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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## Project 1 : Histograms

There is also one important thing to be note here that during histogram equalization the overall shape of the histogram changes, where equailsation in histogram stretching the overall shape of histogram remains same. The last thing equlisation need to know that we know the histogramm is to create the output image by assigning to each pixel it’s new value.

The histogram of a digital image is a distribution of its discrete intensity levels in the range [0,L-1]. This aspect is also present on the second image because there is a noise issue that makes harder the determination of an accurate threshold value.

Then we have to find the point where both distribution cross each other. After applying we got the following image and its following histogram.

### Image Processing

So let’s look what we obtain if we use this value. We only used the raw Gaussian pdf. One of the method to do that is thresholding which consist in converting a gray-scale image into a binary image. This is the optimum method to get a threshold, the implementation of such a solution is for example Otsu’s method to equalisatiin thresholding based on minization of the intra class variance.

In most cases palette change is better as it preserves the original data. Which could encode different colors.

## Histogram equalization

This method usually increases the global contrast of images when its usable data is represented by close contrast values. It returns a vector containing the relative frequencies associated to the histogram. In that cases histlgram contrast is decreased.

MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms and a lot of many other things. There is a test running before computing the histogram. In this part we are only going to consider Gray scale images. The MATLAB function computing the mean when we give it a 2 dimensional array our image is returning an average per column. As presented before, I’m in this part equalieation the formula presented in the theoretical definitions at the beginning of this report.

The goal of these methods, especially MBOBHE, is to improve the contrast eqjalisation producing brightness mean-shift and detail loss artifacts by modifying the HE algorithm. Which works well with bins, in other cases the display of Gaussian pdf is not going to fit the histogram very well if there are too few bins.

CLAHE was developed to prevent the over amplification of noise that adaptive histogram equalization can give rise to. To be able to perform further transformations on the image, we have to normalize the histogram. 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.

The background is black and is representing a big part of the image.

Red, Green and Blue. To be able to segment the image, we need to find a threshold that is representing a good equualisation to separate the two different gray level.

### Point Operations – Histogram Equalization

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. A detailed explanation of the code is available in the Implementation part.

As presented in section IV of the theoretical definitions, a Gaussian distribution is characterized by two parameters: Let’s interpret the resulting cumulative distribution. So we are considering only the range of values equaoisation 50 and We developed a function that is taking as input a 2 dimension array a digital image containing for each pixel an associated intensity value.

To do so, several methods are available, manually select a value, determine an average, use a function. Each one of this elements contains a value or a set of value coding the intensity level at each position.

On the previous image, we display the original Gaussian pdf computed using the mean and the standard deviation determined with the patches in both areas. The last part involving Gaussian mixture, allows us equalisatiom determine the characteristics of a Gaussian noise in a image and based on the pdf to determine a value to threshold an image.

For consistency with statistical usage, “CDF” i.

The histogram for this image is shown in the following table. Indeed, a linear cdf is associated to the uniform histogram that we want the resulting image histogrm have.

Now we have is the last step, in which we have to map the new gray level values into number of pixels. Indeed, here the noise is making things a bit harder.

So two explanations, maybe this issue with the cdf is really screwing things or the equalisation is compressing our histogram.