granicus.if.org Git - imagemagick/blob - MagickCore/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 %                                   Cristy                                    %
  17 %                                April 1993                                   %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2015 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 "MagickCore/studio.h"
  86 #include "MagickCore/cache.h"
  87 #include "MagickCore/color.h"
  88 #include "MagickCore/colormap.h"
  89 #include "MagickCore/colorspace.h"
  90 #include "MagickCore/colorspace-private.h"
  91 #include "MagickCore/exception.h"
  92 #include "MagickCore/exception-private.h"
  93 #include "MagickCore/image.h"
  94 #include "MagickCore/image-private.h"
  95 #include "MagickCore/memory_.h"
  96 #include "MagickCore/monitor.h"
  97 #include "MagickCore/monitor-private.h"
  98 #include "MagickCore/pixel-accessor.h"
  99 #include "MagickCore/pixel-private.h"
 100 #include "MagickCore/quantize.h"
 101 #include "MagickCore/quantum.h"
 102 #include "MagickCore/quantum-private.h"
 103 #include "MagickCore/resource_.h"
 104 #include "MagickCore/segment.h"
 105 #include "MagickCore/string_.h"
 106 #include "MagickCore/thread-private.h"
 107 \f
 108 /*
 109   Define declarations.
 110 */
 111 #define MaxDimension  3
 112 #define DeltaTau  0.5f
 113 #if defined(FastClassify)
 114 #define WeightingExponent  2.0
 115 #define SegmentPower(ratio) (ratio)
 116 #else
 117 #define WeightingExponent  2.5
 118 #define SegmentPower(ratio) pow(ratio,(double) (1.0/(weighting_exponent-1.0)));
 119 #endif
 120 #define Tau  5.2f
 121 \f
 122 /*
 123   Typedef declarations.
 124 */
 125 typedef struct _ExtentPacket
 126 {
 127   double
 128     center;
 129
 130   ssize_t
 131     index,
 132     left,
 133     right;
 134 } ExtentPacket;
 135
 136 typedef struct _Cluster
 137 {
 138   struct _Cluster
 139     *next;
 140
 141   ExtentPacket
 142     red,
 143     green,
 144     blue;
 145
 146   ssize_t
 147     count,
 148     id;
 149 } Cluster;
 150
 151 typedef struct _IntervalTree
 152 {
 153   double
 154     tau;
 155
 156   ssize_t
 157     left,
 158     right;
 159
 160   double
 161     mean_stability,
 162     stability;
 163
 164   struct _IntervalTree
 165     *sibling,
 166     *child;
 167 } IntervalTree;
 168
 169 typedef struct _ZeroCrossing
 170 {
 171   double
 172     tau,
 173     histogram[256];
 174
 175   short
 176     crossings[256];
 177 } ZeroCrossing;
 178 \f
 179 /*
 180   Constant declarations.
 181 */
 182 static const int
 183   Blue = 2,
 184   Green = 1,
 185   Red = 0,
 186   SafeMargin = 3,
 187   TreeLength = 600;
 188 \f
 189 /*
 190   Method prototypes.
 191 */
 192 static double
 193   OptimalTau(const ssize_t *,const double,const double,const double,
 194     const double,short *);
 195
 196 static ssize_t
 197   DefineRegion(const short *,ExtentPacket *);
 198
 199 static void
 200   InitializeHistogram(const Image *,ssize_t **,ExceptionInfo *),
 201   ScaleSpace(const ssize_t *,const double,double *),
 202   ZeroCrossHistogram(double *,const double,short *);
 203 \f
 204 /*
 205 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 206 %                                                                             %
 207 %                                                                             %
 208 %                                                                             %
 209 +   C l a s s i f y                                                           %
 210 %                                                                             %
 211 %                                                                             %
 212 %                                                                             %
 213 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 214 %
 215 %  Classify() defines one or more classes.  Each pixel is thresholded to
 216 %  determine which class it belongs to.  If the class is not identified it is
 217 %  assigned to the closest class based on the fuzzy c-Means technique.
 218 %
 219 %  The format of the Classify method is:
 220 %
 221 %      MagickBooleanType Classify(Image *image,short **extrema,
 222 %        const double cluster_threshold,
 223 %        const double weighting_exponent,
 224 %        const MagickBooleanType verbose,ExceptionInfo *exception)
 225 %
 226 %  A description of each parameter follows.
 227 %
 228 %    o image: the image.
 229 %
 230 %    o extrema:  Specifies a pointer to an array of integers.  They
 231 %      represent the peaks and valleys of the histogram for each color
 232 %      component.
 233 %
 234 %    o cluster_threshold:  This double represents the minimum number of
 235 %      pixels contained in a hexahedra before it can be considered valid
 236 %      (expressed as a percentage).
 237 %
 238 %    o weighting_exponent: Specifies the membership weighting exponent.
 239 %
 240 %    o verbose:  A value greater than zero prints detailed information about
 241 %      the identified classes.
 242 %
 243 %    o exception: return any errors or warnings in this structure.
 244 %
 245 */
 246 static MagickBooleanType Classify(Image *image,short **extrema,
 247   const double cluster_threshold,
 248   const double weighting_exponent,const MagickBooleanType verbose,
 249   ExceptionInfo *exception)
 250 {
 251 #define SegmentImageTag  "Segment/Image"
 252
 253   CacheView
 254     *image_view;
 255
 256   Cluster
 257     *cluster,
 258     *head,
 259     *last_cluster,
 260     *next_cluster;
 261
 262   ExtentPacket
 263     blue,
 264     green,
 265     red;
 266
 267   MagickOffsetType
 268     progress;
 269
 270   double
 271     *free_squares;
 272
 273   MagickStatusType
 274     status;
 275
 276   register ssize_t
 277     i;
 278
 279   register double
 280     *squares;
 281
 282   size_t
 283     number_clusters;
 284
 285   ssize_t
 286     count,
 287     y;
 288
 289   /*
 290     Form clusters.
 291   */
 292   cluster=(Cluster *) NULL;
 293   head=(Cluster *) NULL;
 294   (void) ResetMagickMemory(&red,0,sizeof(red));
 295   (void) ResetMagickMemory(&green,0,sizeof(green));
 296   (void) ResetMagickMemory(&blue,0,sizeof(blue));
 297   while (DefineRegion(extrema[Red],&red) != 0)
 298   {
 299     green.index=0;
 300     while (DefineRegion(extrema[Green],&green) != 0)
 301     {
 302       blue.index=0;
 303       while (DefineRegion(extrema[Blue],&blue) != 0)
 304       {
 305         /*
 306           Allocate a new class.
 307         */
 308         if (head != (Cluster *) NULL)
 309           {
 310             cluster->next=(Cluster *) AcquireMagickMemory(
 311               sizeof(*cluster->next));
 312             cluster=cluster->next;
 313           }
 314         else
 315           {
 316             cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
 317             head=cluster;
 318           }
 319         if (cluster == (Cluster *) NULL)
 320           ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 321             image->filename);
 322         /*
 323           Initialize a new class.
 324         */
 325         cluster->count=0;
 326         cluster->red=red;
 327         cluster->green=green;
 328         cluster->blue=blue;
 329         cluster->next=(Cluster *) NULL;
 330       }
 331     }
 332   }
 333   if (head == (Cluster *) NULL)
 334     {
 335       /*
 336         No classes were identified-- create one.
 337       */
 338       cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
 339       if (cluster == (Cluster *) NULL)
 340         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 341           image->filename);
