granicus.if.org Git - imagemagick/blob - magick/segment.c

   1 /*
   2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   3 %                                                                             %
   4 %                                                                             %
   5 %                                                                             %
   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                 %
  11 %                                                                             %
  12 %                                                                             %
  13 %    MagickCore Methods to Segment an Image with Thresholding Fuzzy c-Means   %
  14 %                                                                             %
  15 %                              Software Design                                %
  16 %                                John Cristy                                  %
  17 %                                April 1993                                   %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2009 ImageMagick Studio LLC, a non-profit organization      %
  21 %  dedicated to making software imaging solutions freely available.           %
  22 %                                                                             %
  23 %  You may not use this file except in compliance with the License.  You may  %
  24 %  obtain a copy of the License at                                            %
  25 %                                                                             %
  26 %    http://www.imagemagick.org/script/license.php                            %
  27 %                                                                             %
  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.                                             %
  33 %                                                                             %
  34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  35 %
  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.
  45 %
  46 %  The fuzzy c-Means algorithm can be summarized as follows:
  47 %
  48 %    o Build a histogram, one for each color component of the image.
  49 %
  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
  54 %      predominant.
  55 %
  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
  60 %      class number.
  61 %
  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
  65 %      phase.
  66 %
  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.
  71 %
  72 %  Segment is strongly based on software written by Andy Gallo,
  73 %  University of Delaware.
  74 %
  75 %  The following reference was used in creating this program:
  76 %
  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
  80 %    935-952, 1990.
  81 %
  82 %
  83 */
  84 \f
  85 #include "magick/studio.h"
  86 #include "magick/cache.h"
  87 #include "magick/color.h"
  88 #include "magick/colorspace.h"
  89 #include "magick/exception.h"
  90 #include "magick/exception-private.h"
  91 #include "magick/image.h"
  92 #include "magick/image-private.h"
  93 #include "magick/memory_.h"
  94 #include "magick/monitor.h"
  95 #include "magick/monitor-private.h"
  96 #include "magick/quantize.h"
  97 #include "magick/quantum.h"
  98 #include "magick/quantum-private.h"
  99 #include "magick/segment.h"
 100 #include "magick/string_.h"
 101 \f
 102 /*
 103   Define declarations.
 104 */
 105 #define MaxDimension  3
 106 #define DeltaTau  0.5f
 107 #if defined(FastClassify)
 108 #define WeightingExponent  2.0
 109 #define SegmentPower(ratio) (ratio)
 110 #else
 111 #define WeightingExponent  2.5
 112 #define SegmentPower(ratio) pow(ratio,(double) (1.0/(weighting_exponent-1.0)));
 113 #endif
 114 #define Tau  5.2f
 115 \f
 116 /*
 117   Typedef declarations.
 118 */
 119 typedef struct _ExtentPacket
 120 {
 121   MagickRealType
 122     center;
 123
 124   long
 125     index,
 126     left,
 127     right;
 128 } ExtentPacket;
 129
 130 typedef struct _Cluster
 131 {
 132   struct _Cluster
 133     *next;
 134
 135   ExtentPacket
 136     red,
 137     green,
 138     blue;
 139
 140   long
 141     count,
 142     id;
 143 } Cluster;
 144
 145 typedef struct _IntervalTree
 146 {
 147   MagickRealType
 148     tau;
 149
 150   long
 151     left,
 152     right;
 153
 154   MagickRealType
 155     mean_stability,
 156     stability;
 157
 158   struct _IntervalTree
 159     *sibling,
 160     *child;
 161 } IntervalTree;
 162
 163 typedef struct _ZeroCrossing
 164 {
 165   MagickRealType
 166     tau,
 167     histogram[256];
 168
 169   short
 170     crossings[256];
 171 } ZeroCrossing;
 172 \f
 173 /*
 174   Constant declarations.
 175 */
 176 static const int
 177   Blue = 2,
 178   Green = 1,
 179   Red = 0,
 180   SafeMargin = 3,
 181   TreeLength = 600;
 182 \f
 183 /*
 184   Method prototypes.
 185 */
 186 static MagickRealType
 187   OptimalTau(const long *,const double,const double,const double,
 188     const double,short *);
 189
 190 static long
 191   DefineRegion(const short *,ExtentPacket *);
 192
 193 static void
 194   InitializeHistogram(const Image *,long **,ExceptionInfo *),
 195   ScaleSpace(const long *,const MagickRealType,MagickRealType *),
 196   ZeroCrossHistogram(MagickRealType *,const MagickRealType,short *);
 197 \f
 198 /*
 199 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 200 %                                                                             %
 201 %                                                                             %
 202 %                                                                             %
 203 +   C l a s s i f y                                                           %
 204 %                                                                             %
 205 %                                                                             %
 206 %                                                                             %
 207 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 208 %
 209 %  Classify() defines one or more classes.  Each pixel is thresholded to
 210 %  determine which class it belongs to.  If the class is not identified it is
 211 %  assigned to the closest class based on the fuzzy c-Means technique.
 212 %
 213 %  The format of the Classify method is:
 214 %
 215 %      MagickBooleanType Classify(Image *image,short **extrema,
 216 %        const MagickRealType cluster_threshold,
 217 %        const MagickRealType weighting_exponent,
 218 %        const MagickBooleanType verbose)
 219 %
 220 %  A description of each parameter follows.
 221 %
 222 %    o image: the image.
 223 %
 224 %    o extrema:  Specifies a pointer to an array of integers.  They
 225 %      represent the peaks and valleys of the histogram for each color
 226 %      component.
 227 %
 228 %    o cluster_threshold:  This MagickRealType represents the minimum number of
 229 %      pixels contained in a hexahedra before it can be considered valid
 230 %      (expressed as a percentage).
 231 %
 232 %    o weighting_exponent: Specifies the membership weighting exponent.
 233 %
 234 %    o verbose:  A value greater than zero prints detailed information about
 235 %      the identified classes.
 236 %
 237 */
 238 static MagickBooleanType Classify(Image *image,short **extrema,
 239   const MagickRealType cluster_threshold,
 240   const MagickRealType weighting_exponent,const MagickBooleanType verbose)
 241 {
 242 #define SegmentImageTag  "Segment/Image"
 243
 244   Cluster
 245     *cluster,
 246     *head,
 247     *last_cluster,
 248     *next_cluster;
 249
 250   ExceptionInfo
 251     *exception;
 252
 253   ExtentPacket
 254     blue,
 255     green,
 256     red;
 257
 258   long
 259     count,
 260     progress,
 261     y;
 262
 263   MagickRealType
 264     *free_squares;
 265
 266   MagickStatusType
 267     status;
 268
 269   register long
 270     i;
 271
 272   register MagickRealType
 273     *squares;
 274
 275   unsigned long
 276     number_clusters;
 277
 278   CacheView
 279     *image_view;
 280
 281   /*
 282     Form clusters.
 283   */
 284   cluster=(Cluster *) NULL;
 285   head=(Cluster *) NULL;
 286   (void) ResetMagickMemory(&red,0,sizeof(red));
 287   (void) ResetMagickMemory(&green,0,sizeof(green));
 288   (void) ResetMagickMemory(&blue,0,sizeof(blue));
 289   while (DefineRegion(extrema[Red],&red) != 0)
 290   {
 291     green.index=0;
 292     while (DefineRegion(extrema[Green],&green) != 0)
 293     {
 294       blue.index=0;
 295       while (DefineRegion(extrema[Blue],&blue) != 0)
