## HISTOGRAM EQUALISATION PDF

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, here the noise is making things a bit harder. To do so, several methods are available, manually select a value, determine an average, use a function.

Trahanias and Venetsanopoulos applied histogram equalization in 3D color space [5] However, it results in “whitening” where the probability of bright pixels are higher than that of dark ones. These pixels are false positive or false negative and we will discuss this later.

Then we have to find the point where both distribution cross each other. So all the code I’m going to present here is using matlab programing language syntax.

Which works well with bins, in other cases the display of Gaussian pdf is not going to fit the eaualisation very well if there are too few bins.

Several methods exists to determine it. But we could still lower the value and get good results. The general histogram equalization formula is:.

Indeed, if we consider an image where the pdf is already almost uniform, what is going to happen? The display parameter is a Boolean parameter which activate the display of the input image and the associated histogram. So, here we can see many things, firstly that there is an issue in the display of the cdf which is not ending at the right value.

To do so, we will need to perform as a first step the computation of the histogram of our input image. It allows us to have a better understanding of the global techniques to process an image. The code evolved a lot while I was writing this report, so some images produced may not be the exact same as the one I’ve used in this report.

## Histogram equalization

Once we have the cdf, we are going to “stretch” the histogram to get a “uniform” distribution. In this part we are only going to consider Gray scale images. The number of possible levels intensity values depends on the numerical type encoding the image.

So, to be able to model the two distributions, we need to know these parameters. We also consider the ration between dark and bright area to have a better estimation of the threshold. Here, the histogram shows the number of pixels for each brightness level from black to whiteand when there equalisayion more pixels, the peak at the certain brightness level is higher.

## Histogram Equalization

As we can see on the previous image, we can get a fairly good segmentation of the image but because of the noise, we have a certain number of pixel that are associated to the wrong color.

In this tutorial we will see that how histogram equalization can be used to enhance contrast. Due to the complexity of such a thing I just mention it here as a quick conclusion to say that there exists some solutions. So we just need here the two original intensity levels before applying noise. So this is why the result doesn’t seem to be changed a lot and the contrast stays quite the same.

Pixel values that have a zero count are excluded for the sake of brevity. So as we can see on its histogram, we have a peak of dark gray values that probably represent the background of the image and then a wide range of values on more brighter intensities.

On these images, the histogram equalization is really stretching the histogram and allow us to really see the details of the image that we were not able to see before. Histogram equalization is a method in image processing of contrast adjustment using the image ‘s histogram.

We developed a function that is taking as input a 2 dimension array a digital image containing for each pixel an associated intensity value. We worked on histograms which are the best tool to understand the distribution of an image intensities. 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.

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. Again, pixel values that do not contribute to an increase in the cdf are excluded for brevity.

### Histogram Equalization

It accomplishes this by effectively spreading out the most frequent intensity values, i. This is the optimum method to get a threshold, the implementation of such a solution is for example Otsu’s method to perform thresholding based on minization of the intra class variance.

Each image can be decomposed into three different layers according to the three color channels encoded: So we computed again the threshold introducing this ratio and we got some the following threshold: In terms of statistics, the value of each output image pixel characterizes the probability that the corresponding input pixel group belongs to the object whose histogram is used.

As we mentioned before, there are two sources of Gaussian noise on this images and it appears that they are overlaying each other. This has been hisfogram in particular in the fly retina.