elbg.c
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1 /*
2  * Copyright (C) 2007 Vitor Sessak <vitor1001@gmail.com>
3  *
4  * This file is part of Libav.
5  *
6  * Libav is free software; you can redistribute it and/or
7  * modify it under the terms of the GNU Lesser General Public
8  * License as published by the Free Software Foundation; either
9  * version 2.1 of the License, or (at your option) any later version.
10  *
11  * Libav is distributed in the hope that it will be useful,
12  * but WITHOUT ANY WARRANTY; without even the implied warranty of
13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14  * Lesser General Public License for more details.
15  *
16  * You should have received a copy of the GNU Lesser General Public
17  * License along with Libav; if not, write to the Free Software
18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
19  */
20 
26 #include <string.h>
27 
28 #include "libavutil/lfg.h"
29 #include "elbg.h"
30 #include "avcodec.h"
31 
32 #define DELTA_ERR_MAX 0.1
33 
34 
37 typedef struct cell_s {
38  int index;
39  struct cell_s *next;
40 } cell;
41 
45 typedef struct{
46  int error;
47  int dim;
48  int numCB;
49  int *codebook;
51  int *utility;
53  int *nearest_cb;
54  int *points;
56  int *scratchbuf;
57 } elbg_data;
58 
59 static inline int distance_limited(int *a, int *b, int dim, int limit)
60 {
61  int i, dist=0;
62  for (i=0; i<dim; i++) {
63  dist += (a[i] - b[i])*(a[i] - b[i]);
64  if (dist > limit)
65  return INT_MAX;
66  }
67 
68  return dist;
69 }
70 
71 static inline void vect_division(int *res, int *vect, int div, int dim)
72 {
73  int i;
74  if (div > 1)
75  for (i=0; i<dim; i++)
76  res[i] = ROUNDED_DIV(vect[i],div);
77  else if (res != vect)
78  memcpy(res, vect, dim*sizeof(int));
79 
80 }
81 
82 static int eval_error_cell(elbg_data *elbg, int *centroid, cell *cells)
83 {
84  int error=0;
85  for (; cells; cells=cells->next)
86  error += distance_limited(centroid, elbg->points + cells->index*elbg->dim, elbg->dim, INT_MAX);
87 
88  return error;
89 }
90 
91 static int get_closest_codebook(elbg_data *elbg, int index)
92 {
93  int i, pick=0, diff, diff_min = INT_MAX;
94  for (i=0; i<elbg->numCB; i++)
95  if (i != index) {
96  diff = distance_limited(elbg->codebook + i*elbg->dim, elbg->codebook + index*elbg->dim, elbg->dim, diff_min);
97  if (diff < diff_min) {
98  pick = i;
99  diff_min = diff;
100  }
101  }
102  return pick;
103 }
104 
106 {
107  int i=0;
108  /* Using linear search, do binary if it ever turns to be speed critical */
109  int r = av_lfg_get(elbg->rand_state)%elbg->utility_inc[elbg->numCB-1] + 1;
110  while (elbg->utility_inc[i] < r)
111  i++;
112 
113  assert(elbg->cells[i]);
114 
115  return i;
116 }
117 
121 static int simple_lbg(elbg_data *elbg,
122  int dim,
123  int *centroid[3],
124  int newutility[3],
125  int *points,
126  cell *cells)
127 {
128  int i, idx;
129  int numpoints[2] = {0,0};
130  int *newcentroid[2] = {
131  elbg->scratchbuf + 3*dim,
132  elbg->scratchbuf + 4*dim
133  };
134  cell *tempcell;
135 
136  memset(newcentroid[0], 0, 2 * dim * sizeof(*newcentroid[0]));
137 
138  newutility[0] =
139  newutility[1] = 0;
140 
141  for (tempcell = cells; tempcell; tempcell=tempcell->next) {
142  idx = distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX)>=
143  distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX);
144  numpoints[idx]++;
145  for (i=0; i<dim; i++)
146  newcentroid[idx][i] += points[tempcell->index*dim + i];
147  }
148 
149  vect_division(centroid[0], newcentroid[0], numpoints[0], dim);
150  vect_division(centroid[1], newcentroid[1], numpoints[1], dim);
151 
152  for (tempcell = cells; tempcell; tempcell=tempcell->next) {
153  int dist[2] = {distance_limited(centroid[0], points + tempcell->index*dim, dim, INT_MAX),
154  distance_limited(centroid[1], points + tempcell->index*dim, dim, INT_MAX)};
155  int idx = dist[0] > dist[1];
156  newutility[idx] += dist[idx];
