2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6 % SSSSS EEEEE GGGG M M EEEEE N N TTTTT %
7 % SS E G MM MM E NN N T %
8 % SSS EEE G GGG M M M EEE N N N T %
9 % SS E G G M M E N NN T %
10 % SSSSS EEEEE GGGG M M EEEEE N N T %
13 % MagickCore Methods to Segment an Image with Thresholding Fuzzy c-Means %
20 % Copyright 1999-2010 ImageMagick Studio LLC, a non-profit organization %
21 % dedicated to making software imaging solutions freely available. %
23 % You may not use this file except in compliance with the License. You may %
24 % obtain a copy of the License at %
26 % http://www.imagemagick.org/script/license.php %
28 % Unless required by applicable law or agreed to in writing, software %
29 % distributed under the License is distributed on an "AS IS" BASIS, %
30 % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
31 % See the License for the specific language governing permissions and %
32 % limitations under the License. %
34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
36 % Segment segments an image by analyzing the histograms of the color
37 % components and identifying units that are homogeneous with the fuzzy
38 % c-means technique. The scale-space filter analyzes the histograms of
39 % the three color components of the image and identifies a set of
40 % classes. The extents of each class is used to coarsely segment the
41 % image with thresholding. The color associated with each class is
42 % determined by the mean color of all pixels within the extents of a
43 % particular class. Finally, any unclassified pixels are assigned to
44 % the closest class with the fuzzy c-means technique.
46 % The fuzzy c-Means algorithm can be summarized as follows:
48 % o Build a histogram, one for each color component of the image.
50 % o For each histogram, successively apply the scale-space filter and
51 % build an interval tree of zero crossings in the second derivative
52 % at each scale. Analyze this scale-space ``fingerprint'' to
53 % determine which peaks and valleys in the histogram are most
56 % o The fingerprint defines intervals on the axis of the histogram.
57 % Each interval contains either a minima or a maxima in the original
58 % signal. If each color component lies within the maxima interval,
59 % that pixel is considered ``classified'' and is assigned an unique
62 % o Any pixel that fails to be classified in the above thresholding
63 % pass is classified using the fuzzy c-Means technique. It is
64 % assigned to one of the classes discovered in the histogram analysis
67 % The fuzzy c-Means technique attempts to cluster a pixel by finding
68 % the local minima of the generalized within group sum of squared error
69 % objective function. A pixel is assigned to the closest class of
70 % which the fuzzy membership has a maximum value.
72 % Segment is strongly based on software written by Andy Gallo,
73 % University of Delaware.
75 % The following reference was used in creating this program:
77 % Young Won Lim, Sang Uk Lee, "On The Color Image Segmentation
78 % Algorithm Based on the Thresholding and the Fuzzy c-Means
79 % Techniques", Pattern Recognition, Volume 23, Number 9, pages
85 #include "magick/studio.h"
86 #include "magick/cache.h"
87 #include "magick/color.h"
88 #include "magick/colormap.h"
89 #include "magick/colorspace.h"
90 #include "magick/exception.h"
91 #include "magick/exception-private.h"
92 #include "magick/image.h"
93 #include "magick/image-private.h"
94 #include "magick/memory_.h"
95 #include "magick/monitor.h"
96 #include "magick/monitor-private.h"
97 #include "magick/quantize.h"
98 #include "magick/quantum.h"
99 #include "magick/quantum-private.h"
100 #include "magick/segment.h"
101 #include "magick/string_.h"
106 #define MaxDimension 3
107 #define DeltaTau 0.5f
108 #if defined(FastClassify)
109 #define WeightingExponent 2.0
110 #define SegmentPower(ratio) (ratio)
112 #define WeightingExponent 2.5
113 #define SegmentPower(ratio) pow(ratio,(double) (1.0/(weighting_exponent-1.0)));
118 Typedef declarations.
120 typedef struct _ExtentPacket
131 typedef struct _Cluster
146 typedef struct _IntervalTree
164 typedef struct _ZeroCrossing
175 Constant declarations.
187 static MagickRealType
188 OptimalTau(const ssize_t *,const double,const double,const double,
189 const double,short *);
192 DefineRegion(const short *,ExtentPacket *);
195 InitializeHistogram(const Image *,ssize_t **,ExceptionInfo *),
196 ScaleSpace(const ssize_t *,const MagickRealType,MagickRealType *),
197 ZeroCrossHistogram(MagickRealType *,const MagickRealType,short *);
200 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
208 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
210 % Classify() defines one or more classes. Each pixel is thresholded to
211 % determine which class it bessize_ts to. If the class is not identified it is
212 % assigned to the closest class based on the fuzzy c-Means technique.
214 % The format of the Classify method is:
216 % MagickBooleanType Classify(Image *image,short **extrema,
217 % const MagickRealType cluster_threshold,
218 % const MagickRealType weighting_exponent,
219 % const MagickBooleanType verbose)
221 % A description of each parameter follows.
223 % o image: the image.
225 % o extrema: Specifies a pointer to an array of integers. They
226 % represent the peaks and valleys of the histogram for each color
229 % o cluster_threshold: This MagickRealType represents the minimum number of
230 % pixels contained in a hexahedra before it can be considered valid
231 % (expressed as a percentage).
233 % o weighting_exponent: Specifies the membership weighting exponent.
235 % o verbose: A value greater than zero prints detailed information about
236 % the identified classes.
