Convolutions in Image Processing | Week 1, lecture 6 | MIT 18.S191 Fall 2020

The basics of convolutions in the context of image processing.

Contents
00:00 Introduction
01:12 Box blur as an average
03:00 Dealing with the edges
04:31 Gaussian blur
05:30 Visualizing gaussian blur
06:04 Convolution
06:40 Kernels and the gaussian kernel
07:26 Looking at the convolution in Julia
08:45 Julia: `ImageFiltering` package and Kernels
09:08 Julia: `OffsetArray` with different indices
10:15 Visualizing a kernel
11:25 Computational complexity
12:00 Julia: `prod` function for a product
13:00 Example of a non-blurring kernel
16:00 Sharpening edges in an image
17:13 Edge detection with Sobel filters
21:25 Relation to polynomial multiplication
25:00 Convolution in polynomial multiplication
26:08 Relation to Fourier transforms
28:50 Fourier transform of an image
31:50 Convolution via Fourier transform is faster
34:00 Final thoughts

[passerby]

If I were the students, I would be so freaked out about the professor sounding like that moving pi on the interwebz.

[nickh]

congrats on getting literally the best teacher ever for this class

[ca-ke]

i'm 3 weeks behind on my actual lectures, but 3b1b has tricked me into watching a half an hr lecture that has nothing to do with my degree

[halian.vilela]

The moment you finally realize what was that "gaussian blur" filter you've seen in Photoshop since forever!

[quahntasy]

*Wish Universities would hire faculty like Grant instead of PowerPoint slide readers that we got*

[sumitgupta]

I am a simple man, I see 3blue1 brown I click.

[DipietroGuido]

Wtf imagine having him as your actual professor

[LuisAlonzoRivero]

Teachers that are also content creators is the future of online learning.
The quality of this course was off the charts.

[ijeremyoliver]

19:47 "This will really accentuate the points where this Sobel filter, convolved across the image, ends up non-zero."

I love that moment in a lecture where the professor says something that 20 minutes early would have been absolute nonsense to me.

[Thomas.P.C]

AAAA I was so jealous when one of my MIT friends said they got Grant Sanderson to be teaching. MIT is super lucky to have you! Feel free to teach at Caltech too though ;-;

[lafasanagnuhd]

I don't think Grant is gonna see this but still... I am so glad to see a teachter who is so passionated about teaching the world and sharing his knowledge. If you happen to read this, thank you so much!!! u helped me so much for understanding mathmatical concepts for my engineering bachelor

[SDoylerrs]

I can't believe this is a live stream. It's so well planned and executed. Can't wait for next week.

[nostradingus]

Mr. Sanderson; thank you. I am deeply appreciative of your ability to intuitively explain these oft challenging concepts, and your willingness to do it so prolifically and on an open platform, and I’m sure that this sentiment is near universal for anyone who tunes in!

[abc]

This guy can't be appreciated enough. There are so many minute nuances to his videos that really make a big difference when you add all up. His dedication to make the content as intuitive as possible is awe inspiring. God bless him

[guikich]

You can think the image as an Electrical signal. As you apply the Fourier Transform you get the frequencies in the "signal" (Image). As you make the convolution again on the Fourier version, you are actually returning to the "pixels" domain and Filtering the image, which get rids of higher spacial frequencies.

[enisten]

15:46 So, what was the correct answer here? "C. Sharpen" appears at the top with 143 clicks. "B. Detect edges" is marked green. But Grant says, "So, looks like most people thought that it would detect edges. But if we actually play with this . . . the effect that it has on the picture of the cat here is that actually it kind of sharpens it up . . . Now, for those of you who did answer 'edge detecting, ' you definitely are on the right track."

So, is it that most people actually were right to say "C. Sharpen" and Grant mistakenly marked "B. Detect edges" as the correct answer of the poll and then thought green means the most number of clicks?

[vierikristianto]

Watching this has taken 36 minutes of my time in the most pleasant way I can imagine

[Hiyori___]

Acoustic engineering student here. So glad I've found this video... it's amazing to see convolution applied to images. Makes the concept much more clear and intuitive. Superb lecture

[mdpaula]

I thought I was watching a class that had have nothing to do with what I should actually learn for my degree, and he suddenly makes me understand kernels, which was actually a topic I needed to learn. Thank you!!

[xintongbian]

20:41 how he just explained the whole idea of convolution neural network in just 3 seconds ...