 342       /*
 343         Initialize a new class.
 344       */
 345       cluster->count=0;
 346       cluster->red=red;
 347       cluster->green=green;
 348       cluster->blue=blue;
 349       cluster->next=(Cluster *) NULL;
 350       head=cluster;
 351     }
 352   /*
 353     Count the pixels for each cluster.
 354   */
 355   status=MagickTrue;
 356   count=0;
 357   progress=0;
 358   image_view=AcquireVirtualCacheView(image,exception);
 359   for (y=0; y < (ssize_t) image->rows; y++)
 360   {
 361     register const Quantum
 362       *p;
 363
 364     register ssize_t
 365       x;
 366
 367     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 368     if (p == (const Quantum *) NULL)
 369       break;
 370     for (x=0; x < (ssize_t) image->columns; x++)
 371     {
 372       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 373         if (((ssize_t) ScaleQuantumToChar(GetPixelRed(image,p)) >=
 374              (cluster->red.left-SafeMargin)) &&
 375             ((ssize_t) ScaleQuantumToChar(GetPixelRed(image,p)) <=
 376              (cluster->red.right+SafeMargin)) &&
 377             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p)) >=
 378              (cluster->green.left-SafeMargin)) &&
 379             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p)) <=
 380              (cluster->green.right+SafeMargin)) &&
 381             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p)) >=
 382              (cluster->blue.left-SafeMargin)) &&
 383             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p)) <=
 384              (cluster->blue.right+SafeMargin)))
 385           {
 386             /*
 387               Count this pixel.
 388             */
 389             count++;
 390             cluster->red.center+=(double) ScaleQuantumToChar(
 391               GetPixelRed(image,p));
 392             cluster->green.center+=(double) ScaleQuantumToChar(
 393               GetPixelGreen(image,p));
 394             cluster->blue.center+=(double) ScaleQuantumToChar(
 395               GetPixelBlue(image,p));
 396             cluster->count++;
 397             break;
 398           }
 399       p+=GetPixelChannels(image);
 400     }
 401     if (image->progress_monitor != (MagickProgressMonitor) NULL)
 402       {
 403         MagickBooleanType
 404           proceed;
 405
 406 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 407         #pragma omp critical (MagickCore_Classify)
 408 #endif
 409         proceed=SetImageProgress(image,SegmentImageTag,progress++,2*
 410           image->rows);
 411         if (proceed == MagickFalse)
 412           status=MagickFalse;
 413       }
 414   }
 415   image_view=DestroyCacheView(image_view);
 416   /*
 417     Remove clusters that do not meet minimum cluster threshold.
 418   */
 419   count=0;
 420   last_cluster=head;
 421   next_cluster=head;
 422   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
 423   {
 424     next_cluster=cluster->next;
 425     if ((cluster->count > 0) &&
 426         (cluster->count >= (count*cluster_threshold/100.0)))
 427       {
 428         /*
 429           Initialize cluster.
 430         */
 431         cluster->id=count;
 432         cluster->red.center/=cluster->count;
 433         cluster->green.center/=cluster->count;
 434         cluster->blue.center/=cluster->count;
 435         count++;
 436         last_cluster=cluster;
 437         continue;
 438       }
 439     /*
 440       Delete cluster.
 441     */
 442     if (cluster == head)
 443       head=next_cluster;
 444     else
 445       last_cluster->next=next_cluster;
 446     cluster=(Cluster *) RelinquishMagickMemory(cluster);
 447   }
 448   number_clusters=(size_t) count;
 449   if (verbose != MagickFalse)
 450     {
 451       /*
 452         Print cluster statistics.
 453       */
 454       (void) FormatLocaleFile(stdout,"Fuzzy C-means Statistics\n");
 455       (void) FormatLocaleFile(stdout,"===================\n\n");
 456       (void) FormatLocaleFile(stdout,"\tCluster Threshold = %g\n",(double)
 457         cluster_threshold);
 458       (void) FormatLocaleFile(stdout,"\tWeighting Exponent = %g\n",(double)
 459         weighting_exponent);
 460       (void) FormatLocaleFile(stdout,"\tTotal Number of Clusters = %.20g\n\n",
 461         (double) number_clusters);
 462       /*
 463         Print the total number of points per cluster.
 464       */
 465       (void) FormatLocaleFile(stdout,"\n\nNumber of Vectors Per Cluster\n");
 466       (void) FormatLocaleFile(stdout,"=============================\n\n");
 467       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 468         (void) FormatLocaleFile(stdout,"Cluster #%.20g = %.20g\n",(double)
 469           cluster->id,(double) cluster->count);
 470       /*
 471         Print the cluster extents.
 472       */
 473       (void) FormatLocaleFile(stdout,
 474         "\n\n\nCluster Extents:        (Vector Size: %d)\n",MaxDimension);
 475       (void) FormatLocaleFile(stdout,"================");
 476       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 477       {
 478         (void) FormatLocaleFile(stdout,"\n\nCluster #%.20g\n\n",(double)
 479           cluster->id);
 480         (void) FormatLocaleFile(stdout,
 481           "%.20g-%.20g  %.20g-%.20g  %.20g-%.20g\n",(double)
 482           cluster->red.left,(double) cluster->red.right,(double)
 483           cluster->green.left,(double) cluster->green.right,(double)
 484           cluster->blue.left,(double) cluster->blue.right);
 485       }
 486       /*
 487         Print the cluster center values.
 488       */
 489       (void) FormatLocaleFile(stdout,
 490         "\n\n\nCluster Center Values:        (Vector Size: %d)\n",MaxDimension);
 491       (void) FormatLocaleFile(stdout,"=====================");
 492       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 493       {
 494         (void) FormatLocaleFile(stdout,"\n\nCluster #%.20g\n\n",(double)
 495           cluster->id);
 496         (void) FormatLocaleFile(stdout,"%g  %g  %g\n",(double)
 497           cluster->red.center,(double) cluster->green.center,(double)
 498           cluster->blue.center);
 499       }
 500       (void) FormatLocaleFile(stdout,"\n");
 501     }
 502   if (number_clusters > 256)
 503     ThrowBinaryException(ImageError,"TooManyClusters",image->filename);
 504   /*
 505     Speed up distance calculations.
 506   */
 507   squares=(double *) AcquireQuantumMemory(513UL,sizeof(*squares));
 508   if (squares == (double *) NULL)
 509     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 510       image->filename);
 511   squares+=255;
 512   for (i=(-255); i <= 255; i++)
 513     squares[i]=(double) i*(double) i;
 514   /*
 515     Allocate image colormap.
 516   */
 517   if (AcquireImageColormap(image,number_clusters,exception) == MagickFalse)
 518     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 519       image->filename);
 520   i=0;
 521   for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 522   {
 523     image->colormap[i].red=(double) ScaleCharToQuantum((unsigned char)
 524       (cluster->red.center+0.5));
 525     image->colormap[i].green=(double) ScaleCharToQuantum((unsigned char)
 526       (cluster->green.center+0.5));
 527     image->colormap[i].blue=(double) ScaleCharToQuantum((unsigned char)
 528       (cluster->blue.center+0.5));
 529     i++;