239 static MagickBooleanType Classify(Image *image,short **extrema,
240 const MagickRealType cluster_threshold,
241 const MagickRealType weighting_exponent,const MagickBooleanType verbose)
243 #define SegmentImageTag "Segment/Image"
276 register MagickRealType
285 cluster=(Cluster *) NULL;
286 head=(Cluster *) NULL;
287 (void) ResetMagickMemory(&red,0,sizeof(red));
288 (void) ResetMagickMemory(&green,0,sizeof(green));
289 (void) ResetMagickMemory(&blue,0,sizeof(blue));
290 while (DefineRegion(extrema[Red],&red) != 0)
293 while (DefineRegion(extrema[Green],&green) != 0)
296 while (DefineRegion(extrema[Blue],&blue) != 0)
299 Allocate a new class.
301 if (head != (Cluster *) NULL)
303 cluster->next=(Cluster *) AcquireMagickMemory(
304 sizeof(*cluster->next));
305 cluster=cluster->next;
309 cluster=(Cluster *) AcquireAlignedMemory(1,sizeof(*cluster));
312 if (cluster == (Cluster *) NULL)
313 ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
316 Initialize a new class.
320 cluster->green=green;
322 cluster->next=(Cluster *) NULL;
326 if (head == (Cluster *) NULL)
329 No classes were identified-- create one.
331 cluster=(Cluster *) AcquireAlignedMemory(1,sizeof(*cluster));
332 if (cluster == (Cluster *) NULL)
333 ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
336 Initialize a new class.
340 cluster->green=green;
342 cluster->next=(Cluster *) NULL;
346 Count the pixels for each cluster.
351 exception=(&image->exception);
352 image_view=AcquireCacheView(image);
353 for (y=0; y < (ssize_t) image->rows; y++)
355 register const PixelPacket
361 p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
362 if (p == (const PixelPacket *) NULL)
364 for (x=0; x < (ssize_t) image->columns; x++)
366 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
367 if (((ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p)) >=
368 (cluster->red.left-SafeMargin)) &&
369 ((ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p)) <=
370 (cluster->red.right+SafeMargin)) &&
371 ((ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p)) >=
372 (cluster->green.left-SafeMargin)) &&
373 ((ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p)) <=
374 (cluster->green.right+SafeMargin)) &&
375 ((ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p)) >=
376 (cluster->blue.left-SafeMargin)) &&
377 ((ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p)) <=
378 (cluster->blue.right+SafeMargin)))
384 cluster->red.center+=(MagickRealType) ScaleQuantumToChar(GetRedPixelComponent(p));
385 cluster->green.center+=(MagickRealType)
386 ScaleQuantumToChar(GetGreenPixelComponent(p));
387 cluster->blue.center+=(MagickRealType) ScaleQuantumToChar(GetBluePixelComponent(p));
393 if (image->progress_monitor != (MagickProgressMonitor) NULL)
398 #if defined(MAGICKCORE_OPENMP_SUPPORT)
399 #pragma omp critical (MagickCore_Classify)
401 proceed=SetImageProgress(image,SegmentImageTag,progress++,
403 if (proceed == MagickFalse)
407 image_view=DestroyCacheView(image_view);
409 Remove clusters that do not meet minimum cluster threshold.
414 for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
416 next_cluster=cluster->next;
417 if ((cluster->count > 0) &&
418 (cluster->count >= (count*cluster_threshold/100.0)))
424 cluster->red.center/=cluster->count;
425 cluster->green.center/=cluster->count;
426 cluster->blue.center/=cluster->count;
428 last_cluster=cluster;
437 last_cluster->next=next_cluster;
438 cluster=(Cluster *) RelinquishMagickMemory(cluster);
440 number_clusters=(size_t) count;
441 if (verbose != MagickFalse)
444 Print cluster statistics.
446 (void) fprintf(stdout,"Fuzzy C-means Statistics\n");
447 (void) fprintf(stdout,"===================\n\n");
448 (void) fprintf(stdout,"\tCluster Threshold = %g\n",(double)
450 (void) fprintf(stdout,"\tWeighting Exponent = %g\n",(double)
452 (void) fprintf(stdout,"\tTotal Number of Clusters = %lu\n\n",
455 Print the total number of points per cluster.
457 (void) fprintf(stdout,"\n\nNumber of Vectors Per Cluster\n");
458 (void) fprintf(stdout,"=============================\n\n");
459 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
460 (void) fprintf(stdout,"Cluster #%ld = %ld\n",cluster->id,
463 Print the cluster extents.
465 (void) fprintf(stdout,
466 "\n\n\nCluster Extents: (Vector Size: %d)\n",MaxDimension);
467 (void) fprintf(stdout,"================");
468 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
470 (void) fprintf(stdout,"\n\nCluster #%ld\n\n",cluster->id);
471 (void) fprintf(stdout,"%ld-%ld %ld-%ld %ld-%ld\n",cluster->red.left,
472 cluster->red.right,cluster->green.left,cluster->green.right,
473 cluster->blue.left,cluster->blue.right);
476 Print the cluster center values.
478 (void) fprintf(stdout,
479 "\n\n\nCluster Center Values: (Vector Size: %d)\n",MaxDimension);
480 (void) fprintf(stdout,"=====================");
481 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
483 (void) fprintf(stdout,"\n\nCluster #%ld\n\n",cluster->id);
484 (void) fprintf(stdout,"%g %g %g\n",(double)
485 cluster->red.center,(double) cluster->green.center,(double)
486 cluster->blue.center);
488 (void) fprintf(stdout,"\n");
490 if (number_clusters > 256)
