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 Want to help add timestamps to our YouTube videos to help with discoverability? Find out more here: https://github.com/JuliaCommunity/YouTubeVideoTimestamps Interested in improving the auto generated captions? Get involved here: https://github.com/JuliaCommunity/YouTubeVideoSubtitles