 296       {
 297         /*
 298           Allocate a new class.
 299         */
 300         if (head != (Cluster *) NULL)
 301           {
 302             cluster->next=(Cluster *) AcquireMagickMemory(
 303               sizeof(*cluster->next));
 304             cluster=cluster->next;
 305           }
 306         else
 307           {
 308             cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
 309             head=cluster;
 310           }
 311         if (cluster == (Cluster *) NULL)
 312           ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 313             image->filename);
 314         /*
 315           Initialize a new class.
 316         */
 317         cluster->count=0;
 318         cluster->red=red;
 319         cluster->green=green;
 320         cluster->blue=blue;
 321         cluster->next=(Cluster *) NULL;
 322       }
 323     }
 324   }
 325   if (head == (Cluster *) NULL)
 326     {
 327       /*
 328         No classes were identified-- create one.
 329       */
 330       cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
 331       if (cluster == (Cluster *) NULL)
 332         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 333           image->filename);
 334       /*
 335         Initialize a new class.
 336       */
 337       cluster->count=0;
 338       cluster->red=red;
 339       cluster->green=green;
 340       cluster->blue=blue;
 341       cluster->next=(Cluster *) NULL;
 342       head=cluster;
 343     }
 344   /*
 345     Count the pixels for each cluster.
 346   */
 347   status=MagickTrue;
 348   count=0;
 349   progress=0;
 350   exception=(&image->exception);
 351   image_view=AcquireCacheView(image);
 352   for (y=0; y < (long) image->rows; y++)
 353   {
 354     register const PixelPacket
 355       *p;
 356
 357     register long
 358       x;
 359
 360     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 361     if (p == (const PixelPacket *) NULL)
 362       break;
 363     for (x=0; x < (long) image->columns; x++)
 364     {
 365       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 366         if (((long) ScaleQuantumToChar(p->red) >=
 367              (cluster->red.left-SafeMargin)) &&
 368             ((long) ScaleQuantumToChar(p->red) <=
 369              (cluster->red.right+SafeMargin)) &&
 370             ((long) ScaleQuantumToChar(p->green) >=
 371              (cluster->green.left-SafeMargin)) &&
 372             ((long) ScaleQuantumToChar(p->green) <=
 373              (cluster->green.right+SafeMargin)) &&
 374             ((long) ScaleQuantumToChar(p->blue) >=
 375              (cluster->blue.left-SafeMargin)) &&
 376             ((long) ScaleQuantumToChar(p->blue) <=
 377              (cluster->blue.right+SafeMargin)))
 378           {
 379             /*
 380               Count this pixel.
 381             */
 382             count++;
 383             cluster->red.center+=(MagickRealType) ScaleQuantumToChar(p->red);
 384             cluster->green.center+=(MagickRealType)
 385               ScaleQuantumToChar(p->green);
 386             cluster->blue.center+=(MagickRealType) ScaleQuantumToChar(p->blue);
 387             cluster->count++;
 388             break;
 389           }
 390       p++;
 391     }
 392     if (image->progress_monitor != (MagickProgressMonitor) NULL)
 393       {
 394         MagickBooleanType
 395           proceed;
 396
 397 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 398         #pragma omp critical (MagickCore_Classify)
 399 #endif
 400         proceed=SetImageProgress(image,SegmentImageTag,progress++,
 401           2*image->rows);
 402         if (proceed == MagickFalse)
 403           status=MagickFalse;
 404       }
 405   }
 406   image_view=DestroyCacheView(image_view);
 407   /*
 408     Remove clusters that do not meet minimum cluster threshold.
 409   */
 410   count=0;
 411   last_cluster=head;
 412   next_cluster=head;
 413   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
 414   {
 415     next_cluster=cluster->next;
 416     if ((cluster->count > 0) &&
 417         (cluster->count >= (count*cluster_threshold/100.0)))
 418       {
 419         /*
 420           Initialize cluster.
 421         */
 422         cluster->id=count;
 423         cluster->red.center/=cluster->count;
 424         cluster->green.center/=cluster->count;
 425         cluster->blue.center/=cluster->count;
 426         count++;
 427         last_cluster=cluster;
 428         continue;
 429       }
 430     /*
 431       Delete cluster.
 432     */
 433     if (cluster == head)
 434       head=next_cluster;
 435     else
 436       last_cluster->next=next_cluster;
 437     cluster=(Cluster *) RelinquishMagickMemory(cluster);
 438   }
 439   number_clusters=(unsigned long) count;
 440   if (verbose != MagickFalse)
 441     {
 442       /*
 443         Print cluster statistics.
 444       */
 445       (void) fprintf(stdout,"Fuzzy C-means Statistics\n");
 446       (void) fprintf(stdout,"===================\n\n");
 447       (void) fprintf(stdout,"\tCluster Threshold = %g\n",cluster_threshold);
 448       (void) fprintf(stdout,"\tWeighting Exponent = %g\n",weighting_exponent);
 449       (void) fprintf(stdout,"\tTotal Number of Clusters = %lu\n\n",
 450         number_clusters);
 451       /*
 452         Print the total number of points per cluster.
 453       */
 454       (void) fprintf(stdout,"\n\nNumber of Vectors Per Cluster\n");
 455       (void) fprintf(stdout,"=============================\n\n");
 456       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 457         (void) fprintf(stdout,"Cluster #%ld = %ld\n",cluster->id,
 458           cluster->count);
 459       /*
 460         Print the cluster extents.
 461       */
 462       (void) fprintf(stdout,
 463         "\n\n\nCluster Extents:        (Vector Size: %d)\n",MaxDimension);
 464       (void) fprintf(stdout,"================");
 465       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 466       {
 467         (void) fprintf(stdout,"\n\nCluster #%ld\n\n",cluster->id);
 468         (void) fprintf(stdout,"%ld-%ld  %ld-%ld  %ld-%ld\n",cluster->red.left,
 469           cluster->red.right,cluster->green.left,cluster->green.right,
 470           cluster->blue.left,cluster->blue.right);
 471       }
 472       /*
 473         Print the cluster center values.
 474       */
 475       (void) fprintf(stdout,
 476         "\n\n\nCluster Center Values:        (Vector Size: %d)\n",MaxDimension);
 477       (void) fprintf(stdout,"=====================");
 478       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 479       {
 480         (void) fprintf(stdout,"\n\nCluster #%ld\n\n",cluster->id);
 481         (void) fprintf(stdout,"%g  %g  %g\n",(double) cluster->red.center,
 482           (double) cluster->green.center,(double) cluster->blue.center);
 483       }
 484       (void) fprintf(stdout,"\n");
 485     }
 486   if (number_clusters > 256)
 487     ThrowBinaryException(ImageError,"TooManyClusters",image->filename);
 488   /*
 489     Speed up distance calculations.
 490   */
 491   squares=(MagickRealType *) AcquireQuantumMemory(513UL,sizeof(*squares));
 492   if (squares == (MagickRealType *) NULL)
 493     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 494       image->filename);
 495   squares+=255;
 496   for (i=(-255); i <= 255; i++)
 497     squares[i]=(MagickRealType) i*(MagickRealType) i;
 498   /*
 499     Allocate image colormap.
 500   */
 501   if (AcquireImageColormap(image,number_clusters) == MagickFalse)
 502     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 503       image->filename);
 504   i=0;
 505   for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 506   {
 507     image->colormap[i].red=ScaleCharToQuantum((unsigned char)
 508       (cluster->red.center+0.5));
 509     image->colormap[i].green=ScaleCharToQuantum((unsigned char)
 510       (cluster->green.center+0.5));
 511     image->colormap[i].blue=ScaleCharToQuantum((unsigned char)
 512       (cluster->blue.center+0.5));
 513     i++;