491 ThrowBinaryException(ImageError,"TooManyClusters",image->filename);
493 Speed up distance calculations.
495 squares=(MagickRealType *) AcquireQuantumMemory(513UL,sizeof(*squares));
496 if (squares == (MagickRealType *) NULL)
497 ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
500 for (i=(-255); i <= 255; i++)
501 squares[i]=(MagickRealType) i*(MagickRealType) i;
503 Allocate image colormap.
505 if (AcquireImageColormap(image,number_clusters) == MagickFalse)
506 ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
509 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
511 image->colormap[i].red=ScaleCharToQuantum((unsigned char)
512 (cluster->red.center+0.5));
513 image->colormap[i].green=ScaleCharToQuantum((unsigned char)
514 (cluster->green.center+0.5));
515 image->colormap[i].blue=ScaleCharToQuantum((unsigned char)
516 (cluster->blue.center+0.5));
520 Do course grain classes.
522 exception=(&image->exception);
523 image_view=AcquireCacheView(image);
524 #if defined(MAGICKCORE_OPENMP_SUPPORT)
525 #pragma omp parallel for schedule(dynamic,4) shared(progress,status)
527 for (y=0; y < (ssize_t) image->rows; y++)
532 register const PixelPacket
544 if (status == MagickFalse)
546 q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
547 if (q == (PixelPacket *) NULL)
552 indexes=GetCacheViewAuthenticIndexQueue(image_view);
553 for (x=0; x < (ssize_t) image->columns; x++)
555 indexes[x]=(IndexPacket) 0;
556 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
558 if (((ssize_t) ScaleQuantumToChar(q->red) >=
559 (cluster->red.left-SafeMargin)) &&
560 ((ssize_t) ScaleQuantumToChar(q->red) <=
561 (cluster->red.right+SafeMargin)) &&
562 ((ssize_t) ScaleQuantumToChar(q->green) >=
563 (cluster->green.left-SafeMargin)) &&
564 ((ssize_t) ScaleQuantumToChar(q->green) <=
565 (cluster->green.right+SafeMargin)) &&
566 ((ssize_t) ScaleQuantumToChar(q->blue) >=
567 (cluster->blue.left-SafeMargin)) &&
568 ((ssize_t) ScaleQuantumToChar(q->blue) <=
569 (cluster->blue.right+SafeMargin)))
574 indexes[x]=(IndexPacket) cluster->id;
578 if (cluster == (Cluster *) NULL)
592 Compute fuzzy membership.
595 for (j=0; j < (ssize_t) image->colors; j++)
599 distance_squared=squares[(ssize_t) ScaleQuantumToChar(q->red)-
600 (ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p))]+
601 squares[(ssize_t) ScaleQuantumToChar(q->green)-
602 (ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p))]+
603 squares[(ssize_t) ScaleQuantumToChar(q->blue)-
604 (ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p))];
605 numerator=distance_squared;
606 for (k=0; k < (ssize_t) image->colors; k++)
609 distance_squared=squares[(ssize_t) ScaleQuantumToChar(q->red)-
610 (ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p))]+
611 squares[(ssize_t) ScaleQuantumToChar(q->green)-
612 (ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p))]+
613 squares[(ssize_t) ScaleQuantumToChar(q->blue)-
614 (ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p))];
615 ratio=numerator/distance_squared;
616 sum+=SegmentPower(ratio);
618 if ((sum != 0.0) && ((1.0/sum) > local_minima))
623 local_minima=1.0/sum;
624 indexes[x]=(IndexPacket) j;
630 if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
632 if (image->progress_monitor != (MagickProgressMonitor) NULL)
637 #if defined(MAGICKCORE_OPENMP_SUPPORT)
638 #pragma omp critical (MagickCore_Classify)
640 proceed=SetImageProgress(image,SegmentImageTag,progress++,
642 if (proceed == MagickFalse)
646 image_view=DestroyCacheView(image_view);
647 status&=SyncImage(image);
649 Relinquish resources.
651 for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
653 next_cluster=cluster->next;
654 cluster=(Cluster *) RelinquishMagickMemory(cluster);
657 free_squares=squares;
658 free_squares=(MagickRealType *) RelinquishMagickMemory(free_squares);
663 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
667 + C o n s o l i d a t e C r o s s i n g s %
671 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
673 % ConsolidateCrossings() guarantees that an even number of zero crossings
674 % always lie between two crossings.
676 % The format of the ConsolidateCrossings method is:
678 % ConsolidateCrossings(ZeroCrossing *zero_crossing,
679 % const size_t number_crossings)
681 % A description of each parameter follows.
683 % o zero_crossing: Specifies an array of structures of type ZeroCrossing.
685 % o number_crossings: This size_t specifies the number of elements
686 % in the zero_crossing array.
