Opencv Cumulative = true difference to false - c++

Question

i have this part of code. im beginner and want to understand this code. can someone explain me what happens if i set cumulative to true. Where is the difference to false. Would be nice if someone could explain me the difference.
i just see that the output is difference but i dont know why
#include <opencv2/highgui/highgui.hpp>
#include <iostream>
#include <opencv2/imgproc.hpp>
using namespace std;
using namespace cv;
cv::Mat plotHistogram(cv::Mat &image, bool cumulative = false, int histSize = 256);
int main()
{
cv::Mat img = cv::imread("\\schrott.png"); // Read the file
if (img.empty()) // Check for invalid input
{
std::cout << "Could not open or find the frame" << std::endl;
return -1;
}
cv::Mat img_gray;
cv::cvtColor(img, img_gray, cv::COLOR_BGR2GRAY); // In case img is colored
cv::namedWindow("Input Image", cv::WINDOW_AUTOSIZE); // Create a window for display.
cv::imshow("Input Image", img);
cv::Mat hist;
hist = plotHistogram(img_gray);
cv::namedWindow("Histogram", cv::WINDOW_NORMAL); // Create a window for display.
cv::imshow("Histogram", hist);
cv::waitKey(0);
}
cv::Mat plotHistogram(cv::Mat &image, bool cumulative, int histSize) {
// Create Image for Histogram
int hist_w = 1024; int hist_h = 800;
int bin_w = cvRound((double)hist_w / histSize);
cv::Mat histImage(hist_h, hist_w, CV_8UC1, Scalar(255, 255, 255));
if (image.channels() > 1) {
cerr << "plotHistogram: Please insert only gray images." << endl;
return histImage;
}
// Calculate Histogram
float range[] = { 0, 256 };
const float* histRange = { range };
cv::Mat hist;
calcHist(&image, 1, 0, Mat(), hist, 1, &histSize, &histRange);
if (cumulative) {
cv::Mat accumulatedHist = hist.clone();
for (int i = 1; i < histSize; i++) {
accumulatedHist.at<float>(i) += accumulatedHist.at<float>(i - 1);
}
hist = accumulatedHist;
}
// Normalize the result to [ 0, histImage.rows ]
normalize(hist, hist, 0, histImage.rows, NORM_MINMAX, -1, Mat());
// Draw bars
for (int i = 1; i < histSize; i++) {
cv::rectangle(histImage, Point(bin_w * (i - 1), hist_h),
Point(bin_w * (i), hist_h - cvRound(hist.at<float>(i))),
Scalar(50, 50, 50), 1);
}
return histImage; // Not really call by value, as cv::Mat only saves a pointer to the image data
}
``

Answer 1

Without looking at the code: the difference between a histogram and a cumulative histogram is that the cumulative histogram at index i has the value of the normal histogram at index i, plus the value of the cumulative histogram at index i - 1. There is a c++ stl algorithm that does the same, and it's called std::partial_sum.
In other words, in image processing a cumulative histogram tells you how many pixels have at most a given color value c
For example, given an array [0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 4] we can plot the histogram and cumulative histogram like so:
The X axis here is the value of the array element while the Y axis is the number of times this element occurs in the array. This is a typical pattern in image processing: in a color histogram the X axis is usually the value of your color. In a 8bpp grayscale image, for example, the X axis has values in the range 0..255. The Y axis then is the number of pixels that have that specific color value.
One important property of a cumulative histogram (in contrast to a normal histogram) is that it's monotonically increasing, i.e. h[i] >= h[i - 1] where i = 1..length(h) and h is the cumulative histogram. This allows operations like histogram equalization. Since a monotonically increasing sequence is by definition also a sorted sequence, you can also perform operation on it that are only allowed on sorted sequences, like binary search.
The next step is usually to calculate a normalized cumulative histogram, which is done by dividing each value in the cumulative histogram by the number of values in your original array. For example
a = [1, 2, 3, 4]
h = hist(a) // histogram of a
ch = partial_sum(h) // cumulative histogram of a
nch = ch / length(a) // normalized, cumulative histogram of a
Another example, given an array [1, 2, 3, 4, 3, 2, 1] we can plot the histogram and cumulative histogram like so:
The X axis here is the 1 based index in the array and the Y axis is the value of that element.
Here is another figure:
And another one, explaining the same:

Answer 2

Starting with what the cumulative histogram is might be good. A histogram is a distribution of the number of pixels according to their intensities but if the thing in question is a cumulative histogram; we don't find counts for a single bin in the vertical axis, but rather we map that counts the cumulative number of pixel intensity values in all of the bins up to the current bin. And linear cumulative distribution or cumulative histogram is essential for some image processing algorithms e.g image equalization.
Histogram (H):
For each pixel of the image
value = Intensity(pixel)
H(value)++
end
The cumulative histogram of the H:
When you set cumulative to true; you are now calculating the cumulative histogram therefore, it is normal for the outputs to be different. In each step of the iteration, you add the previous histogram value to the cumulative histogram.
if (cumulative) {
cv::Mat accumulatedHist = hist.clone();
for (int i = 1; i < histSize; i++) {
accumulatedHist.at<float>(i) += accumulatedHist.at<float>(i - 1);
}
hist = accumulatedHist;
}
You can think of this as a trick when switching from a normal histogram to a cumulative histogram.
accumulatedHist.at<float>(i) += accumulatedHist.at<float>(i - 1);
These references might be useful to understand the basic structure
Histograms
Histogram Equalization
Cumulative Distribution Function