Visual Servoing Platform version 3.5.0
vpThreshold.cpp
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30 *
31 * Description:
32 * Automatic thresholding functions.
33 *
34 * Authors:
35 * Souriya Trinh
36 *
37 *****************************************************************************/
38
44#include <visp3/core/vpHistogram.h>
45#include <visp3/core/vpImageTools.h>
46#include <visp3/imgproc/vpImgproc.h>
47
48namespace
49{
50bool isBimodal(const std::vector<float> &hist_float)
51{
52 int modes = 0;
53
54 for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
55 if (hist_float[cpt - 1] < hist_float[cpt] && hist_float[cpt] > hist_float[cpt + 1]) {
56 modes++;
57 }
58
59 if (modes > 2) {
60 return false;
61 }
62 }
63
64 return (modes == 2);
65}
66
67int computeThresholdHuang(const vpHistogram &hist)
68{
69 // Code ported from the AutoThreshold ImageJ plugin:
70 // Implements Huang's fuzzy thresholding method
71 // Uses Shannon's entropy function (one can also use Yager's entropy
72 // function) Huang L.-K. and Wang M.-J.J. (1995) "Image Thresholding by
73 // Minimizing the Measures of Fuzziness" Pattern Recognition, 28(1): 41-51
74 // Reimplemented (to handle 16-bit efficiently) by Johannes Schindelin Jan
75 // 31, 2011
76
77 // Find first and last non-empty bin
78 size_t first, last;
79 for (first = 0; first < (size_t)hist.getSize() && hist[(unsigned char)first] == 0; first++) {
80 // do nothing
81 }
82
83 for (last = (size_t)hist.getSize() - 1; last > first && hist[(unsigned char)last] == 0; last--) {
84 // do nothing
85 }
86
87 if (first == last) {
88 return 0;
89 }
90
91 // Calculate the cumulative density and the weighted cumulative density
92 std::vector<float> S(last + 1);
93 std::vector<float> W(last + 1);
94
95 S[0] = (float)hist[0];
96 W[0] = 0.0f;
97 for (size_t i = std::max((size_t)1, first); i <= last; i++) {
98 S[i] = S[i - 1] + hist[(unsigned char)i];
99 W[i] = W[i - 1] + i * (float)hist[(unsigned char)i];
100 }
101
102 // Precalculate the summands of the entropy given the absolute difference x
103 // - mu (integral)
104 float C = (float)(last - first);
105 std::vector<float> Smu(last + 1 - first);
106
107 for (size_t i = 1; i < Smu.size(); i++) {
108 float mu = 1 / (1 + i / C);
109 Smu[i] = -mu * std::log(mu) - (1 - mu) * std::log(1 - mu);
110 }
111
112 // Calculate the threshold
113 int bestThreshold = 0;
114 float bestEntropy = std::numeric_limits<float>::max();
115
116 for (size_t threshold = first; threshold <= last; threshold++) {
117 float entropy = 0;
118 int mu = vpMath::round(W[threshold] / S[threshold]);
119 for (size_t i = first; i <= threshold; i++) {
120 entropy += Smu[(size_t)std::abs((int)i - mu)] * hist[(unsigned char)i];
121 }
122
123 mu = vpMath::round((W[last] - W[threshold]) / (S[last] - S[threshold]));
124 for (size_t i = threshold + 1; i <= last; i++) {
125 entropy += Smu[(size_t)std::abs((int)i - mu)] * hist[(unsigned char)i];
126 }
127
128 if (bestEntropy > entropy) {
129 bestEntropy = entropy;
130 bestThreshold = (int)threshold;
131 }
132 }
133
134 return bestThreshold;
135}
136
137int computeThresholdIntermodes(const vpHistogram &hist)
138{
139 if (hist.getSize() < 3) {
140 return -1;
141 }
142
143 // Code based on the AutoThreshold ImageJ plugin:
144 // J. M. S. Prewitt and M. L. Mendelsohn, "The analysis of cell images," in
145 // Annals of the New York Academy of Sciences, vol. 128, pp. 1035-1053,
146 // 1966. ported to ImageJ plugin by G.Landini from Antti Niemisto's Matlab
147 // code (GPL) Original Matlab code Copyright (C) 2004 Antti Niemisto See
148 // http://www.cs.tut.fi/~ant/histthresh/ for an excellent slide presentation
149 // and the original Matlab code.
