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Equalization implies mapping one distribution (the given histogram) to another distribution (a wider and more uniform distribution of intensity values) so the. Histogram equalization is a technique for adjusting image intensities to enhance contrast. normalized histogram of f with a bin for each possible intensity. So. Histogram is a graphical representation of the intensity distribution of an image. In simple terms, it represents the number of pixels for each.

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Indeed, if we consider an image where the pdf is already almost uniform, what is going to happen? To do so, several methods are available, manually select a value, determine an average, use a function. The issue here is if the mean is not an integer, because we will have to either round, ceil or floor it. A color histogram of an image represents the number of pixels in each type of color component.

Indeed, here the noise is making things a bit harder. For example, the cdf of 78 is One of the method to do that is thresholding which consist in converting a gray-scale image into a binary image. So we are considering only the range of values between 50 and But this is not the point here because even without we can determine histlgram threshold by looking at the bone Gaussian approximation. We also consider the ration between dark and equlaisation area to have a better estimation of the threshold.

Let’s start by displaying the histograms of the two checker board. So we need then to average again the column to get an overall average. To determine them, we are going to consider some patches in the image where we compute the mean and the standard deviation. This solution is providing the optimum thresholding function for a monodimensional problem involving two Gaussian distributions.

Indeed, we make sure that the parameters given to the function are correct, so we verify that the number of bins is positive and that the minimum value of the range is inferior to the maximum value. The MATLAB function computing the mean when we give it a 2 dimensional array our image is returning an average per column.

## Histogram equalization

To perform this operation, we are going to implement the formula presented in the section IIIB of theoretical part at the beginning of this report. The color image is obtained while combining the three layers. The second solution would be probably a bit more accurate, by computing the mean value between the two peaks which will give the exact value.

Here is a result when applied to the crowd image, very dark initially and maybe euqalisation bright at the end. We can see this aspect while looking at the associated normalized histogram where we can see that the histogram is located on the left side which correspond to the darkest gray levels.

Scaling from 1 to preserves the non-zero-ness of the minimum equalixation. The normalization will give to our distribution the properties of a probability density function.

### Histogram Equalization – Towards Data Science

Indeed, we can consider a threshold of which will give us the following result:. Then the first thing to do is to equakisation the three different color channels: To extract the bone structure from this image, we need to segment the image with a high intensity value because the bone is white and other structures are darker.

The last part involving Gaussian mixture, allows us to determine the characteristics of a Gaussian noise in a image and based on the pdf to determine a value to threshold an image. As uistogram can see on the previous picture, this method is working pretty well, it gives histogdam nice Gaussian distributions which describe our histogram. Through this adjustment, the intensities can be better distributed on the histogram.

The function used for this part is defined with the following prototype histogram Image,nbins,min,max,display where nbins is the number of bins chosen to perform the histogram, and min and max the two values for the range of the histogram.

Indeed the explanation is easy, each Gaussian pdf has the sum of its density equal to one, so here we want the sum of both densities being equal to one, so we have to scale them according to the amount of pixel of the image they are representing. To do so, we are going to assign to each new pixel the mapped value of the input pixel. The cdf of 64 for value coincides with the number of pixels in the image.

After applying we got the following image and its following histogram. To conclude this first project, we can say that we had the opportunity to implement the basic functions of Image Histoggram. So Here, we will firstly use the first approach to get some initial results and then we will try to equalisatioh maybe a better solution.

In this part the implementation is quite similar as before except that we consider 3 patches instead of 2 and that the threshold is manually selected because the Gaussian pdf distributions are helpful to locate an area to threshold but not to automatically determine a specific value. In scientific equalisatipn where spatial correlation is more important than intensity of signal such as separating DNA fragments of quantized lengththe small signal to noise ratio usually hampers visual detection.

Which could encode different colors. An histogram being a distribution of the number of pixel according to their intensities, we have in this part to analyze the image to determine this distribution. The properties of the CDF equalksation us to perform such a transform see Inverse distribution function ; it is defined as. In the previous result, we are just displaying the absolute frequency which is the number of pixel.

### Point Operations – Histogram Equalization

But it histoggam be for sure the method to use to get the best possible threshold to obtain a binary image. A gray scale image is a digital image in which each pixel only contains one scalar value which is its intensity.

I made all the other drawing or images so there is no Copyright infringement in this work. Another interesting thing to test is the opposite thing of what we want.

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