 530   }
 531   /*
 532     Do course grain classes.
 533   */
 534   image_view=AcquireAuthenticCacheView(image,exception);
 535 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 536   #pragma omp parallel for schedule(static,4) shared(progress,status) \
 537     magick_threads(image,image,image->rows,1)
 538 #endif
 539   for (y=0; y < (ssize_t) image->rows; y++)
 540   {
 541     Cluster
 542       *cluster;
 543
 544     register const PixelInfo
 545       *restrict p;
 546
 547     register ssize_t
 548       x;
 549
 550     register Quantum
 551       *restrict q;
 552
 553     if (status == MagickFalse)
 554       continue;
 555     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
 556     if (q == (Quantum *) NULL)
 557       {
 558         status=MagickFalse;
 559         continue;
 560       }
 561     for (x=0; x < (ssize_t) image->columns; x++)
 562     {
 563       SetPixelIndex(image,0,q);
 564       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
 565       {
 566         if (((ssize_t) ScaleQuantumToChar(GetPixelRed(image,q)) >=
 567              (cluster->red.left-SafeMargin)) &&
 568             ((ssize_t) ScaleQuantumToChar(GetPixelRed(image,q)) <=
 569              (cluster->red.right+SafeMargin)) &&
 570             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,q)) >=
 571              (cluster->green.left-SafeMargin)) &&
 572             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,q)) <=
 573              (cluster->green.right+SafeMargin)) &&
 574             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,q)) >=
 575              (cluster->blue.left-SafeMargin)) &&
 576             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,q)) <=
 577              (cluster->blue.right+SafeMargin)))
 578           {
 579             /*
 580               Classify this pixel.
 581             */
 582             SetPixelIndex(image,(Quantum) cluster->id,q);
 583             break;
 584           }
 585       }
 586       if (cluster == (Cluster *) NULL)
 587         {
 588           double
 589             distance_squared,
 590             local_minima,
 591             numerator,
 592             ratio,
 593             sum;
 594
 595           register ssize_t
 596             j,
 597             k;
 598
 599           /*
 600             Compute fuzzy membership.
 601           */
 602           local_minima=0.0;
 603           for (j=0; j < (ssize_t) image->colors; j++)
 604           {
 605             sum=0.0;
 606             p=image->colormap+j;
 607             distance_squared=squares[(ssize_t) ScaleQuantumToChar(
 608               GetPixelRed(image,q))-(ssize_t)
 609               ScaleQuantumToChar(ClampToQuantum(p->red))]+squares[(ssize_t)
 610               ScaleQuantumToChar(GetPixelGreen(image,q))-(ssize_t)
 611               ScaleQuantumToChar(ClampToQuantum(p->green))]+squares[(ssize_t)
 612               ScaleQuantumToChar(GetPixelBlue(image,q))-(ssize_t)
 613               ScaleQuantumToChar(ClampToQuantum(p->blue))];
 614             numerator=distance_squared;
 615             for (k=0; k < (ssize_t) image->colors; k++)
 616             {
 617               p=image->colormap+k;
 618                 distance_squared=squares[(ssize_t) ScaleQuantumToChar(
 619                   GetPixelRed(image,q))-(ssize_t)
 620                   ScaleQuantumToChar(ClampToQuantum(p->red))]+squares[
 621                   (ssize_t) ScaleQuantumToChar(GetPixelGreen(image,q))-(ssize_t)
 622                   ScaleQuantumToChar(ClampToQuantum(p->green))]+squares[
 623                   (ssize_t) ScaleQuantumToChar(GetPixelBlue(image,q))-(ssize_t)
 624                   ScaleQuantumToChar(ClampToQuantum(p->blue))];
 625               ratio=numerator/distance_squared;
 626               sum+=SegmentPower(ratio);
 627             }
 628             if ((sum != 0.0) && ((1.0/sum) > local_minima))
 629               {
 630                 /*
 631                   Classify this pixel.
 632                 */
 633                 local_minima=1.0/sum;
 634                 SetPixelIndex(image,(Quantum) j,q);
 635               }
 636           }
 637         }
 638       q+=GetPixelChannels(image);
 639     }
 640     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 641       status=MagickFalse;
 642     if (image->progress_monitor != (MagickProgressMonitor) NULL)
 643       {
 644         MagickBooleanType
 645           proceed;
 646
 647 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 648         #pragma omp critical (MagickCore_Classify)
 649 #endif
 650         proceed=SetImageProgress(image,SegmentImageTag,progress++,
 651           2*image->rows);
 652         if (proceed == MagickFalse)
 653           status=MagickFalse;
 654       }
 655   }
 656   image_view=DestroyCacheView(image_view);
 657   status&=SyncImage(image,exception);
 658   /*
 659     Relinquish resources.
 660   */
 661   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
 662   {
 663     next_cluster=cluster->next;
 664     cluster=(Cluster *) RelinquishMagickMemory(cluster);
 665   }
 666   squares-=255;
 667   free_squares=squares;
 668   free_squares=(double *) RelinquishMagickMemory(free_squares);
 669   return(MagickTrue);
 670 }
 671 \f
 672 /*
 673 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 674 %                                                                             %
 675 %                                                                             %
 676 %                                                                             %
 677 +   C o n s o l i d a t e C r o s s i n g s                                   %
 678 %                                                                             %
 679 %                                                                             %
 680 %                                                                             %
 681 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 682 %
 683 %  ConsolidateCrossings() guarantees that an even number of zero crossings
 684 %  always lie between two crossings.
 685 %
 686 %  The format of the ConsolidateCrossings method is:
 687 %
 688 %      ConsolidateCrossings(ZeroCrossing *zero_crossing,
 689 %        const size_t number_crossings)
 690 %
 691 %  A description of each parameter follows.
 692 %
 693 %    o zero_crossing: Specifies an array of structures of type ZeroCrossing.
 694 %
 695 %    o number_crossings: This size_t specifies the number of elements
 696 %      in the zero_crossing array.
 697 %
 698 */
 699 static void ConsolidateCrossings(ZeroCrossing *zero_crossing,
 700   const size_t number_crossings)
 701 {
 702   register ssize_t
 703     i,
 704     j,
 705     k,
 706     l;
 707
 708   ssize_t
 709     center,
 710     correct,
 711     count,
 712     left,
 713     right;
 714
 715   /*
 716     Consolidate zero crossings.
 717   */
 718   for (i=(ssize_t) number_crossings-1; i >= 0; i--)
 719     for (j=0; j <= 255; j++)
 720     {
 721       if (zero_crossing[i].crossings[j] == 0)
 722         continue;
 723       /*
 724         Find the entry that is closest to j and still preserves the
 725         property that there are an even number of crossings between
 726         intervals.
 727       */
 728       for (k=j-1; k > 0; k--)
 729         if (zero_crossing[i+1].crossings[k] != 0)
 730           break;
 731       left=MagickMax(k,0);
 732       center=j;
 733       for (k=j+1; k < 255; k++)
 734         if (zero_crossing[i+1].crossings[k] != 0)
 735           break;
 736       right=MagickMin(k,255);
 737       /*
 738         K is the zero crossing just left of j.
 739       */
 740       for (k=j-1; k > 0; k--)
 741         if (zero_crossing[i].crossings[k] != 0)
 742           break;
 743       if (k < 0)
 744         k=0;
 745       /*
 746         Check center for an even number of crossings between k and j.
 747       */
 748       correct=(-1);
 749       if (zero_crossing[i+1].crossings[j] != 0)
 750         {
 751           count=0;
 752           for (l=k+1; l < center; l++)
 753             if (zero_crossing[i+1].crossings[l] != 0)
 754               count++;
 755           if (((count % 2) == 0) && (center != k))
 756             correct=center;
 757         }
 758       /*
 759         Check left for an even number of crossings between k and j.
 760       */
 761       if (correct == -1)
 762         {
 763           count=0;
 764           for (l=k+1; l < left; l++)
 765             if (zero_crossing[i+1].crossings[l] != 0)
 766               count++;
 767           if (((count % 2) == 0) && (left != k))
 768             correct=left;
 769         }
 770       /*
 771         Check right for an even number of crossings between k and j.
 772       */
 773       if (correct == -1)
 774         {
 775           count=0;
 776           for (l=k+1; l < right; l++)
 777             if (zero_crossing[i+1].crossings[l] != 0)
 778               count++;
 779           if (((count % 2) == 0) && (right != k))
 780             correct=right;
 781         }
 782       l=(ssize_t) zero_crossing[i].crossings[j];
 783       zero_crossing[i].crossings[j]=0;
 784       if (correct != -1)
 785         zero_crossing[i].crossings[correct]=(short) l;
 786     }
 787 }
 788 \f
 789 /*
 790 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 791 %                                                                             %
 792 %                                                                             %
 793 %                                                                             %
 794 +   D e f i n e R e g i o n                                                   %
 795 %                                                                             %
 796 %                                                                             %
 797 %                                                                             %
 798 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 799 %
 800 %  DefineRegion() defines the left and right boundaries of a peak region.
