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

This course introduces convolution in image processing, covering blur, kernels, edge sharpening, Sobel edge detection, and Fourier-transform-based computation. It includes implementations and visualizations in Julia.

Syllabus

- 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.