Now that we are experts on noise, let's see what happens to the histogram of an

image when you add noise to it. For that, we are going to use a very

simple example. We see here an image that has only three

regions and then only three values. If we were to draw the histogram of this

image, we will see a different heights but we actually see on the three,

basically, delta functions. One that stands for the black region,

one that stands for the gray region, and one that stands for this lighter region

and the height of these depends on the area of each one of the regions.

So, when we add noise, with each one of these

distribution, how is this histogram going to change?

It's going to change from this three delta function to something.

let's see what happens. So, here we see three examples already.

In the first example, we took the original image and we added Gaussian

noise. This the type of the probability

distribution of the noise. And we actually see it reflected here.

It's very clearly, they are kind of three Gaussian distributions.

This is going to be very important, it's going to help us to estimate the noise,

if we are only given the image, as we are going to see in the next video.

Here, we see a shape which is very similar to the shape of their Rayleigh

noise. It's kind of tilted and then it goes down

almost like a Gaussian, slightly different.

So clearly, the shapes here are very different.

For example, this is kind of symmetric. This is not.

Remember, these are probability distributional functions for the noise so

we are not expecting to see a perfect function.

This all in probability. And here, we see the gamma noise.

Once again, a shape very similar around each one of the pixel values,

a shape that is very similar to the actual probability distribution function.

So, these are the three of them. They just continue seeing some additional

examples. I'm going to ask you now a question.

Which noise do you think we added here to the original image?

So, this is how the, basically, the image looks after we add the noise.

Which one of these six do you think we have added here?

Please give me an answer to that. I think it's not very hard to get to the

answer if we just compare the shapes. Once again, remember, if we only had the

original image, we have kind of three delta functions with different heights

representing the black, the gray, and the white regions.

And now, we see very clearly, exponential functions.

So, it was these noise, okay? We cannot see that from the image

itself. It's very hard to see.

Is this Gaussian, is this exponential, is this Rayleigh?

You have to really be trained to observe that just from the image.

But it's much easier from the histogram. So now, that we are really experts I'm

going to ask you again, what's the noise here?

Please give me an answer. Just think for a second, and give me an

answer. Once again, this was the original

histogram and now, we actually see kind of uniform distributions.

So, we see clearly that this is the noise.

It's basically around the area of the original histogram with the flat regions.

So, this is a type of noise. Now, please note that in this image, the

same type of noise was added all around the image.

Otherwise, for example, if we add Gaussian noise inside this region and

uniform noise to everything else, we will see actually a Gaussian here and uniform

in the other two. So, we will see combinations of these

distributions. Finally, this is the salt and pepper.

Salt and pepper actually is not hard, in general, to recognize from the original

image. We see the black dots or the white dots.

But I also want to illustrate that in the histogram.

The histogram stays with kind of delta functions but, of course, if there was no

black there would be a new delta function of black,

or if there was black it would be a larger basically a taller delta function

there and the same for y. So, we can see from the histograms what

actually happens sometimes. And therefore, we can use the histograms

to estimate the type of noise and to estimate the parameters of the noise as

we're going to see in the next video. Thank you.