How to select threshold values automatically uses the peaks of the histogram? - c++

Question

By the OpenCV library, I want to threshold an image like this:
threshold(image, thresh, 220, 255, THRESH_BINARY_INV)
But I want to automatically find the threshold value (220).
I use Otsu to estimate the threshold. But it doesn't work in my case.
therefore, I should use Histogram Peak Technique. I want to find the two peaks in the histogram corresponding to the background and object of the image. It sets the threshold value automatically halfway between the two peaks.
I use this book (pages: 117 and 496-505): "Image Processing in C" by Dwayne Phillips (http://homepages.inf.ed.ac.uk/rbf/BOOKS/PHILLIPS/). And I use source code for find the two peaks in the histogram corresponding to the background and object of the image. this is my image:
this is my c++ code:
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/opencv.hpp>
#include <iostream>
#include <stdio.h>
#include <fstream>
using namespace std;
using namespace cv;
int main()
{
Mat image0 = imread("C:/Users/Alireza/Desktop/contrast950318/2.bmp");
imshow("image0", image0);
Mat image, thresh, Tafrigh;
cvtColor(image0, image, CV_RGB2GRAY);
int N = image.rows*image.cols;
int histogram[256];
for (int i = 0; i < 256; i++) {
histogram[i] = 0;
}
//create histo
for (int i = 0; i < image.rows; i++){
for (int j = 0; j < image.cols; j++){
histogram[((int)image.at<uchar>(i, j))]++;
}
}
int peak1, peak2;
#define PEAKS 30
int distance[PEAKS], peaks[PEAKS][2];
int i, j = 0, max = 0, max_place = 0;
for (int i = 0; i<PEAKS; i++){
distance[i] = 0;
peaks[i][0] = -1;
peaks[i][1] = -1;
}
for (i = 0; i <= 255; i++){
max = histogram[i];
max_place = i;
//insert_into_peaks(peaks, max, max_place);
//int max, max_place, peaks[PEAKS][2];
//int i, j;
/* first case */
if (max > peaks[0][0]){
for (i = PEAKS - 1; i > 0; i--){
peaks[i][0] = peaks[i - 1][0];
peaks[i][1] = peaks[i - 1][1];
}
peaks[0][0] = max;
peaks[0][1] = max_place;
} /* ends if */
/* middle cases */
for (j = 0; j < PEAKS - 3; j++){
if (max < peaks[j][0] && max > peaks[j + 1][0]){
for (i = PEAKS - 1; i > j + 1; i--){
peaks[i][0] = peaks[i - 1][0];
peaks[i][1] = peaks[i - 1][1];
}
peaks[j + 1][0] = max;
peaks[j + 1][1] = max_place;
} /* ends if */
} /* ends loop over j */
/* last case */
if (max < peaks[PEAKS - 2][0] &&
max > peaks[PEAKS - 1][0]){
peaks[PEAKS - 1][0] = max;
peaks[PEAKS - 1][1] = max_place;
} /* ends if */
}/* ends loop over i */
for (int i = 1; i<PEAKS; i++){
distance[i] = peaks[0][1] - peaks[i][1];
if (distance[i] < 0)
distance[i] = distance[i] * (-1);
}
peak1 = peaks[0][1];
cout << " peak1= " << peak1;
for (int i = PEAKS - 1; i > 0; i--){
if (distance[i] > 1)
peak2 = peaks[i][1];
}
cout << " peak2= " << peak2;
int mid_point;
//int peak1, peak2;
short hi, low;
unsigned long sum1 = 0, sum2 = 0;
if (peak1 > peak2)
mid_point = ((peak1 - peak2) / 2) + peak2;
if (peak1 < peak2)
mid_point = ((peak2 - peak1) / 2) + peak1;
for (int i = 0; i<mid_point; i++)
sum1 = sum1 + histogram[i];
for (int i = mid_point; i <= 255; i++)
sum2 = sum2 + histogram[i];
if (sum1 >= sum2){
low = mid_point;
hi = 255;
}
else{
low = 0;
hi = mid_point;
}
cout << " low= " << low << " hi= " << hi;
double threshnum = 0.5* (low + hi);
threshold(image, thresh, threshnum, hi, THRESH_BINARY_INV);
waitKey(0);
return 0;
}
But I don't know this code correct is or not. If it correct, why is threshold value 202?
What ideas on how to solve this task would you suggest? Or on what resource on the internet can I find help?

Answer 1

You can use also the Max Entropy. In some cases using only the high frequency of the entropy could be better
int maxentropie(const cv::Mat1b& src)
{
// Histogram
cv::Mat1d hist(1, 256, 0.0);
for (int r=0; r<src.rows; ++r)
for (int c=0; c<src.cols; ++c)
hist(src(r,c))++;
// Normalize
hist /= double(src.rows * src.cols);
// Cumulative histogram
cv::Mat1d cumhist(1, 256, 0.0);
float sum = 0;
for (int i = 0; i < 256; ++i)
{
sum += hist(i);
cumhist(i) = sum;
}
cv::Mat1d hl(1, 256, 0.0);
cv::Mat1d hh(1, 256, 0.0);
for (int t = 0; t < 256; ++t)
{
// low range entropy
double cl = cumhist(t);
if (cl > 0)
{
for (int i = 0; i <= t; ++i)
{
if (hist(i) > 0)
{
hl(t) = hl(t) - (hist(i) / cl) * log(hist(i) / cl);
}
}
}
// high range entropy
double ch = 1.0 - cl; // constraint cl + ch = 1
if (ch > 0)
{
for (int i = t+1; i < 256; ++i)
{
if (hist(i) > 0)
{
hh(t) = hh(t) - (hist(i) / ch) * log(hist(i) / ch);
}
}
}
}
// choose best threshold
cv::Mat1d entropie(1, 256, 0.0);
double h_max = hl(0) + hh(0);
int threshold = 0;
entropie(0) = h_max;
for (int t = 1; t < 256; ++t)
{
entropie(t) = hl(t) + hh(t);
if (entropie(t) > h_max)
{
h_max = entropie(t);
threshold = uchar(t);
}
}
if(threshold==0) threshold=255;
return threshold;
}