150 //
151 // Assumes a bimodal histogram. The histogram needs is smoothed (using a
152 // running average of size 3, iteratively) until there are only two local
153 // maxima. j and k Threshold t is (j+k)/2. Images with histograms having
154 // extremely unequal peaks or a broad and flat valley are unsuitable for this
155 // method.
156
157 std::vector<float> hist_float(hist.getSize());
158 for (unsigned int cpt = 0; cpt < hist.getSize(); cpt++) {
159 hist_float[cpt] = (float)hist[cpt];
160 }
161
162 int iter = 0;
163 while (!isBimodal(hist_float)) {
164 // Smooth with a 3 point running mean filter
165 for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
166 hist_float[cpt] = (hist_float[cpt - 1] + hist_float[cpt] + hist_float[cpt + 1]) / 3;
167 }
168
169 // First value
170 hist_float[0] = (hist_float[0] + hist_float[1]) / 2.0f;
171
172 // Last value
173 hist_float[hist_float.size() - 1] = (hist_float.size() - 2 + hist_float.size() - 1) / 2.0f;
174
175 iter++;
176
177 if (iter > 10000) {
178 std::cerr << "Intermodes Threshold not found after 10000 iterations!" << std::endl;
179 return -1;
180 }
181 }
182
183 // The threshold is the mean between the two peaks.
184 int tt = 0;
185 for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
186 if (hist_float[cpt - 1] < hist_float[cpt] && hist_float[cpt] > hist_float[cpt + 1]) {
187 // Mode
188 tt += (int)cpt;
189 }
190 }
191
192 return (int)std::floor(tt / 2.0); // vpMath::round(tt / 2.0);
193}
194
195int computeThresholdIsoData(const vpHistogram &hist, unsigned int imageSize)
196{
197 int threshold = 0;
198
199 // Code based on BSD Matlab isodata implementation by zephyr
200 // STEP 1: Compute mean intensity of image from histogram, set T=mean(I)
201 std::vector<float> cumsum(hist.getSize(), 0.0f);
202 std::vector<float> sum_ip(hist.getSize(), 0.0f);
203 cumsum[0] = (float)hist[0];
204 for (unsigned int cpt = 1; cpt < hist.getSize(); cpt++) {
205 sum_ip[cpt] = cpt * (float)hist[cpt] + sum_ip[cpt - 1];
206 cumsum[cpt] = (float)hist[cpt] + cumsum[cpt - 1];
207 }
208
209 int T = vpMath::round(sum_ip[255] / imageSize);
210
211 // STEP 2: compute Mean above T (MAT) and Mean below T (MBT) using T from
212 float MBT = sum_ip[(size_t)(T - 2)] / cumsum[(size_t)(T - 2)];
213 float MAT = (sum_ip.back() - sum_ip[(size_t)(T - 1)]) / (cumsum.back() - cumsum[(size_t)(T - 1)]);
214
215 int T2 = vpMath::round((MAT + MBT) / 2.0f);
216
217 //% STEP 3 to n: repeat step 2 if T(i)~=T(i-1)
218 while (std::abs(T2 - T) >= 1) {
219 MBT = sum_ip[(size_t)(T2 - 2)] / cumsum[(size_t)(T2 - 2)];
220 MAT = (sum_ip.back() - sum_ip[(size_t)(T2 - 1)]) / (cumsum.back() - cumsum[(size_t)(T2 - 1)]);
221
222 T = T2;
223 T2 = vpMath::round((MAT + MBT) / 2.0f);
224 threshold = T2;
225 }
226
227 return threshold;
228}
229
230int computeThresholdMean(const vpHistogram &hist, unsigned int imageSize)
231{
232 // C. A. Glasbey, "An analysis of histogram-based thresholding algorithms,"
233 // CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993.
