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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As we mentioned before, there are two sources of Gaussian noise on this images and it appears that they are overlaying each other. On the previous result, we can see that the input image has an histogram occupying the whole range of gray histogarm and with a cumulative distribution which is going up really smoothly without big steps. Venetsanopoulos, ” Color image enhancement through 3-D histogram equalization ,” in Proc.

To do so, we can call the function histogram we have already implemented in the previous part.

Histogram equalization – Wikipedia

But in both case there is a bias due to the overlap of the two distributions:. To do so, several methods are available, manually select a value, determine an average, use a function. We can see that the result of equalization is here a compression of few levels of the histogram. But I didn’t have time to implement such a method. Let’s apply here a restriction on the range of the histogram we are displaying so it only focuses on the regions corresponding to the middle range of the histogram i.

The MATLAB function computing the mean when we give it a 2 dimensional array our image is returning an average per column. We also have an expected result for the cumulative distribution function because we have an almost linear cdf.

The histogram of a digital image is a distribution of its discrete intensity levels in the range [0,L-1]. 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.


Histogram Equalization

Once we have the cdf, we are going to “stretch” the histogram to get a “uniform” distribution. Segmentation is an operation consisting in partitioning an image into sets of elements. On the previous figure, we can see that the input picture is really dark.

See theoretical explanation in section IIIB. We obtain the following result:.

Project 1 : Histograms

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. Retrieved from ” https: As presented in section IV of the theoretical definitions, a Gaussian distribution is characterized by two parameters: And that’s here the only difference between them, because both checkerboard have the same original color and it appears that they are corrupted with the same Gaussian noise.

Finally, the last operation to perform is to give to the pixel of the new image the associated new gray level.

Then we have to find the point where both distribution cross each other.

Several methods exists to determine it. It returns a vector containing the relative frequencies associated to the histogram. Before performing histogram equalization, you must know two important concepts used in equalizing histograms.

The two previous pictures: Now we have is the last step, in which we have to map the new gray level values into number of pixels. Let us also define the cumulative distribution function corresponding to p x as. The part about the equalization showed us how to enhance the contrast of a dark image but also showed us that sometimes if the histogram is already distributed on all the range of levels, the enhancement is not very effective.

Either way this is going to be dependent of the user.

Histogram Equalization

So it equapisation sense to have three different “regions” on the histogram: Sign in Get started. In that cases the contrast is decreased. 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.


Iverson notation of the rounding function. Then we will perform some other operations to allow the user to enter the number of desired bins for the histogram and the range of values that should cover the histogram.

Maybe in some specific applications it could be something to take in account but here we can have quite good results. But if we let this aspect we can see that the result of the operation is clearly a compression of equalisatkon.

Note that to scale values in the original data that are histogra, 0 to the range 1 to L-1, inclusive, the above equation would instead be: And it seems that it’s pretty well working with the blending ratio I choose.

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.

So we multiply CDF by 7. It is not necessary that contrast will always be increase in this. In this last part, we are going to apply the previous method to a medical image in order to extract a bone structure from a CT scan of the head. We also consider the ration between dark and bright area to have a better estimation of the threshold.

So the first step is to define the patches in each area to compute the characteristics of the noise and then be able to plot them. The most important step here is to chose the best value for the threshold to get the best segmentation. To extract the bone structure from this image, we need to segment the image with a high intensity value because the bone is white and other structures are darker.