# 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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### Point Operations – Histogram Equalization

On the previous figure, we can see that the input picture is really dark. Let’s interpret the resulting cumulative distribution. To conclude this part, I think that the method using Gaussian pdf hisotgram is pretty accurate and provide a good segmentation which is automatic contrary to the manual selection.

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 histogrsm associated to the wrong color. The calculation is not computationally intensive. To find which threshold was better we could have substracted the different results to each other to see what was different between them, but it’s maybe not the point of this part.

As presented in section IV of the theoretical definitions, a Gaussian distribution is characterized by two parameters: It hjstogram a vector containing the relative frequencies associated to the histogram. Never miss a story from Towards Data Sciencewhen you sign up for Medium. Our next step involves calculation of CDF cumulative distributive function.

To do so we are going to look for hietogram point where the difference between the two curves is really small and this point will be the place where both curves meet and it will be our threshold. We have already seen that contrast can be increased using histogram stretching. Either way this is going to be dependent of the user.

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To do so, several equalusation are available, manually select a value, determine an average, use a function. The operation can be expressed as P M I where I is the original image, M is histogram equalization mapping operation and P is a palette. Hkstogram more detailed presentation of the code is available in the Implementation section.

In this part the implementation is quite similar as before equalisatiin 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 that cases the contrast is decreased.

## Project 1 : Histograms

The MATLAB function computing the mean when we give it a 2 dimensional array our image is returning an average per column. However, applying the same method on the Red, Green, and Blue components of an RGB image may yield dramatic changes in the image’s color balance since the relative distributions of the color channels change as a result of applying the algorithm.

To call the function, you need to use the following prototype and parameters: To be able to segment the image, we need to find a threshold that is representing a good value to separate the two different gray level.

A key advantage of the method is that it is a fairly straightforward technique and an histograk operator. As we can see on the previous figure, if we compare the two images we can see that the contrast of the image has clearly been enhanced by performing equalization. It is not necessary that contrast will always be increase in this.

The core of the function is the computation of the histogram in number of pixels and then in relative frequency respecting the range and the histoyram of bins. The goal of these methods, especially MBOBHE, is to improve the contrast without producing brightness mean-shift and detail loss artifacts by modifying the HE algorithm.

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## Histogram Equalization

hisogram But we could still lower the value and get good results. So we need to determine the size of each new bin and then perform a test on the value of the histogram to find in which bins it lies. But if we let this aspect we can see that the result of the operation is clearly a compression of level. So based on the histogram we have, it seems possible to perform such an operation.

### Histogram equalization – Wikipedia

Retrieved from ” https: This allows for areas of lower local contrast to gain a higher contrast. Histogram equalization often produces unrealistic effects in photographs; however it is very useful for scientific images like thermalsatellite or x-ray images, often the same class of images to which one would apply false-color.

To call the function, you need to use the following prototype: Indeed, there one main things that could be improved. So two explanations, maybe this issue with the cdf is really screwing things or equailsation equalisation is compressing our histogram. The success of the procedure is proven by the histogram associated to each image, showing that it’s range has been stretched to occupy the whole spectrum of levels. To do so, I generated a noise image I assume it’s white noise occupying the whole range of level and I used it as input of the equalization function.

The most important step here is to chose the best value for the threshold to get the best segmentation.