157  }
158 
159  return newutility[0] + newutility[1];
160 }
161 
162 static void get_new_centroids(elbg_data *elbg, int huc, int *newcentroid_i,
163  int *newcentroid_p)
164 {
165  cell *tempcell;
166  int *min = newcentroid_i;
167  int *max = newcentroid_p;
168  int i;
169 
170  for (i=0; i< elbg->dim; i++) {
171  min[i]=INT_MAX;
172  max[i]=0;
173  }
174 
175  for (tempcell = elbg->cells[huc]; tempcell; tempcell = tempcell->next)
176  for(i=0; i<elbg->dim; i++) {
177  min[i]=FFMIN(min[i], elbg->points[tempcell->index*elbg->dim + i]);
178  max[i]=FFMAX(max[i], elbg->points[tempcell->index*elbg->dim + i]);
179  }
180 
181  for (i=0; i<elbg->dim; i++) {
182  int ni = min[i] + (max[i] - min[i])/3;
183  int np = min[i] + (2*(max[i] - min[i]))/3;
184  newcentroid_i[i] = ni;
185  newcentroid_p[i] = np;
186  }
187 }
188 
198 static void shift_codebook(elbg_data *elbg, int *indexes,
199  int *newcentroid[3])
200 {
201  cell *tempdata;
202  cell **pp = &elbg->cells[indexes[2]];
203 
204  while(*pp)
205  pp= &(*pp)->next;
206 
207  *pp = elbg->cells[indexes[0]];
208 
209  elbg->cells[indexes[0]] = NULL;
210  tempdata = elbg->cells[indexes[1]];
211  elbg->cells[indexes[1]] = NULL;
212 
213  while(tempdata) {
214  cell *tempcell2 = tempdata->next;
215  int idx = distance_limited(elbg->points + tempdata->index*elbg->dim,
216  newcentroid[0], elbg->dim, INT_MAX) >
217  distance_limited(elbg->points + tempdata->index*elbg->dim,
218  newcentroid[1], elbg->dim, INT_MAX);
219 
220  tempdata->next = elbg->cells[indexes[idx]];
221  elbg->cells[indexes[idx]] = tempdata;
222  tempdata = tempcell2;
223  }
224 }
225 
226 static void evaluate_utility_inc(elbg_data *elbg)
227 {
228  int i, inc=0;
229 
230  for (i=0; i < elbg->numCB; i++) {
231  if (elbg->numCB*elbg->utility[i] > elbg->error)
232  inc += elbg->utility[i];
233  elbg->utility_inc[i] = inc;
234  }
235 }
236 
237 
238 static void update_utility_and_n_cb(elbg_data *elbg, int idx, int newutility)
239 {
240  cell *tempcell;
241 
242  elbg->utility[idx] = newutility;
243  for (tempcell=elbg->cells[idx]; tempcell; tempcell=tempcell->next)
244  elbg->nearest_cb[tempcell->index] = idx;
245 }
246 
254 static void try_shift_candidate(elbg_data *elbg, int idx[3])
255 {
256  int j, k, olderror=0, newerror, cont=0;
257  int newutility[3];
258  int *newcentroid[3] = {
259  elbg->scratchbuf,
260  elbg->scratchbuf + elbg->dim,
261  elbg->scratchbuf + 2*elbg->dim
262  };
263  cell *tempcell;
264 
265  for (j=0; j<3; j++)
266  olderror += elbg->utility[idx[j]];
267 
268  memset(newcentroid[2], 0, elbg->dim*sizeof(int));
269 
270  for (k=0; k<2; k++)
271  for (tempcell=elbg->cells[idx[2*k]]; tempcell; tempcell=tempcell->next) {
272  cont++;
273  for (j=0; j<elbg->dim; j++)
274  newcentroid[2][j] += elbg->points[tempcell->index*elbg->dim + j];
275  }
276 
277  vect_division(newcentroid[2], newcentroid[2], cont, elbg->dim);
278 
279  get_new_centroids(elbg, idx[1], newcentroid[0], newcentroid[1]);
280 
281  newutility[2] = eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[0]]);
282  newutility[2] += eval_error_cell(elbg, newcentroid[2], elbg->cells[idx[2]]);
283 
284  newerror = newutility[2];
285 
286  newerror += simple_lbg(elbg, elbg->dim, newcentroid, newutility, elbg->points,
287  elbg->cells[idx[1]]);
288 
289  if (olderror > newerror) {
290  shift_codebook(elbg, idx, newcentroid);
291 
292  elbg->error += newerror - olderror;
293 
294  for (j=0; j<3; j++)
295  update_utility_and_n_cb(elbg, idx[j], newutility[j]);
296 
297  evaluate_utility_inc(elbg);
298  }
299  }
300 
304 static void do_shiftings(elbg_data *elbg)
305 {
306  int idx[3];
307 
308  evaluate_utility_inc(elbg);
309 
310  for (idx[0]=0; idx[0] < elbg->numCB; idx[0]++)
311  if (elbg->numCB*elbg->utility[idx[0]] < elbg->error) {
312  if (elbg->utility_inc[elbg->numCB-1] == 0)
313  return;
314 
315  idx[1] = get_high_utility_cell(elbg);
316  idx[2] = get_closest_codebook(elbg, idx[0]);
