Hello everyone and welcome back to Compute Vision Lecture Series.

This is Lecture 3, Part 2.

We will continue talking about image filters.

In this part we are specifically going to talk about nonlinear filters.

So let's start.

In the previous lecture we saw how linear filters can be convolved across images and

we can generate different kind of outputs depending on what we are looking for.

We saw Gaussian filters to be one of the very useful filters which are separable as well

as can be convolved with multiple filters.

And also we saw how different examples of box filter as well as sobel filters that can

be applied using convolutional operators.

In this lecture we are talking about nonlinear filters.

Some filters like median morphological operations they are considered to be nonlinear filters.

We are also going to look into a fun application called simulating tilt photography.

So tilt photography is an actual art in photography but we can also fake it and we will see how

we can do that.

So what are median filters?

Median filters you take it operates over a range or window or predefined window.

You calculate the values, you sort the values and then you take the medium intensity in

that video.

So when you sort the pixel values in the neighborhood in the defined neighborhood of the median

filter you are basically doing a nonlinear operation and therefore median filtering is

considered to be a nonlinear operation.

Rank filter also works in some similar sense and therefore it is also considered a median

filter.

The questions that comes to your mind first is how different is median filter from the

mean filter.

Is median filter a kind of convolution?

But as we saw that when you apply median filter it takes it sorts the intensity values and

then takes the median value and therefore it is inherently a nonlinear operation, nonlinear

filter.

However when you apply median filters you are doing actually convolution.

This is an example of salt and pepper noise.

Salt and pepper noise is considered this white and black dots which are spread across the

images.

Now if you want to remove this noise what do we do?

We can start with applying mean filtering like we did in the previous example in the

previous lecture where we saw we can apply mean filtering for smoothing out the images.

So let's start by applying mean filters here.

When we apply a mean filter of 3 x 3 window size the noise is still there.

Although the images resolution or the quality is reduced and it is a bit also smoothed over.

However we see also that the noise of salt and pepper is also a little bit reduced.

So let's apply a bigger sized mean filter and see if we are able to get rid of the salt

and pepper noise.

In this case we are actually getting rid of the salt and pepper noise.

However the image quality is severely reduced.

So what is the solution here?

Here we see that this is the original salt and pepper noisy image.

Let's try to see if median filtering works.

So when you apply a median filter of 3 x 3 in a 3 x 3 salt and pepper noises can in a