april 5 notes

• convolution (wikipedia)
• edge detection with convolution
• image processing fundamentals
• LU decomposition
• graphs as matrices
• 3D projection

key ideas

• convolution combines two functions (or images) by putting one (scaled) at every position of the other.
• for image processing, one function is the image, the other is the "kernel", typically much smaller
• gaussian blur is a primary example; the gaussian is the "kernel"
• by using kernels like [-1,0,1] or [1,-2,1] we can take first or 2nd derivatives
• in horizontal, vertical, or diagonal directions
• which can give a gradient (direction and magnitude of pixel change) at each point
• the length of that gradient is a typical "edge detection"
• inverse of a matrix is typically done by LU decomposition (gaussian elimination)
• sparse matrices are once where most of the entries are zero; there are special storage methods and algorithms for dealing with them, depending on where the zeros are.
• rotations and projections are 3D/2D transformations of objects described by (x,y,z) or (x,y) coordinates in space. Both are accomplished with matrix multiplications using specific rotation or projection matrices.