Basics for Image Processing

What is a kernel?

A kernel is essentially a fixed size array of numerical coefficeints along with an anchor point in that array, which is tipically located at the center.

Laplacian Pyramids

A Laplacian pyramid is very similar to a Gaussian pyramid but saves the difference image of the blurred versions between each levels. Only the smallest level is not a difference image to enable reconstruction of the high resolution image using the difference images on higher levels. This technique can be used in image compression

Gaussian Pyramids

In a Gaussian pyramid, subsequent images are weighted down using a Gaussian average (Gaussian blur) and scaled down. Each pixel containing a local average that corresponds to a pixel neighborhood on a lower level of the pyramid. This technique is used especially in texture synthesis.

Sobel Operator

\[\min _ { s ^ { x } ,s ^ { y } ,\alpha } \sum _ { i = 1} ^ { k } E \left( \alpha _ { i } \mathbf { s } _ { \mathbf { i } } ^ { \mathbf { X } } + \left( 1- \alpha _ { i } \right) \mathbf { s } _ { \dot { i } } ^ { y } \right)\]