Convolutions in image processing | Week 1 | MIT 18.S191 Fall 2020 | Grant Sanderson

2020-09-03

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The basics of convolutions in the context of image processing.

For full course information, visit https://github.com/mitmath/computational-thinking/tree/Fall20

Course website: https://computationalthinking.mit.edu/Fall20/

To learn more about Julia, head to https://julialang.org

Next lecture: https://www.youtube.com/watch?v=rpB6zQNsbQU

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

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