vpThreshold.cpp

/****************************************************************************
 *
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2019 by Inria. All rights reserved.
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 * it under the terms of the GNU General Public License as published by
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 * Campus Universitaire de Beaulieu
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 *
 * Description:
 * Automatic thresholding functions.
 *
 * Authors:
 * Souriya Trinh
 *
 *****************************************************************************/

#include <visp3/core/vpHistogram.h>
#include <visp3/core/vpImageTools.h>
#include <visp3/imgproc/vpImgproc.h>

namespace
{
bool isBimodal(const std::vector<float> &hist_float)
{
  int modes = 0;

  for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
    if (hist_float[cpt - 1] < hist_float[cpt] && hist_float[cpt] > hist_float[cpt + 1]) {
      modes++;
    }

    if (modes > 2) {
      return false;
    }
  }

  return (modes == 2);
}

int computeThresholdHuang(const vpHistogram &hist)
{
  // Code ported from the AutoThreshold ImageJ plugin:
  // Implements Huang's fuzzy thresholding method
  // Uses Shannon's entropy function (one can also use Yager's entropy
  // function) Huang L.-K. and Wang M.-J.J. (1995) "Image Thresholding by
  // Minimizing the Measures of Fuzziness" Pattern Recognition, 28(1): 41-51
  // Reimplemented (to handle 16-bit efficiently) by Johannes Schindelin Jan
  // 31, 2011

  // Find first and last non-empty bin
  size_t first, last;
  for (first = 0; first < (size_t)hist.getSize() && hist[(unsigned char)first] == 0; first++) {
    // do nothing
  }

  for (last = (size_t)hist.getSize() - 1; last > first && hist[(unsigned char)last] == 0; last--) {
    // do nothing
  }

  if (first == last) {
    return 0;
  }

  // Calculate the cumulative density and the weighted cumulative density
  std::vector<float> S(last + 1);
  std::vector<float> W(last + 1);

  S[0] = (float)hist[0];
  W[0] = 0.0f;
  for (size_t i = std::max((size_t)1, first); i <= last; i++) {
    S[i] = S[i - 1] + hist[(unsigned char)i];
    W[i] = W[i - 1] + i * (float)hist[(unsigned char)i];
  }

  // Precalculate the summands of the entropy given the absolute difference x
  // - mu (integral)
  float C = (float)(last - first);
  std::vector<float> Smu(last + 1 - first);

  for (size_t i = 1; i < Smu.size(); i++) {
    float mu = 1 / (1 + i / C);
    Smu[i] = -mu * std::log(mu) - (1 - mu) * std::log(1 - mu);
  }

  // Calculate the threshold
  int bestThreshold = 0;
  float bestEntropy = std::numeric_limits<float>::max();

  for (size_t threshold = first; threshold <= last; threshold++) {
    float entropy = 0;
    int mu = vpMath::round(W[threshold] / S[threshold]);
    for (size_t i = first; i <= threshold; i++) {
      entropy += Smu[(size_t)std::abs((int)i - mu)] * hist[(unsigned char)i];
    }

    mu = vpMath::round((W[last] - W[threshold]) / (S[last] - S[threshold]));
    for (size_t i = threshold + 1; i <= last; i++) {
      entropy += Smu[(size_t)std::abs((int)i - mu)] * hist[(unsigned char)i];
    }

    if (bestEntropy > entropy) {
      bestEntropy = entropy;
      bestThreshold = (int)threshold;
    }
  }

  return bestThreshold;
}

int computeThresholdIntermodes(const vpHistogram &hist)
{
  if (hist.getSize() < 3) {
    return -1;
  }

  // Code based on the AutoThreshold ImageJ plugin:
  // J. M. S. Prewitt and M. L. Mendelsohn, "The analysis of cell images," in
  // Annals of the New York Academy of Sciences, vol. 128, pp. 1035-1053,
  // 1966. ported to ImageJ plugin by G.Landini from Antti Niemisto's Matlab
  // code (GPL) Original Matlab code Copyright (C) 2004 Antti Niemisto See
  // http://www.cs.tut.fi/~ant/histthresh/ for an excellent slide presentation
  // and the original Matlab code.
  //
  // Assumes a bimodal histogram. The histogram needs is smoothed (using a
  // running average of size 3, iteratively) until there are only two local
  // maxima. j and k Threshold t is (j+k)/2. Images with histograms having
  // extremely unequal peaks or a broad and flat valley are unsuitable for this
  // method.

