Hi my name is Michelle and I’m an

academic at Swinburne. A lot of my research is in image processing which is

using computers and computer programs to interpret images. Computers don’t have

the same kind of knowledge about the world that you and I do.

For instance, unless they are specifically programmed to do so, they

couldn’t identify what is in this picture. Whereas you and I can

immediately identify it as an aeroplane however computers can pick up on a lot

of details and nuances that we as humans might miss. For instance a computer

program can identify the differences between these images, whereas we would really struggle with it. One of the tools that we use in image processing is the

Fourier transform. The Fourier transform is an extension of the Fourier series

which we use for periodic continuous signals. The Fourier transform can take

care of non periodic signals like this white noise. One of the things that we

are often interested in with image processing is reading text. The fact is

that while humans are very good at reading handwritten and printer texts,

computers really struggle with it. This is the reason that some websites use

these capture images. These allow the website to make sure that it is dealing

with a real human instead of a computer or a robot. Having a computer read text

is useful for the post office, for transferring books to electronic copies,

for number plate recognition and for automating the input of handwritten

forms. One of the methods that is used for recognising characters is to use the

Fourier transform. When we apply a transform to something, we retain the

information that is captured in the original data but we display it in a

different way. It’s the same as taking these waveforms which are displayed in

Cartesian space and displaying them using a log scale instead. All the

information is still there it is just easier to interpret it in this new form.

If we take the Fourier transform of a signal, we move it from the time domain

to the frequency domain a step function in the time domain becomes a sync

function in the frequency domain. If we move back to the time domain, you

would still get back to the original data. As a quick aside, the sync function

in the time domain becomes a step function in the frequency domain. But a

word of warning it doesn’t work like that for all signals. We can also move

images into the frequency domain. This image of parallel graduated lines

becomes two white dots on a black background in the frequency domain. This

white circle becomes a pattern that looks like ripples from a stone thrown

in the water. And this white square on a black background becomes a cross. The

more you look at the patterns in the frequency domain caused by these simple shapes the more you can predict what might happen if you change the design.

For instance if I change the spacing between the graduated lines, the dots in

the frequency domain move apart. And if I rotate the lines the dots rotate as well.

We can also take the Fourier transform of more complex images . This image is

very famous in the image processing community and here it is in the

frequency domain. The lines in the frequency domain image correspond to the legs of the tripod and the line of the horizon. What researchers have found is

that we can actually exploit the lines and circles and their corresponding

patterns in the frequency domain to use it to recognize characters. Let’s look at

the letter A for example. Pretty much however you draw it it has to upright or

close to upright lines and a crossbar at the bottom. When we transfer these to the frequency domain, they all end up looking quite similar. And they definitely look

more similar to one another than the B or a C or a . In fact, we can use the

representation of written numbers and letters in the frequency domain to

identify what letter or number is in the time domain. And so we use the Fourier

transform to identify letters and numbers. We can also use the frequency

domain to remove noise from an image for instance in this case the image has been

corrupted with diagonal lines. These lines appear as very bright spots and

circles in the frequency domain. So we can remove them using a filter. This is

the filter applied and this is the image with the noise

removed. We can also remove white noise or speckle by removing the low frequency

components of the signal in the frequency domain. These sit at the

extremities of the image. So we only keep the signals in the middle. This is the

filter applied. And this is the result. While it may look a bit blurry to you

and I, there is now no noise so the computer can make better judgments about the image. I’ve only shown you a few examples, but you can see from this short

presentation just how useful the Fourier is for image processing and analysis. And

once you understand the basics, it isn’t too difficult to apply.

very useful!!! Thank You

super helpful

Thank you!

very illuminating! hope to see more of these.

Very good introduction. Thanks !!

thank you!!!

Informative FT you tube. Thank you

excellent introduction!

Hi , is it possible to detect fire and smoke in same analysıs ?

Thanks

cool tut

the best video ever

Amazing presentation. I wish you also had explained how periodic behavior can be seen in the frequency domain because that is what I want to learn now but well, we don't always get what we want. 😛

https://www.youtube.com/watch?v=QgMuHC8lvoI&t

Thank you! Very helpful video.

nice presentation

Hy, what a code can be used to compose image from waves? Thank's

Help

The most intuitive explanation I've seen! Great samples, thank you!