 514   }
 515   /*
 516     Do course grain classes.
 517   */
 518   exception=(&image->exception);
 519   image_view=AcquireCacheView(image);
 520 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 521   #pragma omp parallel for schedule(dynamic,8) shared(progress,status)
 522 #endif
 523   for (y=0; y < (long) image->rows; y++)
 524   {
 525     Cluster
 526       *cluster;
 527
 528     register const PixelPacket
 529       *__restrict p;
 530
 531     register IndexPacket
 532       *__restrict indexes;
 533
 534     register long
 535       x;
 536
 537     register PixelPacket
 538       *__restrict q;
 539
 540     if (status == MagickFalse)
 541       continue;
 542     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
 543     if (q == (PixelPacket *) NULL)
 544       {
 545         status=MagickFalse;
 546         continue;
 547       }
 548     indexes=GetCacheViewAuthenticIndexQueue(image_view);
 549     for (x=0; x < (long) image->columns; x++)
 550     {
 551       indexes[x]=(IndexPacket) 0;
 552       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 553       {
 554         if (((long) ScaleQuantumToChar(q->red) >=
 555              (cluster->red.left-SafeMargin)) &&
 556             ((long) ScaleQuantumToChar(q->red) <=
 557              (cluster->red.right+SafeMargin)) &&
 558             ((long) ScaleQuantumToChar(q->green) >=
 559              (cluster->green.left-SafeMargin)) &&
 560             ((long) ScaleQuantumToChar(q->green) <=
 561              (cluster->green.right+SafeMargin)) &&
 562             ((long) ScaleQuantumToChar(q->blue) >=
 563              (cluster->blue.left-SafeMargin)) &&
 564             ((long) ScaleQuantumToChar(q->blue) <=
 565              (cluster->blue.right+SafeMargin)))
 566           {
 567             /*
 568               Classify this pixel.
 569             */
 570             indexes[x]=(IndexPacket) cluster->id;
 571             break;
 572           }
 573       }
 574       if (cluster == (Cluster *) NULL)
 575         {
 576           MagickRealType
 577             distance_squared,
 578             local_minima,
 579             numerator,
 580             ratio,
 581             sum;
 582
 583           register long
 584             j,
 585             k;
 586
 587           /*
 588             Compute fuzzy membership.
 589           */
 590           local_minima=0.0;
 591           for (j=0; j < (long) image->colors; j++)
 592           {
 593             sum=0.0;
 594             p=image->colormap+j;
 595             distance_squared=squares[(long) ScaleQuantumToChar(q->red)-
 596               (long) ScaleQuantumToChar(p->red)]+
 597               squares[(long) ScaleQuantumToChar(q->green)-
 598               (long) ScaleQuantumToChar(p->green)]+
 599               squares[(long) ScaleQuantumToChar(q->blue)-
 600               (long) ScaleQuantumToChar(p->blue)];
 601             numerator=distance_squared;
 602             for (k=0; k < (long) image->colors; k++)
 603             {
 604               p=image->colormap+k;
 605               distance_squared=squares[(long) ScaleQuantumToChar(q->red)-
 606                 (long) ScaleQuantumToChar(p->red)]+
 607                 squares[(long) ScaleQuantumToChar(q->green)-
 608                 (long) ScaleQuantumToChar(p->green)]+
 609                 squares[(long) ScaleQuantumToChar(q->blue)-
 610                 (long) ScaleQuantumToChar(p->blue)];
 611               ratio=numerator/distance_squared;
 612               sum+=SegmentPower(ratio);
 613             }
 614             if ((sum != 0.0) && ((1.0/sum) > local_minima))
 615               {
 616                 /*
 617                   Classify this pixel.
 618                 */
 619                 local_minima=1.0/sum;
 620                 indexes[x]=(IndexPacket) j;
 621               }
 622           }
 623         }
 624       q++;
 625     }
 626     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 627       status=MagickFalse;
 628     if (image->progress_monitor != (MagickProgressMonitor) NULL)
 629       {
 630         MagickBooleanType
 631           proceed;
 632
 633 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 634         #pragma omp critical (MagickCore_Classify)
 635 #endif
 636         proceed=SetImageProgress(image,SegmentImageTag,progress++,
 637           2*image->rows);
 638         if (proceed == MagickFalse)
 639           status=MagickFalse;
 640       }
 641   }
 642   image_view=DestroyCacheView(image_view);
 643   status&=SyncImage(image);
 644   /*
 645     Relinquish resources.
 646   */
 647   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
 648   {
 649     next_cluster=cluster->next;
 650     cluster=(Cluster *) RelinquishMagickMemory(cluster);
 651   }
 652   squares-=255;
 653   free_squares=squares;
 654   free_squares=(MagickRealType *) RelinquishMagickMemory(free_squares);
 655   return(MagickTrue);
 656 }
 657 \f
 658 /*
 659 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 660 %                                                                             %
 661 %                                                                             %
 662 %                                                                             %
 663 +   C o n s o l i d a t e C r o s s i n g s                                   %
 664 %                                                                             %
 665 %                                                                             %
 666 %                                                                             %
 667 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 668 %
 669 %  ConsolidateCrossings() guarantees that an even number of zero crossings
 670 %  always lie between two crossings.
 671 %
 672 %  The format of the ConsolidateCrossings method is:
 673 %
 674 %      ConsolidateCrossings(ZeroCrossing *zero_crossing,
 675 %        const unsigned long number_crossings)
 676 %
 677 %  A description of each parameter follows.
 678 %
 679 %    o zero_crossing: Specifies an array of structures of type ZeroCrossing.
 680 %
 681 %    o number_crossings: This unsigned long specifies the number of elements
 682 %      in the zero_crossing array.
 683 %
 684 */
 685
 686 static inline long MagickAbsoluteValue(const long x)
 687 {
 688   if (x < 0)
 689     return(-x);
 690   return(x);
 691 }
 692
 693 static inline long MagickMax(const long x,const long y)
 694 {
 695   if (x > y)
 696     return(x);
 697   return(y);
 698 }
 699
 700 static inline long MagickMin(const long x,const long y)
 701 {
 702   if (x < y)
 703     return(x);
 704   return(y);
 705 }
 706
 707 static void ConsolidateCrossings(ZeroCrossing *zero_crossing,
 708   const unsigned long number_crossings)
 709 {
 710   long
 711     center,
 712     correct,
 713     count,
 714     left,
 715     right;
 716
 717   register long
 718     i,
 719     j,
 720     k,
 721     l;
 722
 723   /*
 724     Consolidate zero crossings.
 725   */
 726   for (i=(long) number_crossings-1; i >= 0; i--)
 727     for (j=0; j <= 255; j++)
 728     {
 729       if (zero_crossing[i].crossings[j] == 0)
 730         continue;
 731       /*
 732         Find the entry that is closest to j and still preserves the
 733         property that there are an even number of crossings between
 734         intervals.