690 static inline ssize_t MagickAbsoluteValue(const ssize_t x)
697 static inline ssize_t MagickMax(const ssize_t x,const ssize_t y)
704 static inline ssize_t MagickMin(const ssize_t x,const ssize_t y)
711 static void ConsolidateCrossings(ZeroCrossing *zero_crossing,
712 const size_t number_crossings)
728 Consolidate zero crossings.
730 for (i=(ssize_t) number_crossings-1; i >= 0; i--)
731 for (j=0; j <= 255; j++)
733 if (zero_crossing[i].crossings[j] == 0)
736 Find the entry that is closest to j and still preserves the
737 property that there are an even number of crossings between
740 for (k=j-1; k > 0; k--)
741 if (zero_crossing[i+1].crossings[k] != 0)
745 for (k=j+1; k < 255; k++)
746 if (zero_crossing[i+1].crossings[k] != 0)
748 right=MagickMin(k,255);
750 K is the zero crossing just left of j.
752 for (k=j-1; k > 0; k--)
753 if (zero_crossing[i].crossings[k] != 0)
758 Check center for an even number of crossings between k and j.
761 if (zero_crossing[i+1].crossings[j] != 0)
764 for (l=k+1; l < center; l++)
765 if (zero_crossing[i+1].crossings[l] != 0)
767 if (((count % 2) == 0) && (center != k))
771 Check left for an even number of crossings between k and j.
776 for (l=k+1; l < left; l++)
777 if (zero_crossing[i+1].crossings[l] != 0)
779 if (((count % 2) == 0) && (left != k))
783 Check right for an even number of crossings between k and j.
788 for (l=k+1; l < right; l++)
789 if (zero_crossing[i+1].crossings[l] != 0)
791 if (((count % 2) == 0) && (right != k))
794 l=zero_crossing[i].crossings[j];
795 zero_crossing[i].crossings[j]=0;
797 zero_crossing[i].crossings[correct]=(short) l;
802 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
806 + D e f i n e R e g i o n %
810 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
812 % DefineRegion() defines the left and right boundaries of a peak region.
814 % The format of the DefineRegion method is:
816 % ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
818 % A description of each parameter follows.
820 % o extrema: Specifies a pointer to an array of integers. They
821 % represent the peaks and valleys of the histogram for each color
824 % o extents: This pointer to an ExtentPacket represent the extends
825 % of a particular peak or valley of a color component.
828 static ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
831 Initialize to default values.
837 Find the left side (maxima).
839 for ( ; extents->index <= 255; extents->index++)
840 if (extrema[extents->index] > 0)
842 if (extents->index > 255)
843 return(MagickFalse); /* no left side - no region exists */
844 extents->left=extents->index;
846 Find the right side (minima).
848 for ( ; extents->index <= 255; extents->index++)
849 if (extrema[extents->index] < 0)
851 extents->right=extents->index-1;
856 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
860 + D e r i v a t i v e H i s t o g r a m %
864 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
866 % DerivativeHistogram() determines the derivative of the histogram using
867 % central differencing.
869 % The format of the DerivativeHistogram method is:
871 % DerivativeHistogram(const MagickRealType *histogram,
872 % MagickRealType *derivative)
874 % A description of each parameter follows.
876 % o histogram: Specifies an array of MagickRealTypes representing the number
877 % of pixels for each intensity of a particular color component.
879 % o derivative: This array of MagickRealTypes is initialized by
880 % DerivativeHistogram to the derivative of the histogram using central
884 static void DerivativeHistogram(const MagickRealType *histogram,
885 MagickRealType *derivative)
892 Compute endpoints using second order polynomial interpolation.
895 derivative[0]=(-1.5*histogram[0]+2.0*histogram[1]-0.5*histogram[2]);
896 derivative[n]=(0.5*histogram[n-2]-2.0*histogram[n-1]+1.5*histogram[n]);
898 Compute derivative using central differencing.
900 for (i=1; i < n; i++)
901 derivative[i]=(histogram[i+1]-histogram[i-1])/2.0;
906 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
910 + G e t I m a g e D y n a m i c T h r e s h o l d %
914 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
916 % GetImageDynamicThreshold() returns the dynamic threshold for an image.
918 % The format of the GetImageDynamicThreshold method is:
920 % MagickBooleanType GetImageDynamicThreshold(const Image *image,
921 % const double cluster_threshold,const double smooth_threshold,
922 % MagickPixelPacket *pixel,ExceptionInfo *exception)
924 % A description of each parameter follows.
926 % o image: the image.
928 % o cluster_threshold: This MagickRealType represents the minimum number of
929 % pixels contained in a hexahedra before it can be considered valid
930 % (expressed as a percentage).
932 % o smooth_threshold: the smoothing threshold eliminates noise in the second
933 % derivative of the histogram. As the value is increased, you can expect a
934 % smoother second derivative.
936 % o pixel: return the dynamic threshold here.
938 % o exception: return any errors or warnings in this structure.
941 MagickExport MagickBooleanType GetImageDynamicThreshold(const Image *image,
942 const double cluster_threshold,const double smooth_threshold,
943 MagickPixelPacket *pixel,ExceptionInfo *exception)
960 *histogram[MaxDimension],
969 register const PixelPacket
977 *extrema[MaxDimension];
980 Allocate histogram and extrema.
982 assert(image != (Image *) NULL);
983 assert(image->signature == MagickSignature);
984 if (image->debug != MagickFalse)
985 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
986 GetMagickPixelPacket(image,pixel);
987 for (i=0; i < MaxDimension; i++)
989 histogram[i]=(ssize_t *) AcquireQuantumMemory(256UL,sizeof(**histogram));
990 extrema[i]=(short *) AcquireQuantumMemory(256UL,sizeof(**histogram));
991 if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
993 for (i-- ; i >= 0; i--)
995 extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
996 histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
998 (void) ThrowMagickException(exception,GetMagickModule(),
999 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
1000 return(MagickFalse);