 801 %
 802 %  The format of the DefineRegion method is:
 803 %
 804 %      ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
 805 %
 806 %  A description of each parameter follows.
 807 %
 808 %    o extrema:  Specifies a pointer to an array of integers.  They
 809 %      represent the peaks and valleys of the histogram for each color
 810 %      component.
 811 %
 812 %    o extents:  This pointer to an ExtentPacket represent the extends
 813 %      of a particular peak or valley of a color component.
 814 %
 815 */
 816 static ssize_t DefineRegion(const short *extrema,ExtentPacket *extents)
 817 {
 818   /*
 819     Initialize to default values.
 820   */
 821   extents->left=0;
 822   extents->center=0.0;
 823   extents->right=255;
 824   /*
 825     Find the left side (maxima).
 826   */
 827   for ( ; extents->index <= 255; extents->index++)
 828     if (extrema[extents->index] > 0)
 829       break;
 830   if (extents->index > 255)
 831     return(MagickFalse);  /* no left side - no region exists */
 832   extents->left=extents->index;
 833   /*
 834     Find the right side (minima).
 835   */
 836   for ( ; extents->index <= 255; extents->index++)
 837     if (extrema[extents->index] < 0)
 838       break;
 839   extents->right=extents->index-1;
 840   return(MagickTrue);
 841 }
 842 \f
 843 /*
 844 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 845 %                                                                             %
 846 %                                                                             %
 847 %                                                                             %
 848 +   D e r i v a t i v e H i s t o g r a m                                     %
 849 %                                                                             %
 850 %                                                                             %
 851 %                                                                             %
 852 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 853 %
 854 %  DerivativeHistogram() determines the derivative of the histogram using
 855 %  central differencing.
 856 %
 857 %  The format of the DerivativeHistogram method is:
 858 %
 859 %      DerivativeHistogram(const double *histogram,
 860 %        double *derivative)
 861 %
 862 %  A description of each parameter follows.
 863 %
 864 %    o histogram: Specifies an array of doubles representing the number
 865 %      of pixels for each intensity of a particular color component.
 866 %
 867 %    o derivative: This array of doubles is initialized by
 868 %      DerivativeHistogram to the derivative of the histogram using central
 869 %      differencing.
 870 %
 871 */
 872 static void DerivativeHistogram(const double *histogram,
 873   double *derivative)
 874 {
 875   register ssize_t
 876     i,
 877     n;
 878
 879   /*
 880     Compute endpoints using second order polynomial interpolation.
 881   */
 882   n=255;
 883   derivative[0]=(-1.5*histogram[0]+2.0*histogram[1]-0.5*histogram[2]);
 884   derivative[n]=(0.5*histogram[n-2]-2.0*histogram[n-1]+1.5*histogram[n]);
 885   /*
 886     Compute derivative using central differencing.
 887   */
 888   for (i=1; i < n; i++)
 889     derivative[i]=(histogram[i+1]-histogram[i-1])/2.0;
 890   return;
 891 }
 892 \f
 893 /*
 894 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 895 %                                                                             %
 896 %                                                                             %
 897 %                                                                             %
 898 +  G e t I m a g e D y n a m i c T h r e s h o l d                            %
 899 %                                                                             %
 900 %                                                                             %
 901 %                                                                             %
 902 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 903 %
 904 %  GetImageDynamicThreshold() returns the dynamic threshold for an image.
 905 %
 906 %  The format of the GetImageDynamicThreshold method is:
 907 %
 908 %      MagickBooleanType GetImageDynamicThreshold(const Image *image,
 909 %        const double cluster_threshold,const double smooth_threshold,
 910 %        PixelInfo *pixel,ExceptionInfo *exception)
 911 %
 912 %  A description of each parameter follows.
 913 %
 914 %    o image: the image.
 915 %
 916 %    o cluster_threshold:  This double represents the minimum number of
 917 %      pixels contained in a hexahedra before it can be considered valid
 918 %      (expressed as a percentage).
 919 %
 920 %    o smooth_threshold: the smoothing threshold eliminates noise in the second
 921 %      derivative of the histogram.  As the value is increased, you can expect a
 922 %      smoother second derivative.
 923 %
 924 %    o pixel: return the dynamic threshold here.
 925 %
 926 %    o exception: return any errors or warnings in this structure.
 927 %
 928 */
 929 MagickExport MagickBooleanType GetImageDynamicThreshold(const Image *image,
 930   const double cluster_threshold,const double smooth_threshold,
 931   PixelInfo *pixel,ExceptionInfo *exception)
 932 {
 933   Cluster
 934     *background,
 935     *cluster,
 936     *object,
 937     *head,
 938     *last_cluster,
 939     *next_cluster;
 940
 941   ExtentPacket
 942     blue,
 943     green,
 944     red;
 945
 946   MagickBooleanType
 947     proceed;
 948
 949   double
 950     threshold;
 951
 952   register const Quantum
 953     *p;
 954
 955   register ssize_t
 956     i,
 957     x;
 958
 959   short
 960     *extrema[MaxDimension];
 961
 962   ssize_t
 963     count,
 964     *histogram[MaxDimension],
 965     y;
 966
 967   /*
 968     Allocate histogram and extrema.
 969   */
 970   assert(image != (Image *) NULL);
 971   assert(image->signature == MagickSignature);
 972   if (image->debug != MagickFalse)
 973     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
 974   GetPixelInfo(image,pixel);
 975   for (i=0; i < MaxDimension; i++)
 976   {
 977     histogram[i]=(ssize_t *) AcquireQuantumMemory(256UL,sizeof(**histogram));
 978     extrema[i]=(short *) AcquireQuantumMemory(256UL,sizeof(**histogram));
 979     if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
 980       {
 981         for (i-- ; i >= 0; i--)
 982         {
 983           extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
 984           histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
 985         }
 986         (void) ThrowMagickException(exception,GetMagickModule(),
 987           ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
 988         return(MagickFalse);
 989       }
 990   }
 991   /*
 992     Initialize histogram.
 993   */
 994   InitializeHistogram(image,histogram,exception);
 995   (void) OptimalTau(histogram[Red],Tau,0.2f,DeltaTau,
 996     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Red]);
 997   (void) OptimalTau(histogram[Green],Tau,0.2f,DeltaTau,
 998     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Green]);
 999   (void) OptimalTau(histogram[Blue],Tau,0.2f,DeltaTau,
1000     (smooth_threshold == 0.0f ? 1.0f : smooth_threshold),extrema[Blue]);