 735       */
 736       for (k=j-1; k > 0; k--)
 737         if (zero_crossing[i+1].crossings[k] != 0)
 738           break;
 739       left=MagickMax(k,0);
 740       center=j;
 741       for (k=j+1; k < 255; k++)
 742         if (zero_crossing[i+1].crossings[k] != 0)
 743           break;
 744       right=MagickMin(k,255);
 745       /*
 746         K is the zero crossing just left of j.
 747       */
 748       for (k=j-1; k > 0; k--)
 749         if (zero_crossing[i].crossings[k] != 0)
 750           break;
 751       if (k < 0)
 752         k=0;
 753       /*
 754         Check center for an even number of crossings between k and j.
 755       */
 756       correct=(-1);
 757       if (zero_crossing[i+1].crossings[j] != 0)
 758         {
 759           count=0;
 760           for (l=k+1; l < center; l++)
 761             if (zero_crossing[i+1].crossings[l] != 0)
 762               count++;
 763           if (((count % 2) == 0) && (center != k))
 764             correct=center;
 765         }
 766       /*
 767         Check left for an even number of crossings between k and j.
 768       */
 769       if (correct == -1)
 770         {
 771           count=0;
 772           for (l=k+1; l < left; l++)
 773             if (zero_crossing[i+1].crossings[l] != 0)
 774               count++;
 775           if (((count % 2) == 0) && (left != k))
 776             correct=left;
 777         }
 778       /*
 779         Check right for an even number of crossings between k and j.
 780       */
 781       if (correct == -1)
 782         {
 783           count=0;
 784           for (l=k+1; l < right; l++)
 785             if (zero_crossing[i+1].crossings[l] != 0)
 786               count++;
 787           if (((count % 2) == 0) && (right != k))
 788             correct=right;
 789         }
 790       l=zero_crossing[i].crossings[j];
 791       zero_crossing[i].crossings[j]=0;
 792       if (correct != -1)
 793         zero_crossing[i].crossings[correct]=(short) l;
 794     }
 795 }
 796 \f
 797 /*
 798 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 799 %                                                                             %
 800 %                                                                             %
 801 %                                                                             %
 802 +   D e f i n e R e g i o n                                                   %
 803 %                                                                             %
 804 %                                                                             %
 805 %                                                                             %
 806 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 807 %
 808 %  DefineRegion() defines the left and right boundaries of a peak region.
 809 %
 810 %  The format of the DefineRegion method is:
 811 %
 812 %      long DefineRegion(const short *extrema,ExtentPacket *extents)
 813 %
 814 %  A description of each parameter follows.
 815 %
 816 %    o extrema:  Specifies a pointer to an array of integers.  They
 817 %      represent the peaks and valleys of the histogram for each color
 818 %      component.
 819 %
 820 %    o extents:  This pointer to an ExtentPacket represent the extends
 821 %      of a particular peak or valley of a color component.
 822 %
 823 */
 824 static long DefineRegion(const short *extrema,ExtentPacket *extents)
 825 {
 826   /*
 827     Initialize to default values.
 828   */
 829   extents->left=0;
 830   extents->center=0.0;
 831   extents->right=255;
 832   /*
 833     Find the left side (maxima).
 834   */
 835   for ( ; extents->index <= 255; extents->index++)
 836     if (extrema[extents->index] > 0)
 837       break;
 838   if (extents->index > 255)
 839     return(MagickFalse);  /* no left side - no region exists */
 840   extents->left=extents->index;
 841   /*
 842     Find the right side (minima).
 843   */
 844   for ( ; extents->index <= 255; extents->index++)
 845     if (extrema[extents->index] < 0)
 846       break;
 847   extents->right=extents->index-1;
 848   return(MagickTrue);
 849 }
 850 \f
 851 /*
 852 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 853 %                                                                             %
 854 %                                                                             %
 855 %                                                                             %
 856 +   D e r i v a t i v e H i s t o g r a m                                     %
 857 %                                                                             %
 858 %                                                                             %
 859 %                                                                             %
 860 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 861 %
 862 %  DerivativeHistogram() determines the derivative of the histogram using
 863 %  central differencing.
 864 %
 865 %  The format of the DerivativeHistogram method is:
 866 %
 867 %      DerivativeHistogram(const MagickRealType *histogram,
 868 %        MagickRealType *derivative)
 869 %
 870 %  A description of each parameter follows.
 871 %
 872 %    o histogram: Specifies an array of MagickRealTypes representing the number
 873 %      of pixels for each intensity of a particular color component.
 874 %
 875 %    o derivative: This array of MagickRealTypes is initialized by
 876 %      DerivativeHistogram to the derivative of the histogram using central
 877 %      differencing.
 878 %
 879 */
 880 static void DerivativeHistogram(const MagickRealType *histogram,
 881   MagickRealType *derivative)
 882 {
 883   register long
 884     i,
 885     n;
 886
 887   /*
 888     Compute endpoints using second order polynomial interpolation.
 889   */
 890   n=255;
 891   derivative[0]=(-1.5*histogram[0]+2.0*histogram[1]-0.5*histogram[2]);
 892   derivative[n]=(0.5*histogram[n-2]-2.0*histogram[n-1]+1.5*histogram[n]);
 893   /*
 894     Compute derivative using central differencing.
 895   */
 896   for (i=1; i < n; i++)
 897     derivative[i]=(histogram[i+1]-histogram[i-1])/2.0;
 898   return;
 899 }
 900 \f
 901 /*
 902 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 903 %                                                                             %
 904 %                                                                             %
 905 %                                                                             %
 906 +  G e t I m a g e D y n a m i c T h r e s h o l d                            %
 907 %                                                                             %
 908 %                                                                             %
 909 %                                                                             %
 910 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 911 %
 912 %  GetImageDynamicThreshold() returns the dynamic threshold for an image.
 913 %
 914 %  The format of the GetImageDynamicThreshold method is:
 915 %
 916 %      MagickBooleanType GetImageDynamicThreshold(const Image *image,
 917 %        const double cluster_threshold,const double smooth_threshold,
 918 %        MagickPixelPacket *pixel,ExceptionInfo *exception)
 919 %
 920 %  A description of each parameter follows.
 921 %
 922 %    o image: the image.
 923 %
 924 %    o cluster_threshold:  This MagickRealType represents the minimum number of
 925 %      pixels contained in a hexahedra before it can be considered valid
 926 %      (expressed as a percentage).
 927 %
 928 %    o smooth_threshold: the smoothing threshold eliminates noise in the second
 929 %      derivative of the histogram.  As the value is increased, you can expect a
 930 %      smoother second derivative.
 931 %
 932 %    o pixel: return the dynamic threshold here.
 933 %
 934 %    o exception: return any errors or warnings in this structure.
 935 %
 936 */
 937 MagickExport MagickBooleanType GetImageDynamicThreshold(const Image *image,
 938   const double cluster_threshold,const double smooth_threshold,
 939   MagickPixelPacket *pixel,ExceptionInfo *exception)
 940 {
 941   Cluster
 942     *background,
 943     *cluster,
 944     *object,
 945     *head,
 946     *last_cluster,
 947     *next_cluster;
 948
 949   ExtentPacket
 950     blue,
 951     green,
 952     red;
 953
 954   long
 955     count,
 956     *histogram[MaxDimension],
 957     y;
 958
 959   MagickBooleanType
 960     proceed;
 961
 962   MagickRealType
 963     threshold;
 964
 965   register const PixelPacket
 966     *p;
 967
 968   register long
 969     i,
 970     x;
 971
 972   short
 973     *extrema[MaxDimension];
 974
 975   /*
 976     Allocate histogram and extrema.
 977   */
 978   assert(image != (Image *) NULL);
 979   assert(image->signature == MagickSignature);
 980   if (image->debug != MagickFalse)
 981     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
 982   GetMagickPixelPacket(image,pixel);
 983   for (i=0; i < MaxDimension; i++)
 984   {
 985     histogram[i]=(long *) AcquireQuantumMemory(256UL,sizeof(**histogram));
 986     extrema[i]=(short *) AcquireQuantumMemory(256UL,sizeof(**histogram));
 987     if ((histogram[i] == (long *) NULL) || (extrema[i] == (short *) NULL))
 988       {
 989         for (i-- ; i >= 0; i--)
 990         {
 991           extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
 992           histogram[i]=(long *) RelinquishMagickMemory(histogram[i]);
 993         }
 994         (void) ThrowMagickException(exception,GetMagickModule(),
 995           ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
 996         return(MagickFalse);