1004 Initialize histogram.
1006 InitializeHistogram(image,histogram,exception);
1007 (void) OptimalTau(histogram[Red],Tau,0.2f,DeltaTau,
1008 (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Red]);
1009 (void) OptimalTau(histogram[Green],Tau,0.2f,DeltaTau,
1010 (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Green]);
1011 (void) OptimalTau(histogram[Blue],Tau,0.2f,DeltaTau,
1012 (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Blue]);
1016 cluster=(Cluster *) NULL;
1017 head=(Cluster *) NULL;
1018 (void) ResetMagickMemory(&red,0,sizeof(red));
1019 (void) ResetMagickMemory(&green,0,sizeof(green));
1020 (void) ResetMagickMemory(&blue,0,sizeof(blue));
1021 while (DefineRegion(extrema[Red],&red) != 0)
1024 while (DefineRegion(extrema[Green],&green) != 0)
1027 while (DefineRegion(extrema[Blue],&blue) != 0)
1030 Allocate a new class.
1032 if (head != (Cluster *) NULL)
1034 cluster->next=(Cluster *) AcquireMagickMemory(
1035 sizeof(*cluster->next));
1036 cluster=cluster->next;
1040 cluster=(Cluster *) AcquireAlignedMemory(1,sizeof(*cluster));
1043 if (cluster == (Cluster *) NULL)
1045 (void) ThrowMagickException(exception,GetMagickModule(),
1046 ResourceLimitError,"MemoryAllocationFailed","`%s'",
1048 return(MagickFalse);
1051 Initialize a new class.
1055 cluster->green=green;
1057 cluster->next=(Cluster *) NULL;
1061 if (head == (Cluster *) NULL)
1064 No classes were identified-- create one.
1066 cluster=(Cluster *) AcquireAlignedMemory(1,sizeof(*cluster));
1067 if (cluster == (Cluster *) NULL)
1069 (void) ThrowMagickException(exception,GetMagickModule(),
1070 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
1071 return(MagickFalse);
1074 Initialize a new class.
1078 cluster->green=green;
1080 cluster->next=(Cluster *) NULL;
1084 Count the pixels for each cluster.
1087 for (y=0; y < (ssize_t) image->rows; y++)
1089 p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1090 if (p == (const PixelPacket *) NULL)
1092 for (x=0; x < (ssize_t) image->columns; x++)
1094 for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
1095 if (((ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p)) >=
1096 (cluster->red.left-SafeMargin)) &&
1097 ((ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p)) <=
1098 (cluster->red.right+SafeMargin)) &&
1099 ((ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p)) >=
1100 (cluster->green.left-SafeMargin)) &&
1101 ((ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p)) <=
1102 (cluster->green.right+SafeMargin)) &&
1103 ((ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p)) >=
1104 (cluster->blue.left-SafeMargin)) &&
1105 ((ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p)) <=
1106 (cluster->blue.right+SafeMargin)))
1112 cluster->red.center+=(MagickRealType)
1113 ScaleQuantumToChar(GetRedPixelComponent(p));
1114 cluster->green.center+=(MagickRealType)
1115 ScaleQuantumToChar(GetGreenPixelComponent(p));
1116 cluster->blue.center+=(MagickRealType)
1117 ScaleQuantumToChar(GetBluePixelComponent(p));
1123 proceed=SetImageProgress(image,SegmentImageTag,y,2*image->rows);
1124 if (proceed == MagickFalse)
1128 Remove clusters that do not meet minimum cluster threshold.
1133 for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1135 next_cluster=cluster->next;
1136 if ((cluster->count > 0) &&
1137 (cluster->count >= (count*cluster_threshold/100.0)))
1143 cluster->red.center/=cluster->count;
1144 cluster->green.center/=cluster->count;
1145 cluster->blue.center/=cluster->count;
1147 last_cluster=cluster;
1153 if (cluster == head)
1156 last_cluster->next=next_cluster;
1157 cluster=(Cluster *) RelinquishMagickMemory(cluster);
1164 for (cluster=object; cluster->next != (Cluster *) NULL; )
1166 if (cluster->count < object->count)
1168 cluster=cluster->next;
1170 background=head->next;
1171 for (cluster=background; cluster->next != (Cluster *) NULL; )
1173 if (cluster->count > background->count)
1175 cluster=cluster->next;
1178 threshold=(background->red.center+object->red.center)/2.0;
1179 pixel->red=(MagickRealType) ScaleCharToQuantum((unsigned char)
1181 threshold=(background->green.center+object->green.center)/2.0;
1182 pixel->green=(MagickRealType) ScaleCharToQuantum((unsigned char)
1184 threshold=(background->blue.center+object->blue.center)/2.0;
1185 pixel->blue=(MagickRealType) ScaleCharToQuantum((unsigned char)
1188 Relinquish resources.
1190 for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1192 next_cluster=cluster->next;
1193 cluster=(Cluster *) RelinquishMagickMemory(cluster);
1195 for (i=0; i < MaxDimension; i++)
1197 extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1198 histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1204 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1208 + I n i t i a l i z e H i s t o g r a m %
1212 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1214 % InitializeHistogram() computes the histogram for an image.
1216 % The format of the InitializeHistogram method is:
1218 % InitializeHistogram(const Image *image,ssize_t **histogram)
1220 % A description of each parameter follows.
1222 % o image: Specifies a pointer to an Image structure; returned from
1225 % o histogram: Specifies an array of integers representing the number
1226 % of pixels for each intensity of a particular color component.