1001   /*
1002     Form clusters.
1003   */
1004   cluster=(Cluster *) NULL;
1005   head=(Cluster *) NULL;
1006   (void) ResetMagickMemory(&red,0,sizeof(red));
1007   (void) ResetMagickMemory(&green,0,sizeof(green));
1008   (void) ResetMagickMemory(&blue,0,sizeof(blue));
1009   while (DefineRegion(extrema[Red],&red) != 0)
1010   {
1011     green.index=0;
1012     while (DefineRegion(extrema[Green],&green) != 0)
1013     {
1014       blue.index=0;
1015       while (DefineRegion(extrema[Blue],&blue) != 0)
1016       {
1017         /*
1018           Allocate a new class.
1019         */
1020         if (head != (Cluster *) NULL)
1021           {
1022             cluster->next=(Cluster *) AcquireMagickMemory(
1023               sizeof(*cluster->next));
1024             cluster=cluster->next;
1025           }
1026         else
1027           {
1028             cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
1029             head=cluster;
1030           }
1031         if (cluster == (Cluster *) NULL)
1032           {
1033             (void) ThrowMagickException(exception,GetMagickModule(),
1034               ResourceLimitError,"MemoryAllocationFailed","`%s'",
1035               image->filename);
1036             return(MagickFalse);
1037           }
1038         /*
1039           Initialize a new class.
1040         */
1041         cluster->count=0;
1042         cluster->red=red;
1043         cluster->green=green;
1044         cluster->blue=blue;
1045         cluster->next=(Cluster *) NULL;
1046       }
1047     }
1048   }
1049   if (head == (Cluster *) NULL)
1050     {
1051       /*
1052         No classes were identified-- create one.
1053       */
1054       cluster=(Cluster *) AcquireMagickMemory(sizeof(*cluster));
1055       if (cluster == (Cluster *) NULL)
1056         {
1057           (void) ThrowMagickException(exception,GetMagickModule(),
1058             ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
1059           return(MagickFalse);
1060         }
1061       /*
1062         Initialize a new class.
1063       */
1064       cluster->count=0;
1065       cluster->red=red;
1066       cluster->green=green;
1067       cluster->blue=blue;
1068       cluster->next=(Cluster *) NULL;
1069       head=cluster;
1070     }
1071   /*
1072     Count the pixels for each cluster.
1073   */
1074   count=0;
1075   for (y=0; y < (ssize_t) image->rows; y++)
1076   {
1077     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1078     if (p == (const Quantum *) NULL)
1079       break;
1080     for (x=0; x < (ssize_t) image->columns; x++)
1081     {
1082       for (cluster=head; cluster != (Cluster *) NULL; cluster=cluster->next)
1083         if (((ssize_t) ScaleQuantumToChar(GetPixelRed(image,p)) >=
1084              (cluster->red.left-SafeMargin)) &&
1085             ((ssize_t) ScaleQuantumToChar(GetPixelRed(image,p)) <=
1086              (cluster->red.right+SafeMargin)) &&
1087             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p)) >=
1088              (cluster->green.left-SafeMargin)) &&
1089             ((ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p)) <=
1090              (cluster->green.right+SafeMargin)) &&
1091             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p)) >=
1092              (cluster->blue.left-SafeMargin)) &&
1093             ((ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p)) <=
1094              (cluster->blue.right+SafeMargin)))
1095           {
1096             /*
1097               Count this pixel.
1098             */
1099             count++;
1100             cluster->red.center+=(double) ScaleQuantumToChar(
1101               GetPixelRed(image,p));
1102             cluster->green.center+=(double) ScaleQuantumToChar(
1103               GetPixelGreen(image,p));
1104             cluster->blue.center+=(double) ScaleQuantumToChar(
1105               GetPixelBlue(image,p));
1106             cluster->count++;
1107             break;
1108           }
1109       p+=GetPixelChannels(image);
1110     }
1111     proceed=SetImageProgress(image,SegmentImageTag,(MagickOffsetType) y,
1112       2*image->rows);
1113     if (proceed == MagickFalse)
1114       break;
1115   }
1116   /*
1117     Remove clusters that do not meet minimum cluster threshold.
1118   */
1119   count=0;
1120   last_cluster=head;
1121   next_cluster=head;
1122   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1123   {
1124     next_cluster=cluster->next;
1125     if ((cluster->count > 0) &&
1126         (cluster->count >= (count*cluster_threshold/100.0)))
1127       {
1128         /*
1129           Initialize cluster.
1130         */
1131         cluster->id=count;
1132         cluster->red.center/=cluster->count;
1133         cluster->green.center/=cluster->count;
1134         cluster->blue.center/=cluster->count;
1135         count++;
1136         last_cluster=cluster;
1137         continue;
1138       }
1139     /*
1140       Delete cluster.
1141     */
1142     if (cluster == head)
1143       head=next_cluster;
1144     else
1145       last_cluster->next=next_cluster;
1146     cluster=(Cluster *) RelinquishMagickMemory(cluster);
1147   }
1148   object=head;
1149   background=head;
1150   if (count > 1)
1151     {
1152       object=head->next;
1153       for (cluster=object; cluster->next != (Cluster *) NULL; )
1154       {
1155         if (cluster->count < object->count)
1156           object=cluster;
1157         cluster=cluster->next;
1158       }
1159       background=head->next;
1160       for (cluster=background; cluster->next != (Cluster *) NULL; )
1161       {
1162         if (cluster->count > background->count)
1163           background=cluster;
1164         cluster=cluster->next;
1165       }
1166     }
1167   if (background != (Cluster *) NULL)
1168     {
1169       threshold=(background->red.center+object->red.center)/2.0;
1170       pixel->red=(double) ScaleCharToQuantum((unsigned char)
1171         (threshold+0.5));
1172       threshold=(background->green.center+object->green.center)/2.0;
1173       pixel->green=(double) ScaleCharToQuantum((unsigned char)
1174         (threshold+0.5));
1175       threshold=(background->blue.center+object->blue.center)/2.0;
1176       pixel->blue=(double) ScaleCharToQuantum((unsigned char)
1177         (threshold+0.5));
1178     }
1179   /*
1180     Relinquish resources.
1181   */
1182   for (cluster=head; cluster != (Cluster *) NULL; cluster=next_cluster)
1183   {
1184     next_cluster=cluster->next;
1185     cluster=(Cluster *) RelinquishMagickMemory(cluster);
1186   }
1187   for (i=0; i < MaxDimension; i++)
1188   {
1189     extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1190     histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1191   }
1192   return(MagickTrue);
1193 }
1194 \f
1195 /*
1196 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1197 %                                                                             %
1198 %                                                                             %
1199 %                                                                             %
1200 +  I n i t i a l i z e H i s t o g r a m                                      %
1201 %                                                                             %
1202 %                                                                             %
1203 %                                                                             %
1204 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1205 %
1206 %  InitializeHistogram() computes the histogram for an image.
1207 %
1208 %  The format of the InitializeHistogram method is:
1209 %
1210 %      InitializeHistogram(const Image *image,ssize_t **histogram)
1211 %
1212 %  A description of each parameter follows.
1213 %
1214 %    o image: Specifies a pointer to an Image structure;  returned from
1215 %      ReadImage.
1216 %
1217 %    o histogram: Specifies an array of integers representing the number
1218 %      of pixels for each intensity of a particular color component.