 997       }
 998   }
 999   /*
1000     Initialize histogram.
1001   */
1002   InitializeHistogram(image,histogram,exception);
1003   (void) OptimalTau(histogram[Red],Tau,0.2f,DeltaTau,
1004     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Red]);
1005   (void) OptimalTau(histogram[Green],Tau,0.2f,DeltaTau,
1006     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Green]);
1007   (void) OptimalTau(histogram[Blue],Tau,0.2f,DeltaTau,
1008     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Blue]);
1009   /*
1010     Form clusters.
1011   */
1012   cluster=(Cluster *) NULL;
1013   head=(Cluster *) NULL;
1014   (void) ResetMagickMemory(&red,0,sizeof(red));
1015   (void) ResetMagickMemory(&green,0,sizeof(green));
1016   (void) ResetMagickMemory(&blue,0,sizeof(blue));
1017   while (DefineRegion(extrema[Red],&red) != 0)
1018   {
1019     green.index=0;
1020     while (DefineRegion(extrema[Green],&green) != 0)
1021     {
1022       blue.index=0;
1023       while (DefineRegion(extrema[Blue],&blue) != 0)
1024       {
1025         /*
1026           Allocate a new class.
1027         */
1028         if (head != (Cluster *) NULL)
1029           {
1030             cluster->next=(Cluster *) AcquireMagickMemory(
1031               sizeof(*cluster->next));
1032             cluster=cluster->next;
1033           }
1034         else
1035           {
1036             cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
1037             head=cluster;
1038           }
1039         if (cluster == (Cluster *) NULL)
1040           {
1041             (void) ThrowMagickException(exception,GetMagickModule(),
1042               ResourceLimitError,"MemoryAllocationFailed","`%s'",
1043               image->filename);
1044             return(MagickFalse);
1045           }
1046         /*
1047           Initialize a new class.
1048         */
1049         cluster->count=0;
1050         cluster->red=red;
1051         cluster->green=green;
1052         cluster->blue=blue;
1053         cluster->next=(Cluster *) NULL;
1054       }
1055     }
1056   }
1057   if (head == (Cluster *) NULL)
1058     {
1059       /*
1060         No classes were identified-- create one.
1061       */
1062       cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
1063       if (cluster == (Cluster *) NULL)
1064         {
1065           (void) ThrowMagickException(exception,GetMagickModule(),
1066             ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
1067           return(MagickFalse);
1068         }
1069       /*
1070         Initialize a new class.
1071       */
1072       cluster->count=0;
1073       cluster->red=red;
1074       cluster->green=green;
1075       cluster->blue=blue;
1076       cluster->next=(Cluster *) NULL;
1077       head=cluster;
1078     }
1079   /*
1080     Count the pixels for each cluster.
1081   */
1082   count=0;
1083   for (y=0; y < (long) image->rows; y++)
1084   {
1085     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1086     if (p == (const PixelPacket *) NULL)
1087       break;
1088     for (x=0; x < (long) image->columns; x++)
1089     {
1090       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
1091         if (((long) ScaleQuantumToChar(p->red) >=
1092              (cluster->red.left-SafeMargin)) &&
1093             ((long) ScaleQuantumToChar(p->red) <=
1094              (cluster->red.right+SafeMargin)) &&
1095             ((long) ScaleQuantumToChar(p->green) >=
1096              (cluster->green.left-SafeMargin)) &&
1097             ((long) ScaleQuantumToChar(p->green) <=
1098              (cluster->green.right+SafeMargin)) &&
1099             ((long) ScaleQuantumToChar(p->blue) >=
1100              (cluster->blue.left-SafeMargin)) &&
1101             ((long) ScaleQuantumToChar(p->blue) <=
1102              (cluster->blue.right+SafeMargin)))
1103           {
1104             /*
1105               Count this pixel.
1106             */
1107             count++;
1108             cluster->red.center+=(MagickRealType)
1109               ScaleQuantumToChar(p->red);
1110             cluster->green.center+=(MagickRealType)
1111               ScaleQuantumToChar(p->green);
1112             cluster->blue.center+=(MagickRealType)
1113               ScaleQuantumToChar(p->blue);
1114             cluster->count++;
1115             break;
1116           }
1117       p++;
1118     }
1119     proceed=SetImageProgress(image,SegmentImageTag,y,2*image->rows);
1120     if (proceed == MagickFalse)
1121       break;
1122   }
1123   /*
1124     Remove clusters that do not meet minimum cluster threshold.
1125   */
1126   count=0;
1127   last_cluster=head;
1128   next_cluster=head;
1129   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1130   {
1131     next_cluster=cluster->next;
1132     if ((cluster->count > 0) &&
1133         (cluster->count >= (count*cluster_threshold/100.0)))
1134       {
1135         /*
1136           Initialize cluster.
1137         */
1138         cluster->id=count;
1139         cluster->red.center/=cluster->count;
1140         cluster->green.center/=cluster->count;
1141         cluster->blue.center/=cluster->count;
1142         count++;
1143         last_cluster=cluster;
1144         continue;
1145       }
1146     /*
1147       Delete cluster.
1148     */
1149     if (cluster == head)
1150       head=next_cluster;
1151     else
1152       last_cluster->next=next_cluster;
1153     cluster=(Cluster *) RelinquishMagickMemory(cluster);
1154   }
1155   object=head;
1156   background=head;
1157   if (count > 1)
1158     {
1159       object=head->next;
1160       for (cluster=object; cluster->next != (Cluster *) NULL; )
1161       {
1162         if (cluster->count < object->count)
1163           object=cluster;
1164         cluster=cluster->next;
1165       }
1166       background=head->next;
1167       for (cluster=background; cluster->next != (Cluster *) NULL; )
1168       {
1169         if (cluster->count > background->count)
1170           background=cluster;
1171         cluster=cluster->next;
1172       }
1173     }
1174   threshold=(background->red.center+object->red.center)/2.0;
1175   pixel->red=(MagickRealType) ScaleCharToQuantum((unsigned char)
1176     (threshold+0.5));
1177   threshold=(background->green.center+object->green.center)/2.0;
1178   pixel->green=(MagickRealType) ScaleCharToQuantum((unsigned char)
1179     (threshold+0.5));
1180   threshold=(background->blue.center+object->blue.center)/2.0;
1181   pixel->blue=(MagickRealType) ScaleCharToQuantum((unsigned char)
1182     (threshold+0.5));
1183   /*
1184     Relinquish resources.
1185   */
1186   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1187   {
1188     next_cluster=cluster->next;
1189     cluster=(Cluster *) RelinquishMagickMemory(cluster);
1190   }
1191   for (i=0; i < MaxDimension; i++)
1192   {
1193     extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1194     histogram[i]=(long *) RelinquishMagickMemory(histogram[i]);
1195   }
1196   return(MagickTrue);
1197 }
1198 \f
1199 /*
1200 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1201 %                                                                             %
1202 %                                                                             %
1203 %                                                                             %
1204 +  I n i t i a l i z e H i s t o g r a m                                      %
1205 %                                                                             %
1206 %                                                                             %
1207 %                                                                             %
1208 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1209 %
1210 %  InitializeHistogram() computes the histogram for an image.
1211 %
1212 %  The format of the InitializeHistogram method is:
1213 %
1214 %      InitializeHistogram(const Image *image,long **histogram)
1215 %
1216 %  A description of each parameter follows.
1217 %
1218 %    o image: Specifies a pointer to an Image structure;  returned from
1219 %      ReadImage.