234 // The threshold is the mean of the greyscale data
235 float sum_ip = 0.0f;
236 for (unsigned int cpt = 0; cpt < hist.getSize(); cpt++) {
237 sum_ip += cpt * (float)hist[cpt];
238 }
239
240 return (int)std::floor(sum_ip / imageSize);
241}
242
243int computeThresholdOtsu(const vpHistogram &hist, unsigned int imageSize)
244{
245 // Otsu, N (1979), "A threshold selection method from gray-level
246 // histograms", IEEE Trans. Sys., Man., Cyber. 9: 62-66,
247 // doi:10.1109/TSMC.1979.4310076
248
249 float mu_T = 0.0f;
250 float sum_ip_all[256];
251 for (int cpt = 0; cpt < (int)hist.getSize(); cpt++) {
252 mu_T += cpt * (float)hist[cpt];
253 sum_ip_all[cpt] = mu_T;
254 }
255
256 // Weight Background / Foreground
257 float w_B = 0.0f, w_F = 0.0f;
258
259 float max_sigma_b = 0.0f;
260 int threshold = 0;
261
262 for (int cpt = 0; cpt < 256; cpt++) {
263 w_B += hist[cpt];
264 if (vpMath::nul(w_B, std::numeric_limits<float>::epsilon())) {
265 continue;
266 }
267
268 w_F = (int)imageSize - w_B;
269 if (vpMath::nul(w_F, std::numeric_limits<float>::epsilon())) {
270 break;
271 }
272
273 // Mean Background / Foreground
274 float mu_B = sum_ip_all[cpt] / (float)w_B;
275 float mu_F = (mu_T - sum_ip_all[cpt]) / (float)w_F;
276 // If there is a case where (w_B * w_F) exceed FLT_MAX, normalize
277 // histogram
278 float sigma_b_sqr = w_B * w_F * (mu_B - mu_F) * (mu_B - mu_F);
279
280 if (sigma_b_sqr >= max_sigma_b) {
281 threshold = cpt;
282 max_sigma_b = sigma_b_sqr;
283 }
284 }
285
286 return threshold;
287}
288
289int computeThresholdTriangle(vpHistogram &hist)
290{
291 int threshold = 0;
292
293 // Zack, G. W., Rogers, W. E. and Latt, S. A., 1977,
294 // Automatic Measurement of Sister Chromatid Exchange Frequency,
295 // Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753
296
297 int left_bound = -1, right_bound = -1, max_idx = -1, max_value = 0;
298 // Find max value index and left / right most index
299 for (int cpt = 0; cpt < (int)hist.getSize(); cpt++) {
300 if (left_bound == -1 && hist[cpt] > 0) {
301 left_bound = (int)cpt;
302 }
303
304 if (right_bound == -1 && hist[(int)hist.getSize() - 1 - cpt] > 0) {
305 right_bound = (int)hist.getSize() - 1 - cpt;
306 }
307
308 if ((int)hist[cpt] > max_value) {
309 max_value = (int)hist[cpt];
310 max_idx = cpt;
311 }
312 }
313
314 // First / last index when hist(cpt) == 0
315 left_bound = left_bound > 0 ? left_bound - 1 : left_bound;
316 right_bound = right_bound < (int)hist.getSize() - 1 ? right_bound + 1 : right_bound;
317
318 // Use the largest bound
319 bool flip = false;
320 if (max_idx - left_bound < right_bound - max_idx) {
321 // Flip histogram to get the largest bound to the left
322 flip = true;
323
324 int cpt_left = 0, cpt_right = (int)hist.getSize() - 1;
325 for (; cpt_left < cpt_right; cpt_left++, cpt_right--) {
326 unsigned int temp = hist[cpt_left];
327 hist.set(cpt_left, hist[cpt_right]);
328 hist.set(cpt_right, temp);
329 }
330
331 left_bound = (int)hist.getSize() - 1 - right_bound;