1219 %
1220 */
1221 static void InitializeHistogram(const Image *image,ssize_t **histogram,
1222   ExceptionInfo *exception)
1223 {
1224   register const Quantum
1225     *p;
1226
1227   register ssize_t
1228     i,
1229     x;
1230
1231   ssize_t
1232     y;
1233
1234   /*
1235     Initialize histogram.
1236   */
1237   for (i=0; i <= 255; i++)
1238   {
1239     histogram[Red][i]=0;
1240     histogram[Green][i]=0;
1241     histogram[Blue][i]=0;
1242   }
1243   for (y=0; y < (ssize_t) image->rows; y++)
1244   {
1245     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1246     if (p == (const Quantum *) NULL)
1247       break;
1248     for (x=0; x < (ssize_t) image->columns; x++)
1249     {
1250       histogram[Red][(ssize_t) ScaleQuantumToChar(GetPixelRed(image,p))]++;
1251       histogram[Green][(ssize_t) ScaleQuantumToChar(GetPixelGreen(image,p))]++;
1252       histogram[Blue][(ssize_t) ScaleQuantumToChar(GetPixelBlue(image,p))]++;
1253       p+=GetPixelChannels(image);
1254     }
1255   }
1256 }
1257 \f
1258 /*
1259 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1260 %                                                                             %
1261 %                                                                             %
1262 %                                                                             %
1263 +   I n i t i a l i z e I n t e r v a l T r e e                               %
1264 %                                                                             %
1265 %                                                                             %
1266 %                                                                             %
1267 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1268 %
1269 %  InitializeIntervalTree() initializes an interval tree from the lists of
1270 %  zero crossings.
1271 %
1272 %  The format of the InitializeIntervalTree method is:
1273 %
1274 %      InitializeIntervalTree(IntervalTree **list,ssize_t *number_nodes,
1275 %        IntervalTree *node)
1276 %
1277 %  A description of each parameter follows.
1278 %
1279 %    o zero_crossing: Specifies an array of structures of type ZeroCrossing.
1280 %
1281 %    o number_crossings: This size_t specifies the number of elements
1282 %      in the zero_crossing array.
1283 %
1284 */
1285
1286 static void InitializeList(IntervalTree **list,ssize_t *number_nodes,
1287   IntervalTree *node)
1288 {
1289   if (node == (IntervalTree *) NULL)
1290     return;
1291   if (node->child == (IntervalTree *) NULL)
1292     list[(*number_nodes)++]=node;
1293   InitializeList(list,number_nodes,node->sibling);
1294   InitializeList(list,number_nodes,node->child);
1295 }
1296
1297 static void MeanStability(IntervalTree *node)
1298 {
1299   register IntervalTree
1300     *child;
1301
1302   if (node == (IntervalTree *) NULL)
1303     return;
1304   node->mean_stability=0.0;
1305   child=node->child;
1306   if (child != (IntervalTree *) NULL)
1307     {
1308       register ssize_t
1309         count;
1310
1311       register double
1312         sum;
1313
1314       sum=0.0;
1315       count=0;
1316       for ( ; child != (IntervalTree *) NULL; child=child->sibling)
1317       {
1318         sum+=child->stability;
1319         count++;
1320       }
1321       node->mean_stability=sum/(double) count;
1322     }
1323   MeanStability(node->sibling);
1324   MeanStability(node->child);
1325 }
1326
1327 static void Stability(IntervalTree *node)
1328 {
1329   if (node == (IntervalTree *) NULL)
1330     return;
1331   if (node->child == (IntervalTree *) NULL)
1332     node->stability=0.0;
1333   else
1334     node->stability=node->tau-(node->child)->tau;
1335   Stability(node->sibling);
1336   Stability(node->child);
1337 }
1338
1339 static IntervalTree *InitializeIntervalTree(const ZeroCrossing *zero_crossing,
1340   const size_t number_crossings)
1341 {
1342   IntervalTree
1343     *head,
1344     **list,
1345     *node,
1346     *root;
1347
1348   register ssize_t
1349     i;
1350
1351   ssize_t
1352     j,
1353     k,
1354     left,
1355     number_nodes;
1356
1357   /*
1358     Allocate interval tree.
1359   */
1360   list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1361     sizeof(*list));
1362   if (list == (IntervalTree **) NULL)
1363     return((IntervalTree *) NULL);
1364   /*
1365     The root is the entire histogram.
1366   */
1367   root=(IntervalTree *) AcquireMagickMemory(sizeof(*root));
1368   root->child=(IntervalTree *) NULL;
1369   root->sibling=(IntervalTree *) NULL;
1370   root->tau=0.0;
1371   root->left=0;
1372   root->right=255;
1373   for (i=(-1); i < (ssize_t) number_crossings; i++)
1374   {
1375     /*
1376       Initialize list with all nodes with no children.
1377     */
1378     number_nodes=0;
1379     InitializeList(list,&number_nodes,root);
1380     /*
1381       Split list.
1382     */
1383     for (j=0; j < number_nodes; j++)
1384     {
1385       head=list[j];
1386       left=head->left;
1387       node=head;
1388       for (k=head->left+1; k < head->right; k++)
1389       {
1390         if (zero_crossing[i+1].crossings[k] != 0)
1391           {
1392             if (node == head)
1393               {
1394                 node->child=(IntervalTree *) AcquireMagickMemory(
1395                   sizeof(*node->child));
1396                 node=node->child;
1397               }
1398             else
1399               {
1400                 node->sibling=(IntervalTree *) AcquireMagickMemory(
1401                   sizeof(*node->sibling));
1402                 node=node->sibling;
1403               }
1404             node->tau=zero_crossing[i+1].tau;
1405             node->child=(IntervalTree *) NULL;
1406             node->sibling=(IntervalTree *) NULL;
1407             node->left=left;
1408             node->right=k;
1409             left=k;
1410           }
1411         }
1412       if (left != head->left)
1413         {
1414           node->sibling=(IntervalTree *) AcquireMagickMemory(
1415             sizeof(*node->sibling));
1416           node=node->sibling;
1417           node->tau=zero_crossing[i+1].tau;
1418           node->child=(IntervalTree *) NULL;
1419           node->sibling=(IntervalTree *) NULL;
1420           node->left=left;
1421           node->right=head->right;
1422         }
1423     }
1424   }
1425   /*
1426     Determine the stability: difference between a nodes tau and its child.
1427   */
1428   Stability(root->child);
1429   MeanStability(root->child);
1430   list=(IntervalTree **) RelinquishMagickMemory(list);
1431   return(root);
1432 }
1433 \f
1434 /*
1435 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1436 %                                                                             %
1437 %                                                                             %
1438 %                                                                             %
1439 +   O p t i m a l T a u                                                       %
1440 %                                                                             %
1441 %                                                                             %
1442 %                                                                             %
1443 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1444 %
1445 %  OptimalTau() finds the optimal tau for each band of the histogram.
1446 %
1447 %  The format of the OptimalTau method is:
1448 %
1449 %    double OptimalTau(const ssize_t *histogram,const double max_tau,
1450 %      const double min_tau,const double delta_tau,
1451 %      const double smooth_threshold,short *extrema)
1452 %
1453 %  A description of each parameter follows.
1454 %
1455 %    o histogram: Specifies an array of integers representing the number
1456 %      of pixels for each intensity of a particular color component.
1457 %
1458 %    o extrema:  Specifies a pointer to an array of integers.  They
1459 %      represent the peaks and valleys of the histogram for each color
1460 %      component.