1220 %
1221 %    o histogram: Specifies an array of integers representing the number
1222 %      of pixels for each intensity of a particular color component.
1223 %
1224 */
1225 static void InitializeHistogram(const Image *image,long **histogram,
1226   ExceptionInfo *exception)
1227 {
1228   long
1229     y;
1230
1231   register const PixelPacket
1232     *p;
1233
1234   register long
1235     i,
1236     x;
1237
1238   /*
1239     Initialize histogram.
1240   */
1241   for (i=0; i <= 255; i++)
1242   {
1243     histogram[Red][i]=0;
1244     histogram[Green][i]=0;
1245     histogram[Blue][i]=0;
1246   }
1247   for (y=0; y < (long) image->rows; y++)
1248   {
1249     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1250     if (p == (const PixelPacket *) NULL)
1251       break;
1252     for (x=0; x < (long) image->columns; x++)
1253     {
1254       histogram[Red][(long) ScaleQuantumToChar(p->red)]++;
1255       histogram[Green][(long) ScaleQuantumToChar(p->green)]++;
1256       histogram[Blue][(long) ScaleQuantumToChar(p->blue)]++;
1257       p++;
1258     }
1259   }
1260 }
1261 \f
1262 /*
1263 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1264 %                                                                             %
1265 %                                                                             %
1266 %                                                                             %
1267 +   I n i t i a l i z e I n t e r v a l T r e e                               %
1268 %                                                                             %
1269 %                                                                             %
1270 %                                                                             %
1271 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1272 %
1273 %  InitializeIntervalTree() initializes an interval tree from the lists of
1274 %  zero crossings.
1275 %
1276 %  The format of the InitializeIntervalTree method is:
1277 %
1278 %      InitializeIntervalTree(IntervalTree **list,long *number_nodes,
1279 %        IntervalTree *node)
1280 %
1281 %  A description of each parameter follows.
1282 %
1283 %    o zero_crossing: Specifies an array of structures of type ZeroCrossing.
1284 %
1285 %    o number_crossings: This unsigned long specifies the number of elements
1286 %      in the zero_crossing array.
1287 %
1288 */
1289
1290 static void InitializeList(IntervalTree **list,long *number_nodes,
1291   IntervalTree *node)
1292 {
1293   if (node == (IntervalTree *) NULL)
1294     return;
1295   if (node->child == (IntervalTree *) NULL)
1296     list[(*number_nodes)++]=node;
1297   InitializeList(list,number_nodes,node->sibling);
1298   InitializeList(list,number_nodes,node->child);
1299 }
1300
1301 static void MeanStability(IntervalTree *node)
1302 {
1303   register IntervalTree
1304     *child;
1305
1306   if (node == (IntervalTree *) NULL)
1307     return;
1308   node->mean_stability=0.0;
1309   child=node->child;
1310   if (child != (IntervalTree *) NULL)
1311     {
1312       register long
1313         count;
1314
1315       register MagickRealType
1316         sum;
1317
1318       sum=0.0;
1319       count=0;
1320       for ( ; child != (IntervalTree *) NULL; child=child->sibling)
1321       {
1322         sum+=child->stability;
1323         count++;
1324       }
1325       node->mean_stability=sum/(MagickRealType) count;
1326     }
1327   MeanStability(node->sibling);
1328   MeanStability(node->child);
1329 }
1330
1331 static void Stability(IntervalTree *node)
1332 {
1333   if (node == (IntervalTree *) NULL)
1334     return;
1335   if (node->child == (IntervalTree *) NULL)
1336     node->stability=0.0;
1337   else
1338     node->stability=node->tau-(node->child)->tau;
1339   Stability(node->sibling);
1340   Stability(node->child);
1341 }
1342
1343 static IntervalTree *InitializeIntervalTree(const ZeroCrossing *zero_crossing,
1344   const unsigned long number_crossings)
1345 {
1346   IntervalTree
1347     *head,
1348     **list,
1349     *node,
1350     *root;
1351
1352   long
1353     j,
1354     k,
1355     left,
1356     number_nodes;
1357
1358   register long
1359     i;
1360
1361   /*
1362     Allocate interval tree.
1363   */
1364   list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1365     sizeof(*list));
1366   if (list == (IntervalTree **) NULL)
1367     return((IntervalTree *) NULL);
1368   /*
1369     The root is the entire histogram.
1370   */
1371   root=(IntervalTree *) AcquireMagickMemory(sizeof(*root));
1372   root->child=(IntervalTree *) NULL;
1373   root->sibling=(IntervalTree *) NULL;
1374   root->tau=0.0;
1375   root->left=0;
1376   root->right=255;
1377   for (i=(-1); i < (long) number_crossings; i++)
1378   {
1379     /*
1380       Initialize list with all nodes with no children.
1381     */
1382     number_nodes=0;
1383     InitializeList(list,&number_nodes,root);
1384     /*
1385       Split list.
1386     */
1387     for (j=0; j < number_nodes; j++)
1388     {
1389       head=list[j];
1390       left=head->left;
1391       node=head;
1392       for (k=head->left+1; k < head->right; k++)
1393       {
1394         if (zero_crossing[i+1].crossings[k] != 0)
1395           {
1396             if (node == head)
1397               {
1398                 node->child=(IntervalTree *) AcquireMagickMemory(
1399                   sizeof(*node->child));
1400                 node=node->child;
1401               }
1402             else
1403               {
1404                 node->sibling=(IntervalTree *) AcquireMagickMemory(
1405                   sizeof(*node->sibling));
1406                 node=node->sibling;
1407               }
1408             node->tau=zero_crossing[i+1].tau;
1409             node->child=(IntervalTree *) NULL;
1410             node->sibling=(IntervalTree *) NULL;
1411             node->left=left;
1412             node->right=k;
1413             left=k;
1414           }
1415         }
1416       if (left != head->left)
1417         {
1418           node->sibling=(IntervalTree *) AcquireMagickMemory(
1419             sizeof(*node->sibling));
1420           node=node->sibling;
1421           node->tau=zero_crossing[i+1].tau;
1422           node->child=(IntervalTree *) NULL;
1423           node->sibling=(IntervalTree *) NULL;
1424           node->left=left;
1425           node->right=head->right;
1426         }
1427     }
1428   }
1429   /*
1430     Determine the stability: difference between a nodes tau and its child.
1431   */
1432   Stability(root->child);
1433   MeanStability(root->child);
1434   list=(IntervalTree **) RelinquishMagickMemory(list);
1435   return(root);
1436 }
1437 \f
1438 /*
1439 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1440 %                                                                             %
1441 %                                                                             %
1442 %                                                                             %
1443 +   O p t i m a l T a u                                                       %
1444 %                                                                             %
1445 %                                                                             %
1446 %                                                                             %
1447 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1448 %
1449 %  OptimalTau() finds the optimal tau for each band of the histogram.
1450 %
1451 %  The format of the OptimalTau method is:
1452 %
1453 %    MagickRealType OptimalTau(const long *histogram,const double max_tau,
1454 %      const double min_tau,const double delta_tau,
1455 %      const double smooth_threshold,short *extrema)
1456 %
1457 %  A description of each parameter follows.
1458 %
1459 %    o histogram: Specifies an array of integers representing the number
1460 %      of pixels for each intensity of a particular color component.
1461 %
1462 %    o extrema:  Specifies a pointer to an array of integers.  They
1463 %      represent the peaks and valleys of the histogram for each color
1464 %      component.