317 
318  if (idx[1] != idx[0] && idx[1] != idx[2])
319  try_shift_candidate(elbg, idx);
320  }
321 }
322 
323 #define BIG_PRIME 433494437LL
324 
325 void ff_init_elbg(int *points, int dim, int numpoints, int *codebook,
326  int numCB, int max_steps, int *closest_cb,
327  AVLFG *rand_state)
328 {
329  int i, k;
330 
331  if (numpoints > 24*numCB) {
332  /* ELBG is very costly for a big number of points. So if we have a lot
333  of them, get a good initial codebook to save on iterations */
334  int *temp_points = av_malloc(dim*(numpoints/8)*sizeof(int));
335  for (i=0; i<numpoints/8; i++) {
336  k = (i*BIG_PRIME) % numpoints;
337  memcpy(temp_points + i*dim, points + k*dim, dim*sizeof(int));
338  }
339 
340  ff_init_elbg(temp_points, dim, numpoints/8, codebook, numCB, 2*max_steps, closest_cb, rand_state);
341  ff_do_elbg(temp_points, dim, numpoints/8, codebook, numCB, 2*max_steps, closest_cb, rand_state);
342 
343  av_free(temp_points);
344 
345  } else // If not, initialize the codebook with random positions
346  for (i=0; i < numCB; i++)
347  memcpy(codebook + i*dim, points + ((i*BIG_PRIME)%numpoints)*dim,
348  dim*sizeof(int));
349 
350 }
351 
352 void ff_do_elbg(int *points, int dim, int numpoints, int *codebook,
353  int numCB, int max_steps, int *closest_cb,
354  AVLFG *rand_state)
355 {
356  int dist;
357  elbg_data elbg_d;
358  elbg_data *elbg = &elbg_d;
359  int i, j, k, last_error, steps=0;
360  int *dist_cb = av_malloc(numpoints*sizeof(int));
361  int *size_part = av_malloc(numCB*sizeof(int));
362  cell *list_buffer = av_malloc(numpoints*sizeof(cell));
363  cell *free_cells;
364  int best_dist, best_idx = 0;
365 
366  elbg->error = INT_MAX;
367  elbg->dim = dim;
368  elbg->numCB = numCB;
369  elbg->codebook = codebook;
370  elbg->cells = av_malloc(numCB*sizeof(cell *));
371  elbg->utility = av_malloc(numCB*sizeof(int));
372  elbg->nearest_cb = closest_cb;
373  elbg->points = points;
374  elbg->utility_inc = av_malloc(numCB*sizeof(int));
375  elbg->scratchbuf = av_malloc(5*dim*sizeof(int));
376 
377  elbg->rand_state = rand_state;
378 
379  do {
380  free_cells = list_buffer;
381  last_error = elbg->error;
382  steps++;
383  memset(elbg->utility, 0, numCB*sizeof(int));
384  memset(elbg->cells, 0, numCB*sizeof(cell *));
385 
386  elbg->error = 0;
387 
388  /* This loop evaluate the actual Voronoi partition. It is the most
389  costly part of the algorithm. */
390  for (i=0; i < numpoints; i++) {
391  best_dist = distance_limited(elbg->points + i*elbg->dim, elbg->codebook + best_idx*elbg->dim, dim, INT_MAX);
392  for (k=0; k < elbg->numCB; k++) {
393  dist = distance_limited(elbg->points + i*elbg->dim, elbg->codebook + k*elbg->dim, dim, best_dist);
394  if (dist < best_dist) {
395  best_dist = dist;
396  best_idx = k;
397  }
398  }
399  elbg->nearest_cb[i] = best_idx;
400  dist_cb[i] = best_dist;
401  elbg->error += dist_cb[i];
402  elbg->utility[elbg->nearest_cb[i]] += dist_cb[i];
403  free_cells->index = i;
404  free_cells->next = elbg->cells[elbg->nearest_cb[i]];
405  elbg->cells[elbg->nearest_cb[i]] = free_cells;
406  free_cells++;
407  }
408 
409  do_shiftings(elbg);
410 
411  memset(size_part, 0, numCB*sizeof(int));
412 
413  memset(elbg->codebook, 0, elbg->numCB*dim*sizeof(int));
414 
415  for (i=0; i < numpoints; i++) {
416  size_part[elbg->nearest_cb[i]]++;
417  for (j=0; j < elbg->dim; j++)
418  elbg->codebook[elbg->nearest_cb[i]*elbg->dim + j] +=
419  elbg->points[i*elbg->dim + j];
420  }
421 
422  for (i=0; i < elbg->numCB; i++)
423  vect_division(elbg->codebook + i*elbg->dim,
424  elbg->codebook + i*elbg->dim, size_part[i], elbg->dim);
425 
426  } while(((last_error - elbg->error) > DELTA_ERR_MAX*elbg->error) &&
427  (steps < max_steps));
428 
429  av_free(dist_cb);
430  av_free(size_part);
431  av_free(elbg->utility);
432  av_free(list_buffer);
433  av_free(elbg->cells);
434  av_free(elbg->utility_inc);
435  av_free(elbg->scratchbuf);
436 }