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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Regarding the programming aspect, thanks to MATLAB, we can handle images as matrix which allow us to have a better understanding of equalusation processing. To do so, the easiest method to do that is by doing a manual threshold based on the intensity distribution showed in the histogram.

Indeed, there one main things that could be improved.

### Histogram Equalization – Towards Data Science

As presented before, I’m in this part implementing the formula presented in the theoretical definitions at the beginning of this report. In the previous result, we are just displaying the absolute frequency which is the number of pixel. For example, if applied to 8-bit image displayed with 8-bit gray-scale palette it will further reduce color depth number of unique shades of gray of the image. Here we can clearly bistogram that the distribution of the intensity on each channel is clearly different.

So we are considering only the range of values between 50 and The number of possible levels intensity values depends on the numerical type encoding the image.

So the idea here is clearly to blend them linearly according to what we want to have. It returns a vector containing the relative frequencies associated to the histogram.

### Point Operations – Histogram Equalization

Let’s start equailsation displaying the histograms of the two checker board. As we mentioned before, there are two sources of Gaussian noise on this images and it appears that they are overlaying each other. The calculation is not computationally intensive. This allows for areas of lower local contrast to gain a higher contrast.

Our next step involves calculation of CDF cumulative distributive function.

Here are the results:. So we need then to average again the column to get an overall average. Indeed, a linear cdf is associated to the uniform histogram that we want the resulting image to have.

To find which threshold was better we could have substracted the different results to each other to see what was different between them, histogrm it’s maybe not the point of this part. The MATLAB function computing the mean when we give it a 2 dimensional array our image is returning an average per column.

Note that in this case we consider a rounding for computing the size. 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.

This method usually increases the global contrast of many images, especially when the usable data of the image is represented by close contrast values.

Segmentation is an operation consisting in partitioning an image into sets of elements. Never miss a story from Towards Data Sciencewhen you sign up for Medium.

## Project 1 : Histograms

Equalisatioj methods exists to determine it. 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. In the case of CLAHE, the contrast limiting procedure is applied to each neighborhood from which a transformation function is derived.

So Here, we will firstly use the first approach to get some initial results and then we will try to implement maybe a better solution. Histogram equalization will work the best when applied to images with much higher color depth than palette size, like continuous data or bit gray-scale images. 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.

To get this result, we used the formula given in the theoretical part.

See theoretical explanation in section IIIB. Histogram equalization is a method to process images in order to adjust the contrast of an image by modifying the intensity distribution of the histogram. To do so, we are going to assign to each new pixel the mapped value of the input pixel.

To do so, we are going to loop on the normalized distribution and add up each time a new probability according to the formula given in section IIIB of the theoretical section.

## Histogram equalization

Gistogram methods seek to adjust the image to make it easier to analyze or improve visual quality e. 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.

Views Read Edit View history. Now map these new values you are onto histogram, and you are done. The probability of an occurrence of a pixel of level i in the image is.