Hello everyone and welcome to Computer Vision lecture series.

This is lecture 3 part 3.

Until now we have seen how we can change the pixel values of an image by image filtering.

We can apply different kind of linear and non-linear filtering operations and get different

outputs.

We can get rid of noise and sometimes we can improve the image quality as well.

However, in terms of frequencies there are well established tools like Fourier series

and Fourier transforms which can help us do more rigorous analysis.

But before we jump into how we can handle frequency domain in through our images, we

want to take an overview, a short overview of what does it mean when we say we are sampling

the image and some problem related to that like aliasing.

So we want to take us just understanding and quickly just go through what these things

are before we jump into rigorous analysis of Fourier domain or frequency domain.

Here is an image of a zebra.

We take every other row and every other column and essentially we would have some sample

the image by two and we generate something like this.

This image is smaller in size.

Just I have resized the image just to show visually the comparisons.

Here you can see when you compare both these images you can see that near the edges during

the edges you see a bit of blur and even in the background when you see closely you see

that there are some blurring occurring here.

So while sub sampling aliasing is a very common problem.

How aliasing occurs we are going to look at it now.

A signal can be represented in multidimensional form if it has multidimensions but and usually

physical signals are dependent on time or location or things like that.

So usually signals can be represented in multidimensional manner.

Here we take an example of one dimensional sinusoidal wave and let's sample it here

along this points mentioned along the curve of the sign.

When we draw a curve that passes through all that points we see that we perceive another

wave here which has lower frequency and it has lost the original information.

So the sample signal still looks like looks like the original wave still looks like a

wave but it's not original.

It has because of because of this sub sampling it has lost its original frequency.

So this is an aliasing problem simply shown in one dimensional signal.

It can be dangerous sub sampling can be dangerous.

Why because you might have seen examples when in movies or in videos when you're watching

a video that a car is going forward and the wheels are rotating in the other direction.

This is a very common problem of sub sampling.

Another is checkerboard effects or checkerboards they disintegrate or become disarrayed and

it does not make sense.

And this is not a problem of the original scene it is a problem of image capturing mechanism

basically sub sampling.

Some certain patterns in the scene like checkerboards or even striped shirts can look funny or can

become distorted on color television.

Specifically movie pattern movie pattern can occur.

You can see here an example of movie patterns movie patterns can occur when you're when

there is a pattern like stripes on an object in the scene being photographed and that can

interfere with the shape of the sensors and this kind of patterns can appear in your final

output.

This is an example of how a checkerboard becomes distorted at far sides due to the limitations