  std::vector<float> hist_float(hist.getSize());
  for (unsigned int cpt = 0; cpt < hist.getSize(); cpt++) {
    hist_float[cpt] = (float)hist[cpt];
  }

  int iter = 0;
  while (!isBimodal(hist_float)) {
    // Smooth with a 3 point running mean filter
    for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
      hist_float[cpt] = (hist_float[cpt - 1] + hist_float[cpt] + hist_float[cpt + 1]) / 3;
    }

    // First value
    hist_float[0] = (hist_float[0] + hist_float[1]) / 2.0f;

    // Last value
    hist_float[hist_float.size() - 1] = (hist_float.size() - 2 + hist_float.size() - 1) / 2.0f;

    iter++;

    if (iter > 10000) {
      std::cerr << "Intermodes Threshold not found after 10000 iterations!" << std::endl;
      return -1;
    }
  }

  // The threshold is the mean between the two peaks.
  int tt = 0;
  for (size_t cpt = 1; cpt < hist_float.size() - 1; cpt++) {
    if (hist_float[cpt - 1] < hist_float[cpt] && hist_float[cpt] > hist_float[cpt + 1]) {
      // Mode
      tt += (int)cpt;
    }
  }

  return (int)std::floor(tt / 2.0); // vpMath::round(tt / 2.0);
}

int computeThresholdIsoData(const vpHistogram &hist, const unsigned int imageSize)
{
  int threshold = 0;

  // Code based on BSD Matlab isodata implementation by zephyr
  // STEP 1: Compute mean intensity of image from histogram, set T=mean(I)
  std::vector<float> cumsum(hist.getSize(), 0.0f);
  std::vector<float> sum_ip(hist.getSize(), 0.0f);
  cumsum[0] = (float)hist[0];
  for (unsigned int cpt = 1; cpt < hist.getSize(); cpt++) {
    sum_ip[cpt] = cpt * (float)hist[cpt] + sum_ip[cpt - 1];
    cumsum[cpt] = (float)hist[cpt] + cumsum[cpt - 1];
  }

  int T = vpMath::round(sum_ip[255] / imageSize);

  // STEP 2: compute Mean above T (MAT) and Mean below T (MBT) using T from
  float MBT = sum_ip[(size_t)(T - 2)] / cumsum[(size_t)(T - 2)];
  float MAT = (sum_ip.back() - sum_ip[(size_t)(T - 1)]) / (cumsum.back() - cumsum[(size_t)(T - 1)]);

  int T2 = vpMath::round((MAT + MBT) / 2.0f);

  //% STEP 3 to n: repeat step 2 if T(i)~=T(i-1)
  while (std::abs(T2 - T) >= 1) {
    MBT = sum_ip[(size_t)(T2 - 2)] / cumsum[(size_t)(T2 - 2)];
    MAT = (sum_ip.back() - sum_ip[(size_t)(T2 - 1)]) / (cumsum.back() - cumsum[(size_t)(T2 - 1)]);

    T = T2;
    T2 = vpMath::round((MAT + MBT) / 2.0f);
    threshold = T2;
  }

  return threshold;
}

int computeThresholdMean(const vpHistogram &hist, const unsigned int imageSize)
{
  // C. A. Glasbey, "An analysis of histogram-based thresholding algorithms,"
  // CVGIP: Graphical Models and Image Processing, vol. 55, pp. 532-537, 1993.
  // The threshold is the mean of the greyscale data
  float sum_ip = 0.0f;
  for (unsigned int cpt = 0; cpt < hist.getSize(); cpt++) {
    sum_ip += cpt * (float)hist[cpt];
  }

  return (int)std::floor(sum_ip / imageSize);
}

int computeThresholdOtsu(const vpHistogram &hist, const unsigned int imageSize)
{
  // Otsu, N (1979), "A threshold selection method from gray-level
  // histograms",  IEEE Trans. Sys., Man., Cyber. 9: 62-66,
  // doi:10.1109/TSMC.1979.4310076

  float mu_T = 0.0f;
  float sum_ip_all[256];
  for (int cpt = 0; cpt < (int)hist.getSize(); cpt++) {
    mu_T += cpt * (float)hist[cpt];
    sum_ip_all[cpt] = mu_T;
  }

  // Weight Background / Foreground
  float w_B = 0.0f, w_F = 0.0f;

  float max_sigma_b = 0.0f;
  int threshold = 0;

  for (int cpt = 0; cpt < 256; cpt++) {
    w_B += hist[cpt];
    if (vpMath::nul(w_B, std::numeric_limits<float>::epsilon())) {
      continue;
    }

    w_F = (int)imageSize - w_B;
    if (vpMath::nul(w_F, std::numeric_limits<float>::epsilon())) {
      break;
    }

