# 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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The cdf of 64 for value coincides with the number of pixels in the image.

To solve such an issue it exists a solution based on detection and statistics where we can build a model based on both distribution and a Bayesian analysis which could reduce that issue. Indeed, there one main things that could be improved. To do equallisation, the easiest method to do that is hietogram doing a manual threshold based on the intensity distribution showed in the histogram. Here is the histogram of this picture:.

So all the code I’m going to present here is using matlab programing language syntax. But this could be more accurate than the manual selection if the noise has the same standard deviation. To do so, we need to divide each value of the histogram by the number of pixel. Here is a result when applied to the crowd image, very dark initially and maybe to bright at the end.

We could discuss the choice of considering all values inferior or equal to the threshold but in this case it’s not a very influencing factor.

We only used the raw Gaussian pdf. In this section, we are going to show different histograms associated to different images and try to explain and interpret them in regard to the image we gave as input.

Let’s start by displaying the histograms of the two checker board. Now we have is the last step, in which we equalisahion to map the new gray level values into number of pixels.

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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. Let’s interpret the resulting cumulative distribution. We inplemented the function presented earlier in this report and here is the core implementation of it:.

### Histogram Equalization – Towards Data Science

To do so we are going to look for a point where the difference between the two curves is histogtam small and this point will be the place where both curves meet and it histoggram be our threshold. In terms of qualitative judgment on the image, we can clearly see that the contrast is better because we are now able to see what was at the background and that the picture is really showing a crowd, which was not that obvious before.

As we can see, the result is quite convincing because we really get the skull. Once we have the cdf, we are going uistogram “stretch” the histogram to get a “uniform” distribution. For instance, a 8 eight bits color images encode the Red and Green channel with three bits and the blue with two. We can see some more details but this could maybe be enhanced more.

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. It is therefore suitable for improving the local contrast and enhancing the definitions of edges in each region of an image. The cdf is a cumulative sum of all the probabilities lying in its domain and defined by:. So to do that we can rely on the computation of the first derivative which will be minimum at a local minimum or maximum.

So, the cumulative distribution functions looks more like a line because the histogram hasn’t been stretch as much as the other images because its original histogram was already distributed on the whole range of intensities. 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. To do so, we are going to multiply the cdf by the range of values. A detailed explanation of the code is available in the Implementation part.

This could be implemented of course, but this is not going to be very effective, because the histogram is a discrete structure so we need to have a position described by an integer. Which works well with bins, in other cases the display of Gaussian pdf is not going to fit the histogram very well.

By using this site, you agree to the Terms of Use and Privacy Policy. Histogram is a graphical representation of the intensity distribution of an image. But here it’s a bit more tricky than before to get accurate patches, this is why on the following plot, the Gaussian distributions are not describing correctly the histogram. 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.

So we multiply CDF by 7.

## Project 1 : Histograms

The next step being using convolution with filter kernel to create some special features such as blurring or edge detection.

We worked on histograms which are the best tool to understand the distribution of an image intensities. To conclude this part, I think that the method using Gaussian pdf characteristics is pretty accurate and provide a good segmentation which is automatic contrary to the manual selection.

The method is useful in images with backgrounds and foregrounds that are both bright or both dark. 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 is a method to process images in order to adjust the contrast of an image by modifying the intensity distribution of the histogram.