332 max_idx = (int)hist.getSize() - 1 - max_idx;
333 }
334
335 // Distance from a point to a line defined by two points:
336 //\textbf{distance} \left ( P_1, P_2, \left ( x_0,y_0 \right ) \right )
337 // = \frac{ \left | \left ( y_2-y_1 \right ) x_0 - \left ( x_2-x_1 \right )
338 // y_0 + x_2 y_1 - y_2 x_1 \right | }
339 // { \sqrt{ \left ( y_2 - y_1 \right )^{2} + \left ( x_2 - x_1 \right
340 // )^{2} } }
341 // Constants are ignored
342 float a = (float)max_value; // y_2 - y_1
343 float b = (float)(left_bound - max_idx); //-(x_2 - x_1)
344 float max_dist = 0.0f;
345
346 for (int cpt = left_bound + 1; cpt <= max_idx; cpt++) {
347 float dist = a * cpt + b * hist[cpt];
348
349 if (dist > max_dist) {
350 max_dist = dist;
351 threshold = cpt;
352 }
353 }
354 threshold--;
355
356 if (flip) {
357 threshold = (int)hist.getSize() - 1 - threshold;
358 }
359
360 return threshold;
361}
362} // namespace
363
375 const unsigned char backgroundValue, const unsigned char foregroundValue)
376{
377 if (I.getSize() == 0) {
378 return 0;
379 }
380
381 // Compute image histogram
382 vpHistogram histogram(I);
383 int threshold = -1;
384
385 switch (method) {
387 threshold = computeThresholdHuang(histogram);
388 break;
389
391 threshold = computeThresholdIntermodes(histogram);
392 break;
393
395 threshold = computeThresholdIsoData(histogram, I.getSize());
396 break;
397
399 threshold = computeThresholdMean(histogram, I.getSize());
400 break;
401
403 threshold = computeThresholdOtsu(histogram, I.getSize());
404 break;
405
407 threshold = computeThresholdTriangle(histogram);
408 break;
409
410 default:
411 break;
412 }
413
414 if (threshold != -1) {
415 // Threshold
416 vpImageTools::binarise(I, (unsigned char)threshold, (unsigned char)255, backgroundValue, foregroundValue,
417 foregroundValue);
418 }
419
420 return threshold;
421}
Class to compute a gray level image histogram.
Definition: vpHistogram.h:113
unsigned getSize() const
Definition: vpHistogram.h:267
void set(const unsigned char level, unsigned int value)
Definition: vpHistogram.h:230
static void binarise(vpImage< Type > &I, Type threshold1, Type threshold2, Type value1, Type value2, Type value3, bool useLUT=true)
Definition: vpImageTools.h:459
unsigned int getSize() const
Definition: vpImage.h:227
static bool nul(double x, double s=0.001)
Definition: vpMath.h:286
static int round(double x)
Definition: vpMath.h:247
VISP_EXPORT unsigned char autoThreshold(vpImage< unsigned char > &I, const vp::vpAutoThresholdMethod &method, const unsigned char backgroundValue=0, const unsigned char foregroundValue=255)
vpAutoThresholdMethod
Definition: vpImgproc.h:58
@ AUTO_THRESHOLD_ISODATA
Definition: vpImgproc.h:67
@ AUTO_THRESHOLD_HUANG
Definition: vpImgproc.h:59
@ AUTO_THRESHOLD_INTERMODES
Definition: vpImgproc.h:63
@ AUTO_THRESHOLD_TRIANGLE
Definition: vpImgproc.h:79
@ AUTO_THRESHOLD_MEAN
Definition: vpImgproc.h:71
@ AUTO_THRESHOLD_OTSU
Definition: vpImgproc.h:75