Convolutions in Image Processing - MIT 18.S191 Fall 2020 - Week 1

Explore the fundamentals of convolutions in image processing through this comprehensive 36-minute video lecture from MIT's 18.S191 Fall 2020 course. Delve into topics such as box blur, Gaussian blur, and edge detection using Sobel filters. Learn about kernels, computational complexity, and the relationship between convolutions and polynomial multiplication. Discover the connection to Fourier transforms and their application in image processing. Gain hands-on experience with Julia programming language, including the use of the ImageFiltering package and OffsetArrays. Follow along as the lecturer demonstrates various image processing techniques, from basic blurring to advanced edge sharpening, providing a solid foundation in computational thinking for image manipulation.

- Introduction.
- Box blur as an average.
- Dealing with the edges.
- Gaussian blur.
- Visualizing gaussian blur.
- Convolution.
- Kernels and the gaussian kernel.
- Looking at the convolution in Julia.
- Julia: `ImageFiltering` package and Kernels.
- Julia: `OffsetArray` with different indices.
- Visualizing a kernel.
- Computational complexity.
- Julia: `prod` function for a product.
- Example of a non-blurring kernel.
- Sharpening edges in an image.
- Edge detection with Sobel filters.
- Relation to polynomial multiplication.
- Convolution in polynomial multiplication.
- Relation to Fourier transforms.
- Fourier transform of an image.
- Convolution via Fourier transform is faster.
- Final thoughts.