sum=0.0;
for (u=0; u <= 255; u++)
sum+=(double) histogram[u]*gamma[MagickAbsoluteValue(x-u)];
scale_histogram[x]=alpha*sum;
}
gamma=(double *) RelinquishMagickMemory(gamma);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% S e g m e n t I m a g e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SegmentImage() segment an image by analyzing the histograms of the color
% components and identifying units that are homogeneous with the fuzzy
% C-means technique.
%
% The format of the SegmentImage method is:
%
% MagickBooleanType SegmentImage(Image *image,
% const ColorspaceType colorspace,const MagickBooleanType verbose,
% const double cluster_threshold,const double smooth_threshold,
% ExceptionInfo *exception)
%
% A description of each parameter follows.
%
% o image: the image.
%
% o colorspace: Indicate the colorspace.
%
% o verbose: Set to MagickTrue to print detailed information about the
% identified classes.
%
% o cluster_threshold: This represents the minimum number of pixels
% contained in a hexahedra before it can be considered valid (expressed
% as a percentage).
%
% o smooth_threshold: the smoothing threshold eliminates noise in the second
% derivative of the histogram. As the value is increased, you can expect a
% smoother second derivative.
%
% o exception: return any errors or warnings in this structure.
%
*/
MagickExport MagickBooleanType SegmentImage(Image *image,
const ColorspaceType colorspace,const MagickBooleanType verbose,
const double cluster_threshold,const double smooth_threshold,
ExceptionInfo *exception)
{
ColorspaceType
previous_colorspace;
MagickBooleanType
status;
ssize_t
i;
short
*extrema[MaxDimension];
ssize_t
*histogram[MaxDimension];
/*
Allocate histogram and extrema.
*/
assert(image != (Image *) NULL);
assert(image->signature == MagickCoreSignature);
if (IsEventLogging() != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
for (i=0; i < MaxDimension; i++)
{
histogram[i]=(ssize_t *) AcquireQuantumMemory(256,sizeof(**histogram));
extrema[i]=(short *) AcquireQuantumMemory(256,sizeof(**extrema));
if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
{
for (i-- ; i >= 0; i--)
{
extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
}
ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
image->filename)
}
}
/*
Initialize histogram.
*/
previous_colorspace=image->colorspace;
(void) TransformImageColorspace(image,colorspace,exception);
InitializeHistogram(image,histogram,exception);
(void) OptimalTau(histogram[Red],Tau,0.2,DeltaTau,smooth_threshold == 0.0 ?
1.0 : smooth_threshold,extrema[Red]);
(void) OptimalTau(histogram[Green],Tau,0.2,DeltaTau,smooth_threshold == 0.0 ?
1.0 : smooth_threshold,extrema[Green]);
(void) OptimalTau(histogram[Blue],Tau,0.2,DeltaTau,smooth_threshold == 0.0 ?
1.0 : smooth_threshold,extrema[Blue]);
/*
Classify using the fuzzy c-Means technique.
*/
status=Classify(image,extrema,cluster_threshold,WeightingExponent,verbose,
exception);
(void) TransformImageColorspace(image,previous_colorspace,exception);
/*
Relinquish resources.
*/
for (i=0; i < MaxDimension; i++)
{
extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
}
return(status);
}
␌
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
+ Z e r o C r o s s H i s t o g r a m %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ZeroCrossHistogram() find the zero crossings in a histogram and marks
% directions as: 1 is negative to positive; 0 is zero crossing; and -1
% is positive to negative.
%
% The format of the ZeroCrossHistogram method is:
%
% ZeroCrossHistogram(double *second_derivative,
% const double smooth_threshold,short *crossings)
%
% A description of each parameter follows.
%
% o second_derivative: Specifies an array of doubles representing the
% second derivative of the histogram of a particular color component.
%
% o crossings: This array of integers is initialized with
% -1, 0, or 1 representing the slope of the first derivative of the
% of a particular color component.
%
*/
static void ZeroCrossHistogram(double *second_derivative,
const double smooth_threshold,short *crossings)
{
ssize_t
i;
ssize_t
parity;
/*
Merge low numbers to zero to help prevent noise.
*/
for (i=0; i <= 255; i++)
if ((second_derivative[i] < smooth_threshold) &&
(second_derivative[i] >= -smooth_threshold))
second_derivative[i]=0.0;
/*
Mark zero crossings.
*/
parity=0;
for (i=0; i <= 255; i++)
{
crossings[i]=0;
if (second_derivative[i] < 0.0)
{
if (parity > 0)
crossings[i]=(-1);
parity=1;
}
else
if (second_derivative[i] > 0.0)
{
if (parity < 0)
crossings[i]=1;
parity=(-1);
}
}
}
_Cluster
Definition segment.c:137
_ExtentPacket
Definition segment.c:126
_IntervalTree
Definition segment.c:152
_ZeroCrossing
Definition segment.c:170