1465 %
1466 */
1467
1468 static void ActiveNodes(IntervalTree **list,long *number_nodes,
1469   IntervalTree *node)
1470 {
1471   if (node == (IntervalTree *) NULL)
1472     return;
1473   if (node->stability >= node->mean_stability)
1474     {
1475       list[(*number_nodes)++]=node;
1476       ActiveNodes(list,number_nodes,node->sibling);
1477     }
1478   else
1479     {
1480       ActiveNodes(list,number_nodes,node->sibling);
1481       ActiveNodes(list,number_nodes,node->child);
1482     }
1483 }
1484
1485 static void FreeNodes(IntervalTree *node)
1486 {
1487   if (node == (IntervalTree *) NULL)
1488     return;
1489   FreeNodes(node->sibling);
1490   FreeNodes(node->child);
1491   node=(IntervalTree *) RelinquishMagickMemory(node);
1492 }
1493
1494 static MagickRealType OptimalTau(const long *histogram,const double max_tau,
1495   const double min_tau,const double delta_tau,const double smooth_threshold,
1496   short *extrema)
1497 {
1498   IntervalTree
1499     **list,
1500     *node,
1501     *root;
1502
1503   long
1504     index,
1505     j,
1506     k,
1507     number_nodes;
1508
1509   MagickRealType
1510     average_tau,
1511     *derivative,
1512     *second_derivative,
1513     tau,
1514     value;
1515
1516   register long
1517     i,
1518     x;
1519
1520   MagickBooleanType
1521     peak;
1522
1523   unsigned long
1524     count,
1525     number_crossings;
1526
1527   ZeroCrossing
1528     *zero_crossing;
1529
1530   /*
1531     Allocate interval tree.
1532   */
1533   list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1534     sizeof(*list));
1535   if (list == (IntervalTree **) NULL)
1536     return(0.0);
1537   /*
1538     Allocate zero crossing list.
1539   */
1540   count=(unsigned long) ((max_tau-min_tau)/delta_tau)+2;
1541   zero_crossing=(ZeroCrossing *) AcquireQuantumMemory((size_t) count,
1542     sizeof(*zero_crossing));
1543   if (zero_crossing == (ZeroCrossing *) NULL)
1544     return(0.0);
1545   for (i=0; i < (long) count; i++)
1546     zero_crossing[i].tau=(-1.0);
1547   /*
1548     Initialize zero crossing list.
1549   */
1550   derivative=(MagickRealType *) AcquireQuantumMemory(256,sizeof(*derivative));
1551   second_derivative=(MagickRealType *) AcquireQuantumMemory(256,
1552     sizeof(*second_derivative));
1553   if ((derivative == (MagickRealType *) NULL) ||
1554       (second_derivative == (MagickRealType *) NULL))
1555     ThrowFatalException(ResourceLimitFatalError,
1556       "UnableToAllocateDerivatives");
1557   i=0;
1558   for (tau=max_tau; tau >= min_tau; tau-=delta_tau)
1559   {
1560     zero_crossing[i].tau=tau;
1561     ScaleSpace(histogram,tau,zero_crossing[i].histogram);
1562     DerivativeHistogram(zero_crossing[i].histogram,derivative);
1563     DerivativeHistogram(derivative,second_derivative);
1564     ZeroCrossHistogram(second_derivative,smooth_threshold,
1565       zero_crossing[i].crossings);
1566     i++;
1567   }
1568   /*
1569     Add an entry for the original histogram.
1570   */
1571   zero_crossing[i].tau=0.0;
1572   for (j=0; j <= 255; j++)
1573     zero_crossing[i].histogram[j]=(MagickRealType) histogram[j];
1574   DerivativeHistogram(zero_crossing[i].histogram,derivative);
1575   DerivativeHistogram(derivative,second_derivative);
1576   ZeroCrossHistogram(second_derivative,smooth_threshold,
1577     zero_crossing[i].crossings);
1578   number_crossings=(unsigned long) i;
1579   derivative=(MagickRealType *) RelinquishMagickMemory(derivative);
1580   second_derivative=(MagickRealType *)
1581     RelinquishMagickMemory(second_derivative);
1582   /*
1583     Ensure the scale-space fingerprints form lines in scale-space, not loops.
1584   */
1585   ConsolidateCrossings(zero_crossing,number_crossings);
1586   /*
1587     Force endpoints to be included in the interval.
1588   */
1589   for (i=0; i <= (long) number_crossings; i++)
1590   {
1591     for (j=0; j < 255; j++)
1592       if (zero_crossing[i].crossings[j] != 0)
1593         break;
1594     zero_crossing[i].crossings[0]=(-zero_crossing[i].crossings[j]);
1595     for (j=255; j > 0; j--)
1596       if (zero_crossing[i].crossings[j] != 0)
1597         break;
1598     zero_crossing[i].crossings[255]=(-zero_crossing[i].crossings[j]);
1599   }
1600   /*
1601     Initialize interval tree.
1602   */
1603   root=InitializeIntervalTree(zero_crossing,number_crossings);
1604   if (root == (IntervalTree *) NULL)
1605     return(0.0);
1606   /*
1607     Find active nodes:  stability is greater (or equal) to the mean stability of
1608     its children.
1609   */
1610   number_nodes=0;
1611   ActiveNodes(list,&number_nodes,root->child);
1612   /*
1613     Initialize extrema.
1614   */
1615   for (i=0; i <= 255; i++)
1616     extrema[i]=0;
1617   for (i=0; i < number_nodes; i++)
1618   {
1619     /*
1620       Find this tau in zero crossings list.
1621     */
1622     k=0;
1623     node=list[i];
1624     for (j=0; j <= (long) number_crossings; j++)
1625       if (zero_crossing[j].tau == node->tau)
1626         k=j;
1627     /*
1628       Find the value of the peak.
1629     */
1630     peak=zero_crossing[k].crossings[node->right] == -1 ? MagickTrue :
1631       MagickFalse;
1632     index=node->left;
1633     value=zero_crossing[k].histogram[index];
1634     for (x=node->left; x <= node->right; x++)
1635     {
1636       if (peak != MagickFalse)
1637         {
1638           if (zero_crossing[k].histogram[x] > value)
1639             {
1640               value=zero_crossing[k].histogram[x];
1641               index=x;
1642             }
1643         }
1644       else
1645         if (zero_crossing[k].histogram[x] < value)
1646           {
1647             value=zero_crossing[k].histogram[x];
1648             index=x;
1649           }
1650     }
1651     for (x=node->left; x <= node->right; x++)
1652     {
1653       if (index == 0)
1654         index=256;
1655       if (peak != MagickFalse)
1656         extrema[x]=(short) index;
1657       else
1658         extrema[x]=(short) (-index);
1659     }
1660   }
1661   /*
1662     Determine the average tau.
1663   */
1664   average_tau=0.0;
1665   for (i=0; i < number_nodes; i++)
1666     average_tau+=list[i]->tau;
1667   average_tau/=(MagickRealType) number_nodes;
1668   /*
1669     Relinquish resources.
1670   */
1671   FreeNodes(root);
1672   zero_crossing=(ZeroCrossing *) RelinquishMagickMemory(zero_crossing);
1673   list=(IntervalTree **) RelinquishMagickMemory(list);
1674   return(average_tau);
1675 }
1676 \f
1677 /*
1678 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1679 %                                                                             %
1680 %                                                                             %
1681 %                                                                             %
1682 +   S c a l e S p a c e                                                       %
1683 %                                                                             %
1684 %                                                                             %
1685 %                                                                             %
1686 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1687 %
1688 %  ScaleSpace() performs a scale-space filter on the 1D histogram.
1689 %
1690 %  The format of the ScaleSpace method is:
1691 %
1692 %      ScaleSpace(const long *histogram,const MagickRealType tau,
1693 %        MagickRealType *scale_histogram)
1694 %
1695 %  A description of each parameter follows.