1461 %
1462 */
1463
1464 static void ActiveNodes(IntervalTree **list,ssize_t *number_nodes,
1465   IntervalTree *node)
1466 {
1467   if (node == (IntervalTree *) NULL)
1468     return;
1469   if (node->stability >= node->mean_stability)
1470     {
1471       list[(*number_nodes)++]=node;
1472       ActiveNodes(list,number_nodes,node->sibling);
1473     }
1474   else
1475     {
1476       ActiveNodes(list,number_nodes,node->sibling);
1477       ActiveNodes(list,number_nodes,node->child);
1478     }
1479 }
1480
1481 static void FreeNodes(IntervalTree *node)
1482 {
1483   if (node == (IntervalTree *) NULL)
1484     return;
1485   FreeNodes(node->sibling);
1486   FreeNodes(node->child);
1487   node=(IntervalTree *) RelinquishMagickMemory(node);
1488 }
1489
1490 static double OptimalTau(const ssize_t *histogram,const double max_tau,
1491   const double min_tau,const double delta_tau,const double smooth_threshold,
1492   short *extrema)
1493 {
1494   IntervalTree
1495     **list,
1496     *node,
1497     *root;
1498
1499   MagickBooleanType
1500     peak;
1501
1502   double
1503     average_tau,
1504     *derivative,
1505     *second_derivative,
1506     tau,
1507     value;
1508
1509   register ssize_t
1510     i,
1511     x;
1512
1513   size_t
1514     count,
1515     number_crossings;
1516
1517   ssize_t
1518     index,
1519     j,
1520     k,
1521     number_nodes;
1522
1523   ZeroCrossing
1524     *zero_crossing;
1525
1526   /*
1527     Allocate interval tree.
1528   */
1529   list=(IntervalTree **) AcquireQuantumMemory((size_t) TreeLength,
1530     sizeof(*list));
1531   if (list == (IntervalTree **) NULL)
1532     return(0.0);
1533   /*
1534     Allocate zero crossing list.
1535   */
1536   count=(size_t) ((max_tau-min_tau)/delta_tau)+2;
1537   zero_crossing=(ZeroCrossing *) AcquireQuantumMemory((size_t) count,
1538     sizeof(*zero_crossing));
1539   if (zero_crossing == (ZeroCrossing *) NULL)
1540     return(0.0);
1541   for (i=0; i < (ssize_t) count; i++)
1542     zero_crossing[i].tau=(-1.0);
1543   /*
1544     Initialize zero crossing list.
1545   */
1546   derivative=(double *) AcquireQuantumMemory(256,sizeof(*derivative));
1547   second_derivative=(double *) AcquireQuantumMemory(256,
1548     sizeof(*second_derivative));
1549   if ((derivative == (double *) NULL) ||
1550       (second_derivative == (double *) NULL))
1551     ThrowFatalException(ResourceLimitFatalError,
1552       "UnableToAllocateDerivatives");
1553   i=0;
1554   for (tau=max_tau; tau >= min_tau; tau-=delta_tau)
1555   {
1556     zero_crossing[i].tau=tau;
1557     ScaleSpace(histogram,tau,zero_crossing[i].histogram);
1558     DerivativeHistogram(zero_crossing[i].histogram,derivative);
1559     DerivativeHistogram(derivative,second_derivative);
1560     ZeroCrossHistogram(second_derivative,smooth_threshold,
1561       zero_crossing[i].crossings);
1562     i++;
1563   }
1564   /*
1565     Add an entry for the original histogram.
1566   */
1567   zero_crossing[i].tau=0.0;
1568   for (j=0; j <= 255; j++)
1569     zero_crossing[i].histogram[j]=(double) histogram[j];
1570   DerivativeHistogram(zero_crossing[i].histogram,derivative);
1571   DerivativeHistogram(derivative,second_derivative);
1572   ZeroCrossHistogram(second_derivative,smooth_threshold,
1573     zero_crossing[i].crossings);
1574   number_crossings=(size_t) i;
1575   derivative=(double *) RelinquishMagickMemory(derivative);
1576   second_derivative=(double *)
1577     RelinquishMagickMemory(second_derivative);
1578   /*
1579     Ensure the scale-space fingerprints form lines in scale-space, not loops.
1580   */
1581   ConsolidateCrossings(zero_crossing,number_crossings);
1582   /*
1583     Force endpoints to be included in the interval.
1584   */
1585   for (i=0; i <= (ssize_t) number_crossings; i++)
1586   {
1587     for (j=0; j < 255; j++)
1588       if (zero_crossing[i].crossings[j] != 0)
1589         break;
1590     zero_crossing[i].crossings[0]=(-zero_crossing[i].crossings[j]);
1591     for (j=255; j > 0; j--)
1592       if (zero_crossing[i].crossings[j] != 0)
1593         break;
1594     zero_crossing[i].crossings[255]=(-zero_crossing[i].crossings[j]);
1595   }
1596   /*
1597     Initialize interval tree.
1598   */
1599   root=InitializeIntervalTree(zero_crossing,number_crossings);
1600   if (root == (IntervalTree *) NULL)
1601     return(0.0);
1602   /*
1603     Find active nodes:  stability is greater (or equal) to the mean stability of
1604     its children.
1605   */
1606   number_nodes=0;
1607   ActiveNodes(list,&number_nodes,root->child);
1608   /*
1609     Initialize extrema.
1610   */
1611   for (i=0; i <= 255; i++)
1612     extrema[i]=0;
1613   for (i=0; i < number_nodes; i++)
1614   {
1615     /*
1616       Find this tau in zero crossings list.
1617     */
1618     k=0;
1619     node=list[i];
1620     for (j=0; j <= (ssize_t) number_crossings; j++)
1621       if (zero_crossing[j].tau == node->tau)
1622         k=j;
1623     /*
1624       Find the value of the peak.
1625     */
1626     peak=zero_crossing[k].crossings[node->right] == -1 ? MagickTrue :
1627       MagickFalse;
1628     index=node->left;
1629     value=zero_crossing[k].histogram[index];
1630     for (x=node->left; x <= node->right; x++)
1631     {
1632       if (peak != MagickFalse)
1633         {
1634           if (zero_crossing[k].histogram[x] > value)
1635             {
1636               value=zero_crossing[k].histogram[x];
1637               index=x;
1638             }
1639         }
1640       else
1641         if (zero_crossing[k].histogram[x] < value)
1642           {
1643             value=zero_crossing[k].histogram[x];
1644             index=x;
1645           }
1646     }
1647     for (x=node->left; x <= node->right; x++)
1648     {
1649       if (index == 0)
1650         index=256;
1651       if (peak != MagickFalse)
1652         extrema[x]=(short) index;
1653       else
1654         extrema[x]=(short) (-index);
1655     }
1656   }
1657   /*
1658     Determine the average tau.
1659   */
1660   average_tau=0.0;
1661   for (i=0; i < number_nodes; i++)
1662     average_tau+=list[i]->tau;
1663   average_tau/=(double) number_nodes;
1664   /*
1665     Relinquish resources.
1666   */
1667   FreeNodes(root);
1668   zero_crossing=(ZeroCrossing *) RelinquishMagickMemory(zero_crossing);
1669   list=(IntervalTree **) RelinquishMagickMemory(list);
1670   return(average_tau);
1671 }
1672 \f
1673 /*
1674 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1675 %                                                                             %
1676 %                                                                             %
1677 %                                                                             %
1678 +   S c a l e S p a c e                                                       %
1679 %                                                                             %
1680 %                                                                             %
1681 %                                                                             %
1682 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1683 %
1684 %  ScaleSpace() performs a scale-space filter on the 1D histogram.
1685 %
1686 %  The format of the ScaleSpace method is:
1687 %
1688 %      ScaleSpace(const ssize_t *histogram,const double tau,
1689 %        double *scale_histogram)
1690 %
1691 %  A description of each parameter follows.
1692 %
1693 %    o histogram: Specifies an array of doubles representing the number
1694 %      of pixels for each intensity of a particular color component.