    // Mean Background / Foreground
    float mu_B = sum_ip_all[cpt] / (float)w_B;
    float mu_F = (mu_T - sum_ip_all[cpt]) / (float)w_F;
    // If there is a case where (w_B * w_F) exceed FLT_MAX, normalize
    // histogram
    float sigma_b_sqr = w_B * w_F * (mu_B - mu_F) * (mu_B - mu_F);

    if (sigma_b_sqr >= max_sigma_b) {
      threshold = cpt;
      max_sigma_b = sigma_b_sqr;
    }
  }

  return threshold;
}

int computeThresholdTriangle(vpHistogram &hist)
{
  int threshold = 0;

  // Zack, G. W., Rogers, W. E. and Latt, S. A., 1977,
  // Automatic Measurement of Sister Chromatid Exchange Frequency,
  // Journal of Histochemistry and Cytochemistry 25 (7), pp. 741-753

  int left_bound = -1, right_bound = -1, max_idx = -1, max_value = 0;
  // Find max value index and left / right most index
  for (int cpt = 0; cpt < (int)hist.getSize(); cpt++) {
    if (left_bound == -1 && hist[cpt] > 0) {
      left_bound = (int)cpt;
    }

    if (right_bound == -1 && hist[(int)hist.getSize() - 1 - cpt] > 0) {
      right_bound = (int)hist.getSize() - 1 - cpt;
    }

    if ((int)hist[cpt] > max_value) {
      max_value = (int)hist[cpt];
      max_idx = cpt;
    }
  }

  // First / last index when hist(cpt) == 0
  left_bound = left_bound > 0 ? left_bound - 1 : left_bound;
  right_bound = right_bound < (int)hist.getSize() - 1 ? right_bound + 1 : right_bound;

  // Use the largest bound
  bool flip = false;
  if (max_idx - left_bound < right_bound - max_idx) {
    // Flip histogram to get the largest bound to the left
    flip = true;

    int cpt_left = 0, cpt_right = (int)hist.getSize() - 1;
    for (; cpt_left < cpt_right; cpt_left++, cpt_right--) {
      unsigned int temp = hist[cpt_left];
      hist.set(cpt_left, hist[cpt_right]);
      hist.set(cpt_right, temp);
    }

    left_bound = (int)hist.getSize() - 1 - right_bound;
    max_idx = (int)hist.getSize() - 1 - max_idx;
  }

  // Distance from a point to a line defined by two points:
  //\textbf{distance} \left ( P_1, P_2, \left ( x_0,y_0 \right ) \right )
  // = \frac{ \left | \left ( y_2-y_1 \right ) x_0 - \left ( x_2-x_1 \right )
  // y_0 + x_2 y_1 - y_2 x_1 \right | }
  //        { \sqrt{ \left ( y_2 - y_1 \right )^{2} + \left ( x_2 - x_1 \right
  //        )^{2} } }
  // Constants are ignored
  float a = (float)max_value;              // y_2 - y_1
  float b = (float)(left_bound - max_idx); //-(x_2 - x_1)
  float max_dist = 0.0f;

  for (int cpt = left_bound + 1; cpt <= max_idx; cpt++) {
    float dist = a * cpt + b * hist[cpt];

    if (dist > max_dist) {
      max_dist = dist;
      threshold = cpt;
    }
  }
  threshold--;

  if (flip) {
    threshold = (int)hist.getSize() - 1 - threshold;
  }

  return threshold;
}
} // namespace

unsigned char vp::autoThreshold(vpImage<unsigned char> &I, const vpAutoThresholdMethod &method,
                                const unsigned char backgroundValue, const unsigned char foregroundValue)
{
  if (I.getSize() == 0) {
    return 0;
  }

  // Compute image histogram
  vpHistogram histogram(I);
  int threshold = -1;

  switch (method) {
  case AUTO_THRESHOLD_HUANG:
    threshold = computeThresholdHuang(histogram);
    break;

  case AUTO_THRESHOLD_INTERMODES:
    threshold = computeThresholdIntermodes(histogram);
    break;

  case AUTO_THRESHOLD_ISODATA:
    threshold = computeThresholdIsoData(histogram, I.getSize());
    break;

  case AUTO_THRESHOLD_MEAN:
    threshold = computeThresholdMean(histogram, I.getSize());
    break;

  case AUTO_THRESHOLD_OTSU:
    threshold = computeThresholdOtsu(histogram, I.getSize());
    break;

  case AUTO_THRESHOLD_TRIANGLE:
    threshold = computeThresholdTriangle(histogram);
    break;

  default:
    break;
  }

  if (threshold != -1) {
    // Threshold
    vpImageTools::binarise(I, (unsigned char)threshold, (unsigned char)255, backgroundValue, foregroundValue,
                           foregroundValue);
  }

  return threshold;
}