1696 %
1697 %    o histogram: Specifies an array of MagickRealTypes representing the number
1698 %      of pixels for each intensity of a particular color component.
1699 %
1700 */
1701
1702 static void ScaleSpace(const long *histogram,const MagickRealType tau,
1703   MagickRealType *scale_histogram)
1704 {
1705   MagickRealType
1706     alpha,
1707     beta,
1708     *gamma,
1709     sum;
1710
1711   register long
1712     u,
1713     x;
1714
1715   gamma=(MagickRealType *) AcquireQuantumMemory(256,sizeof(*gamma));
1716   if (gamma == (MagickRealType *) NULL)
1717     ThrowFatalException(ResourceLimitFatalError,
1718       "UnableToAllocateGammaMap");
1719   alpha=1.0/(tau*sqrt(2.0*MagickPI));
1720   beta=(-1.0/(2.0*tau*tau));
1721   for (x=0; x <= 255; x++)
1722     gamma[x]=0.0;
1723   for (x=0; x <= 255; x++)
1724   {
1725     gamma[x]=exp((double) beta*x*x);
1726     if (gamma[x] < MagickEpsilon)
1727       break;
1728   }
1729   for (x=0; x <= 255; x++)
1730   {
1731     sum=0.0;
1732     for (u=0; u <= 255; u++)
1733       sum+=(MagickRealType) histogram[u]*gamma[MagickAbsoluteValue(x-u)];
1734     scale_histogram[x]=alpha*sum;
1735   }
1736   gamma=(MagickRealType *) RelinquishMagickMemory(gamma);
1737 }
1738 \f
1739 /*
1740 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1741 %                                                                             %
1742 %                                                                             %
1743 %                                                                             %
1744 %  S e g m e n t I m a g e                                                    %
1745 %                                                                             %
1746 %                                                                             %
1747 %                                                                             %
1748 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1749 %
1750 %  SegmentImage() segment an image by analyzing the histograms of the color
1751 %  components and identifying units that are homogeneous with the fuzzy
1752 %  C-means technique.
1753 %
1754 %  The format of the SegmentImage method is:
1755 %
1756 %      MagickBooleanType SegmentImage(Image *image,
1757 %        const ColorspaceType colorspace,const MagickBooleanType verbose,
1758 %        const double cluster_threshold,const double smooth_threshold)
1759 %
1760 %  A description of each parameter follows.
1761 %
1762 %    o image: the image.
1763 %
1764 %    o colorspace: Indicate the colorspace.
1765 %
1766 %    o verbose:  Set to MagickTrue to print detailed information about the
1767 %      identified classes.
1768 %
1769 %    o cluster_threshold:  This represents the minimum number of pixels
1770 %      contained in a hexahedra before it can be considered valid (expressed
1771 %      as a percentage).
1772 %
1773 %    o smooth_threshold: the smoothing threshold eliminates noise in the second
1774 %      derivative of the histogram.  As the value is increased, you can expect a
1775 %      smoother second derivative.
1776 %
1777 */
1778 MagickExport MagickBooleanType SegmentImage(Image *image,
1779   const ColorspaceType colorspace,const MagickBooleanType verbose,
1780   const double cluster_threshold,const double smooth_threshold)
1781 {
1782   long
1783     *histogram[MaxDimension];
1784
1785   MagickBooleanType
1786     status;
1787
1788   register long
1789     i;
1790
1791   short
1792     *extrema[MaxDimension];
1793
1794   /*
1795     Allocate histogram and extrema.
1796   */
1797   assert(image != (Image *) NULL);
1798   assert(image->signature == MagickSignature);
1799   if (image->debug != MagickFalse)
1800     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1801   for (i=0; i < MaxDimension; i++)
1802   {
1803     histogram[i]=(long *) AcquireQuantumMemory(256,sizeof(**histogram));
1804     extrema[i]=(short *) AcquireQuantumMemory(256,sizeof(**extrema));
1805     if ((histogram[i] == (long *) NULL) || (extrema[i] == (short *) NULL))
1806       {
1807         for (i-- ; i >= 0; i--)
1808         {
1809           extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1810           histogram[i]=(long *) RelinquishMagickMemory(histogram[i]);
1811         }
1812         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
1813           image->filename)
1814       }
1815   }
1816   if (colorspace != RGBColorspace)
1817     (void) TransformImageColorspace(image,colorspace);
1818   /*
1819     Initialize histogram.
1820   */
1821   InitializeHistogram(image,histogram,&image->exception);
1822   (void) OptimalTau(histogram[Red],Tau,0.2,DeltaTau,
1823     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Red]);
1824   (void) OptimalTau(histogram[Green],Tau,0.2,DeltaTau,
1825     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Green]);
1826   (void) OptimalTau(histogram[Blue],Tau,0.2,DeltaTau,
1827     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Blue]);
1828   /*
1829     Classify using the fuzzy c-Means technique.
1830   */
1831   status=Classify(image,extrema,cluster_threshold,WeightingExponent,verbose);
1832   if (colorspace != RGBColorspace)
1833     (void) TransformImageColorspace(image,colorspace);
1834   /*
1835     Relinquish resources.
1836   */
1837   for (i=0; i < MaxDimension; i++)
1838   {
1839     extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1840     histogram[i]=(long *) RelinquishMagickMemory(histogram[i]);
1841   }
1842   return(status);
1843 }
1844 \f
1845 /*
1846 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1847 %                                                                             %
1848 %                                                                             %
1849 %                                                                             %
1850 +   Z e r o C r o s s H i s t o g r a m                                       %
1851 %                                                                             %
1852 %                                                                             %
1853 %                                                                             %
1854 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1855 %
1856 %  ZeroCrossHistogram() find the zero crossings in a histogram and marks
1857 %  directions as:  1 is negative to positive; 0 is zero crossing; and -1
1858 %  is positive to negative.
1859 %
1860 %  The format of the ZeroCrossHistogram method is:
1861 %
1862 %      ZeroCrossHistogram(MagickRealType *second_derivative,
1863 %        const MagickRealType smooth_threshold,short *crossings)
1864 %
1865 %  A description of each parameter follows.
1866 %
1867 %    o second_derivative: Specifies an array of MagickRealTypes representing the
1868 %      second derivative of the histogram of a particular color component.
1869 %
1870 %    o crossings:  This array of integers is initialized with
1871 %      -1, 0, or 1 representing the slope of the first derivative of the
1872 %      of a particular color component.
1873 %
1874 */
1875 static void ZeroCrossHistogram(MagickRealType *second_derivative,
1876   const MagickRealType smooth_threshold,short *crossings)
1877 {
1878   long
1879     parity;
1880
1881   register long
1882     i;
1883
1884   /*
1885     Merge low numbers to zero to help prevent noise.
1886   */
1887   for (i=0; i <= 255; i++)
1888     if ((second_derivative[i] < smooth_threshold) &&
1889         (second_derivative[i] >= -smooth_threshold))
1890       second_derivative[i]=0.0;
1891   /*
1892     Mark zero crossings.
1893   */
1894   parity=0;
1895   for (i=0; i <= 255; i++)
1896   {
1897     crossings[i]=0;
1898     if (second_derivative[i] < 0.0)
1899       {
1900         if (parity > 0)
1901           crossings[i]=(-1);
1902         parity=1;
1903       }
1904     else
1905       if (second_derivative[i] > 0.0)
1906         {
1907           if (parity < 0)
1908             crossings[i]=1;
1909           parity=(-1);
1910         }
1911   }
1912 }