1229 static void InitializeHistogram(const Image *image,ssize_t **histogram,
1230 ExceptionInfo *exception)
1235 register const PixelPacket
1243 Initialize histogram.
1245 for (i=0; i <= 255; i++)
1247 histogram[Red][i]=0;
1248 histogram[Green][i]=0;
1249 histogram[Blue][i]=0;
1251 for (y=0; y < (ssize_t) image->rows; y++)
1253 p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1254 if (p == (const PixelPacket *) NULL)
1256 for (x=0; x < (ssize_t) image->columns; x++)
1258 histogram[Red][(ssize_t) ScaleQuantumToChar(GetRedPixelComponent(p))]++;
1259 histogram[Green][(ssize_t) ScaleQuantumToChar(GetGreenPixelComponent(p))]++;
1260 histogram[Blue][(ssize_t) ScaleQuantumToChar(GetBluePixelComponent(p))]++;
1267 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1271 + I n i t i a l i z e I n t e r v a l T r e e %
1275 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1277 % InitializeIntervalTree() initializes an interval tree from the lists of
1280 % The format of the InitializeIntervalTree method is:
1282 % InitializeIntervalTree(IntervalTree **list,ssize_t *number_nodes,
1283 % IntervalTree *node)
1285 % A description of each parameter follows.
1287 % o zero_crossing: Specifies an array of structures of type ZeroCrossing.
1289 % o number_crossings: This size_t specifies the number of elements
1290 % in the zero_crossing array.
1294 static void InitializeList(IntervalTree **list,ssize_t *number_nodes,
1297 if (node == (IntervalTree *) NULL)
1299 if (node->child == (IntervalTree *) NULL)
1300 list[(*number_nodes)++]=node;
1301 InitializeList(list,number_nodes,node->sibling);
1302 InitializeList(list,number_nodes,node->child);
1305 static void MeanStability(IntervalTree *node)
1307 register IntervalTree
1310 if (node == (IntervalTree *) NULL)
1312 node->mean_stability=0.0;
1314 if (child != (IntervalTree *) NULL)
1319 register MagickRealType
1324 for ( ; child != (IntervalTree *) NULL; child=child->sibling)
1326 sum+=child->stability;
1329 node->mean_stability=sum/(MagickRealType) count;
1331 MeanStability(node->sibling);
1332 MeanStability(node->child);
1335 static void Stability(IntervalTree *node)
1337 if (node == (IntervalTree *) NULL)
1339 if (node->child == (IntervalTree *) NULL)
1340 node->stability=0.0;
1342 node->stability=node->tau-(node->child)->tau;
1343 Stability(node->sibling);
1344 Stability(node->child);
1347 static IntervalTree *InitializeIntervalTree(const ZeroCrossing *zero_crossing,
1348 const size_t number_crossings)
1366 Allocate interval tree.
1368 list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1370 if (list == (IntervalTree **) NULL)
1371 return((IntervalTree *) NULL);
1373 The root is the entire histogram.
1375 root=(IntervalTree *) AcquireAlignedMemory(1,sizeof(*root));
1376 root->child=(IntervalTree *) NULL;
1377 root->sibling=(IntervalTree *) NULL;
1381 for (i=(-1); i < (ssize_t) number_crossings; i++)
1384 Initialize list with all nodes with no children.
1387 InitializeList(list,&number_nodes,root);
1391 for (j=0; j < number_nodes; j++)
1396 for (k=head->left+1; k < head->right; k++)
1398 if (zero_crossing[i+1].crossings[k] != 0)
1402 node->child=(IntervalTree *) AcquireMagickMemory(
1403 sizeof(*node->child));
1408 node->sibling=(IntervalTree *) AcquireMagickMemory(
1409 sizeof(*node->sibling));
1412 node->tau=zero_crossing[i+1].tau;
1413 node->child=(IntervalTree *) NULL;
1414 node->sibling=(IntervalTree *) NULL;
1420 if (left != head->left)
1422 node->sibling=(IntervalTree *) AcquireMagickMemory(
1423 sizeof(*node->sibling));
1425 node->tau=zero_crossing[i+1].tau;
1426 node->child=(IntervalTree *) NULL;
1427 node->sibling=(IntervalTree *) NULL;
1429 node->right=head->right;
1434 Determine the stability: difference between a nodes tau and its child.
1436 Stability(root->child);
1437 MeanStability(root->child);
1438 list=(IntervalTree **) RelinquishMagickMemory(list);
1443 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1447 + O p t i m a l T a u %
1451 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1453 % OptimalTau() finds the optimal tau for each band of the histogram.
1455 % The format of the OptimalTau method is:
1457 % MagickRealType OptimalTau(const ssize_t *histogram,const double max_tau,
1458 % const double min_tau,const double delta_tau,
1459 % const double smooth_threshold,short *extrema)
1461 % A description of each parameter follows.
1463 % o histogram: Specifies an array of integers representing the number
1464 % of pixels for each intensity of a particular color component.
