# 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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In this part, we implemented a pipeline to segment the checkerboard according to a threshold computed from the two Gaussian pdf. 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. So we can either read the value on the histogram or use a point clicking operation with the mouse. CLAHE was developed to prevent the over amplification of noise that adaptive histogram equalization can give rise to.

This first project was a good way to implement ourselves the major functions used in image processing and that are most of the time performed by image processing software. Because of its discrete nature, the theory used to process digital image will rely on discrete domain, even if the analogy with the continuous domain is possible.

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 number of possible levels intensity values depends on the numerical type encoding the image.

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 number of bins.

These methods seek to adjust the image to make it easier to analyze or improve visual quality e. So two explanations, maybe this issue with the cdf is really screwing things or the equalisation is compressing our histogram. Such an image would have a linearized cumulative distribution function CDF across the value range, i. Due to the complexity of such a thing I just mention it here as a quick conclusion to say that there exists some solutions.

To do so we are going to use the same pipeline of equalization as before except that the resulting image is going to be a linear blending of the original image and the equalized one according to the following formula:. Because a digital image is a discrete set of values that could be seen as a matrix and it’s equivalent to divide each n k by the dimension of the array which is the product of the width by the length of the image.

### Histogram equalization – Wikipedia

So we can conclude this part that histogram equalization really depends on the initial distribution of intensity levels. Corresponding histogram red and cumulative histogram black. Histogram equalization accomplishes this by effectively spreading out the most frequent intensity values.

As presented in section IV of the theoretical definitions, a Gaussian distribution is characterized by two parameters: But all algorithm will work with any other languages. The back projection or “project” of a histogrammed image is the re-application of the modified histogram to the original image, functioning as a look-up table for pixel brightness values.

The image being initially good enough, equalization is not enhancing anything it just makes it brighter by moving the big center peak on the right. Adaptive Histogram Equalization differs from ordinary histogram equalization in the respect that the adaptive method computes several histograms, each corresponding to a distinct section of the image, and uses them to redistribute the lightness values of the image.

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. Here are the results for the first checker board where the algorithm gives us a threshold of which is pretty close to the one we used with manual selection. But this is not the point here because even without we can determine a threshold by looking at the bone Gaussian approximation.

The cumulative distribution function cdf is shown below. So, to be able to model the two distributions, we need to know these parameters. Then number of levels we have are 8.

## Histogram Equalization

The objective in this part is also to be able to modify the different parameters of the histogram. But this could be more accurate than the manual selection if the noise has the same standard deviation.

In simple terms, it represents the number of pixels for each intensity value considered. But we could still lower the value and get good results.

Maybe in some specific applications it could be something to take in account but here we can have quite good results.

So we multiply CDF by 7.