1695 %
1696 */
1697
1698 static void ScaleSpace(const ssize_t *histogram,const double tau,
1699   double *scale_histogram)
1700 {
1701   double
1702     alpha,
1703     beta,
1704     *gamma,
1705     sum;
1706
1707   register ssize_t
1708     u,
1709     x;
1710
1711   gamma=(double *) AcquireQuantumMemory(256,sizeof(*gamma));
1712   if (gamma == (double *) NULL)
1713     ThrowFatalException(ResourceLimitFatalError,
1714       "UnableToAllocateGammaMap");
1715   alpha=PerceptibleReciprocal(tau*sqrt(2.0*MagickPI));
1716   beta=(-1.0*PerceptibleReciprocal(2.0*tau*tau));
1717   for (x=0; x <= 255; x++)
1718     gamma[x]=0.0;
1719   for (x=0; x <= 255; x++)
1720   {
1721     gamma[x]=exp((double) beta*x*x);
1722     if (gamma[x] < MagickEpsilon)
1723       break;
1724   }
1725   for (x=0; x <= 255; x++)
1726   {
1727     sum=0.0;
1728     for (u=0; u <= 255; u++)
1729       sum+=(double) histogram[u]*gamma[MagickAbsoluteValue(x-u)];
1730     scale_histogram[x]=alpha*sum;
1731   }
1732   gamma=(double *) RelinquishMagickMemory(gamma);
1733 }
1734 \f
1735 /*
1736 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1737 %                                                                             %
1738 %                                                                             %
1739 %                                                                             %
1740 %  S e g m e n t I m a g e                                                    %
1741 %                                                                             %
1742 %                                                                             %
1743 %                                                                             %
1744 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1745 %
1746 %  SegmentImage() segment an image by analyzing the histograms of the color
1747 %  components and identifying units that are homogeneous with the fuzzy
1748 %  C-means technique.
1749 %
1750 %  The format of the SegmentImage method is:
1751 %
1752 %      MagickBooleanType SegmentImage(Image *image,
1753 %        const ColorspaceType colorspace,const MagickBooleanType verbose,
1754 %        const double cluster_threshold,const double smooth_threshold,
1755 %        ExceptionInfo *exception)
1756 %
1757 %  A description of each parameter follows.
1758 %
1759 %    o image: the image.
1760 %
1761 %    o colorspace: Indicate the colorspace.
1762 %
1763 %    o verbose:  Set to MagickTrue to print detailed information about the
1764 %      identified classes.
1765 %
1766 %    o cluster_threshold:  This represents the minimum number of pixels
1767 %      contained in a hexahedra before it can be considered valid (expressed
1768 %      as a percentage).
1769 %
1770 %    o smooth_threshold: the smoothing threshold eliminates noise in the second
1771 %      derivative of the histogram.  As the value is increased, you can expect a
1772 %      smoother second derivative.
1773 %
1774 %    o exception: return any errors or warnings in this structure.
1775 %
1776 */
1777 MagickExport MagickBooleanType SegmentImage(Image *image,
1778   const ColorspaceType colorspace,const MagickBooleanType verbose,
1779   const double cluster_threshold,const double smooth_threshold,
1780   ExceptionInfo *exception)
1781 {
1782   ColorspaceType
1783     previous_colorspace;
1784
1785   MagickBooleanType
1786     status;
1787
1788   register ssize_t
1789     i;
1790
1791   short
1792     *extrema[MaxDimension];
1793
1794   ssize_t
1795     *histogram[MaxDimension];
1796
1797   /*
1798     Allocate histogram and extrema.
1799   */
1800   assert(image != (Image *) NULL);
1801   assert(image->signature == MagickSignature);
1802   if (image->debug != MagickFalse)
1803     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1804   for (i=0; i < MaxDimension; i++)
1805   {
1806     histogram[i]=(ssize_t *) AcquireQuantumMemory(256,sizeof(**histogram));
1807     extrema[i]=(short *) AcquireQuantumMemory(256,sizeof(**extrema));
1808     if ((histogram[i] == (ssize_t *) NULL) || (extrema[i] == (short *) NULL))
1809       {
1810         for (i-- ; i >= 0; i--)
1811         {
1812           extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1813           histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1814         }
1815         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
1816           image->filename)
1817       }
1818   }
1819   /*
1820     Initialize histogram.
1821   */
1822   previous_colorspace=image->colorspace;
1823   (void) TransformImageColorspace(image,colorspace,exception);
1824   InitializeHistogram(image,histogram,exception);
1825   (void) OptimalTau(histogram[Red],Tau,0.2,DeltaTau,
1826     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Red]);
1827   (void) OptimalTau(histogram[Green],Tau,0.2,DeltaTau,
1828     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Green]);
1829   (void) OptimalTau(histogram[Blue],Tau,0.2,DeltaTau,
1830     smooth_threshold == 0.0 ? 1.0 : smooth_threshold,extrema[Blue]);
1831   /*
1832     Classify using the fuzzy c-Means technique.
1833   */
1834   status=Classify(image,extrema,cluster_threshold,WeightingExponent,verbose,
1835     exception);
1836   (void) TransformImageColorspace(image,previous_colorspace,exception);
1837   /*
1838     Relinquish resources.
1839   */
1840   for (i=0; i < MaxDimension; i++)
1841   {
1842     extrema[i]=(short *) RelinquishMagickMemory(extrema[i]);
1843     histogram[i]=(ssize_t *) RelinquishMagickMemory(histogram[i]);
1844   }
1845   return(status);
1846 }
1847 \f
1848 /*
1849 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1850 %                                                                             %
1851 %                                                                             %
1852 %                                                                             %
1853 +   Z e r o C r o s s H i s t o g r a m                                       %
1854 %                                                                             %
1855 %                                                                             %
1856 %                                                                             %
1857 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1858 %
1859 %  ZeroCrossHistogram() find the zero crossings in a histogram and marks
1860 %  directions as:  1 is negative to positive; 0 is zero crossing; and -1
1861 %  is positive to negative.
1862 %
1863 %  The format of the ZeroCrossHistogram method is:
1864 %
1865 %      ZeroCrossHistogram(double *second_derivative,
1866 %        const double smooth_threshold,short *crossings)
1867 %
1868 %  A description of each parameter follows.
1869 %
1870 %    o second_derivative: Specifies an array of doubles representing the
1871 %      second derivative of the histogram of a particular color component.
1872 %
1873 %    o crossings:  This array of integers is initialized with
1874 %      -1, 0, or 1 representing the slope of the first derivative of the
1875 %      of a particular color component.
1876 %
1877 */
1878 static void ZeroCrossHistogram(double *second_derivative,
1879   const double smooth_threshold,short *crossings)
1880 {
1881   register ssize_t
1882     i;
1883
1884   ssize_t
1885     parity;
1886
1887   /*
1888     Merge low numbers to zero to help prevent noise.
1889   */
1890   for (i=0; i <= 255; i++)
1891     if ((second_derivative[i] < smooth_threshold) &&
1892         (second_derivative[i] >= -smooth_threshold))
1893       second_derivative[i]=0.0;
1894   /*
1895     Mark zero crossings.
1896   */
1897   parity=0;
1898   for (i=0; i <= 255; i++)
1899   {
1900     crossings[i]=0;
1901     if (second_derivative[i] < 0.0)
1902       {
1903         if (parity > 0)
1904           crossings[i]=(-1);
1905         parity=1;
1906       }
1907     else
1908       if (second_derivative[i] > 0.0)
1909         {
1910           if (parity < 0)
1911             crossings[i]=1;
1912           parity=(-1);
1913         }
1914   }
1915 }