1466 % o extrema: Specifies a pointer to an array of integers. They
1467 % represent the peaks and valleys of the histogram for each color
1472 static void ActiveNodes(IntervalTree **list,ssize_t *number_nodes,
1475 if (node == (IntervalTree *) NULL)
1477 if (node->stability >= node->mean_stability)
1479 list[(*number_nodes)++]=node;
1480 ActiveNodes(list,number_nodes,node->sibling);
1484 ActiveNodes(list,number_nodes,node->sibling);
1485 ActiveNodes(list,number_nodes,node->child);
1489 static void FreeNodes(IntervalTree *node)
1491 if (node == (IntervalTree *) NULL)
1493 FreeNodes(node->sibling);
1494 FreeNodes(node->child);
1495 node=(IntervalTree *) RelinquishMagickMemory(node);
1498 static MagickRealType OptimalTau(const ssize_t *histogram,const double max_tau,
1499 const double min_tau,const double delta_tau,const double smooth_threshold,
1535 Allocate interval tree.
1537 list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1539 if (list == (IntervalTree **) NULL)
1542 Allocate zero crossing list.
1544 count=(size_t) ((max_tau-min_tau)/delta_tau)+2;
1545 zero_crossing=(ZeroCrossing *) AcquireQuantumMemory((size_t) count,
1546 sizeof(*zero_crossing));
1547 if (zero_crossing == (ZeroCrossing *) NULL)
1549 for (i=0; i < (ssize_t) count; i++)
1550 zero_crossing[i].tau=(-1.0);
1552 Initialize zero crossing list.
1554 derivative=(MagickRealType *) AcquireQuantumMemory(256,sizeof(*derivative));
1555 second_derivative=(MagickRealType *) AcquireQuantumMemory(256,
1556 sizeof(*second_derivative));
1557 if ((derivative == (MagickRealType *) NULL) ||
1558 (second_derivative == (MagickRealType *) NULL))
1559 ThrowFatalException(ResourceLimitFatalError,
1560 "UnableToAllocateDerivatives");
1562 for (tau=max_tau; tau >= min_tau; tau-=delta_tau)
1564 zero_crossing[i].tau=tau;
1565 ScaleSpace(histogram,tau,zero_crossing[i].histogram);
1566 DerivativeHistogram(zero_crossing[i].histogram,derivative);
1567 DerivativeHistogram(derivative,second_derivative);
1568 ZeroCrossHistogram(second_derivative,smooth_threshold,
1569 zero_crossing[i].crossings);
1573 Add an entry for the original histogram.
1575 zero_crossing[i].tau=0.0;
1576 for (j=0; j <= 255; j++)
1577 zero_crossing[i].histogram[j]=(MagickRealType) histogram[j];
1578 DerivativeHistogram(zero_crossing[i].histogram,derivative);
1579 DerivativeHistogram(derivative,second_derivative);
1580 ZeroCrossHistogram(second_derivative,smooth_threshold,
1581 zero_crossing[i].crossings);
1582 number_crossings=(size_t) i;
1583 derivative=(MagickRealType *) RelinquishMagickMemory(derivative);
1584 second_derivative=(MagickRealType *)
1585 RelinquishMagickMemory(second_derivative);
1587 Ensure the scale-space fingerprints form lines in scale-space, not loops.
1589 ConsolidateCrossings(zero_crossing,number_crossings);
1591 Force endpoints to be included in the interval.
1593 for (i=0; i <= (ssize_t) number_crossings; i++)
1595 for (j=0; j < 255; j++)
1596 if (zero_crossing[i].crossings[j] != 0)
1598 zero_crossing[i].crossings[0]=(-zero_crossing[i].crossings[j]);
1599 for (j=255; j > 0; j--)
1600 if (zero_crossing[i].crossings[j] != 0)
1602 zero_crossing[i].crossings[255]=(-zero_crossing[i].crossings[j]);
1605 Initialize interval tree.
1607 root=InitializeIntervalTree(zero_crossing,number_crossings);
1608 if (root == (IntervalTree *) NULL)
1611 Find active nodes: stability is greater (or equal) to the mean stability of
1615 ActiveNodes(list,&number_nodes,root->child);
1619 for (i=0; i <= 255; i++)
1621 for (i=0; i < number_nodes; i++)
1624 Find this tau in zero crossings list.
1628 for (j=0; j <= (ssize_t) number_crossings; j++)
1629 if (zero_crossing[j].tau == node->tau)
1632 Find the value of the peak.
1634 peak=zero_crossing[k].crossings[node->right] == -1 ? MagickTrue :
1637 value=zero_crossing[k].histogram[index];
1638 for (x=node->left; x <= node->right; x++)
1640 if (peak != MagickFalse)
1642 if (zero_crossing[k].histogram[x] > value)
1644 value=zero_crossing[k].histogram[x];
1649 if (zero_crossing[k].histogram[x] < value)
1651 value=zero_crossing[k].histogram[x];
1655 for (x=node->left; x <= node->right; x++)
1659 if (peak != MagickFalse)
1660 extrema[x]=(short) index;
1662 extrema[x]=(short) (-index);
1666 Determine the average tau.
1669 for (i=0; i < number_nodes; i++)
1670 average_tau+=list[i]->tau;
1671 average_tau/=(MagickRealType) number_nodes;
1673 Relinquish resources.
1676 zero_crossing=(ZeroCrossing *) RelinquishMagickMemory(zero_crossing);
1677 list=(IntervalTree **) RelinquishMagickMemory(list);
1678 return(average_tau);
1682 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1686 + S c a l e S p a c e %
1690 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1692 % ScaleSpace() performs a scale-space filter on the 1D histogram.
1694 % The format of the ScaleSpace method is:
1696 % ScaleSpace(const ssize_t *histogram,const MagickRealType tau,
1697 % MagickRealType *scale_histogram)
1699 % A description of each parameter follows.
1701 % o histogram: Specifies an array of MagickRealTypes representing the number
1702 % of pixels for each intensity of a particular color component.
1706 static void ScaleSpace(const ssize_t *histogram,const MagickRealType tau,
1707 MagickRealType *scale_histogram)
1719 gamma=(MagickRealType *) AcquireQuantumMemory(256,sizeof(*gamma));
1720 if (gamma == (MagickRealType *) NULL)
1721 ThrowFatalException(ResourceLimitFatalError,
1722 "UnableToAllocateGammaMap");
1723 alpha=1.0/(tau*sqrt(2.0*MagickPI));
1724 beta=(-1.0/(2.0*tau*tau));
1725 for (x=0; x <= 255; x++)
1727 for (x=0; x <= 255; x++)
1729 gamma[x]=exp((double) beta*x*x);
1730 if (gamma[x] < MagickEpsilon)
1733 for (x=0; x <= 255; x++)
1736 for (u=0; u <= 255; u++)
1737 sum+=(MagickRealType) histogram[u]*gamma[MagickAbsoluteValue(x-u)];
1738 scale_histogram[x]=alpha*sum;
1740 gamma=(MagickRealType *) RelinquishMagickMemory(gamma);
1744 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1748 % S e g m e n t I m a g e %
1752 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1754 % SegmentImage() segment an image by analyzing the histograms of the color
1755 % components and identifying units that are homogeneous with the fuzzy
1756 % C-means technique.
1758 % The format of the SegmentImage method is:
1760 % MagickBooleanType SegmentImage(Image *image,
1761 % const ColorspaceType colorspace,const MagickBooleanType verbose,
1762 % const double cluster_threshold,const double smooth_threshold)
1764 % A description of each parameter follows.
1766 % o image: the image.
1768 % o colorspace: Indicate the colorspace.
1770 % o verbose: Set to MagickTrue to print detailed information about the
1771 % identified classes.
1773 % o cluster_threshold: This represents the minimum number of pixels
1774 % contained in a hexahedra before it can be considered valid (expressed
1777 % o smooth_threshold: the smoothing threshold eliminates noise in the second
1778 % derivative of the histogram. As the value is increased, you can expect a
1779 % smoother second derivative.
1782 MagickExport MagickBooleanType SegmentImage(Image *image,
1783 const ColorspaceType colorspace,const MagickBooleanType verbose,
1784 const double cluster_threshold,const double smooth_threshold)
1787 *histogram[MaxDimension];
1796 *extrema[MaxDimension];
1799 Allocate histogram and extrema.
1801 assert(image != (Image *) NULL);
1802 assert(image->signature == MagickSignature);
1803 if (image->debug != MagickFalse)
1804 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1805 for (i=0; i < MaxDimension; i++)
1807 histogram[i]=(ssize_t *) AcquireQuantumMemory(256,sizeof(**histogram));
1808 extrema[i]=(short *) AcquireQuantumMemory(256,sizeof(**extrema));
1809 if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
1811 for (i-- ; i >= 0; i--)
1813 extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1814 histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1816 ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
1820 if (colorspace != RGBColorspace)
1821 (void) TransformImageColorspace(image,colorspace);
1823 Initialize histogram.
1825 InitializeHistogram(image,histogram,&image->exception);
1826 (void) OptimalTau(histogram[Red],Tau,0.2,DeltaTau,
1827 smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Red]);
1828 (void) OptimalTau(histogram[Green],Tau,0.2,DeltaTau,
1829 smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Green]);
1830 (void) OptimalTau(histogram[Blue],Tau,0.2,DeltaTau,
1831 smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Blue]);
1833 Classify using the fuzzy c-Means technique.
1835 status=Classify(image,extrema,cluster_threshold,WeightingExponent,verbose);
1836 if (colorspace != RGBColorspace)
1837 (void) TransformImageColorspace(image,colorspace);
1839 Relinquish resources.
1841 for (i=0; i < MaxDimension; i++)
1843 extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1844 histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1850 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1854 + Z e r o C r o s s H i s t o g r a m %
1858 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1860 % ZeroCrossHistogram() find the zero crossings in a histogram and marks
1861 % directions as: 1 is negative to positive; 0 is zero crossing; and -1
1862 % is positive to negative.
1864 % The format of the ZeroCrossHistogram method is:
1866 % ZeroCrossHistogram(MagickRealType *second_derivative,
1867 % const MagickRealType smooth_threshold,short *crossings)
1869 % A description of each parameter follows.
1871 % o second_derivative: Specifies an array of MagickRealTypes representing the
1872 % second derivative of the histogram of a particular color component.
1874 % o crossings: This array of integers is initialized with
1875 % -1, 0, or 1 representing the slope of the first derivative of the
1876 % of a particular color component.
1879 static void ZeroCrossHistogram(MagickRealType *second_derivative,
1880 const MagickRealType smooth_threshold,short *crossings)
1889 Merge low numbers to zero to help prevent noise.
1891 for (i=0; i <= 255; i++)
1892 if ((second_derivative[i] < smooth_threshold) &&
1893 (second_derivative[i] >= -smooth_threshold))
1894 second_derivative[i]=0.0;
1896 Mark zero crossings.
1899 for (i=0; i <= 255; i++)
1902 if (second_derivative[i] < 0.0)
1909 if (second_derivative[i] > 0.0)