1	Image Sampling
2	Image Scaling
3	Image sub-sampling
4	Image sub-sampling
5	Even worse for synthetic images
6	Sampling and the Nyquist rate Aliasing can arise when you sample a continuous signal or image occurs when your sampling rate is not high enough to capture the amount of detail in your image Can give you the wrong signal/image—an alias formally, the image contains structure at different scales called “frequencies” in the Fourier domain the sampling rate must be high enough to capture the highest frequency in the image To avoid aliasing: sampling rate ≥ 2 * max frequency in the image said another way: ≥ two samples per cycle This minimum sampling rate is called the Nyquist rate
7	2D example
8	Subsampling with Gaussian pre-filtering
9	Subsampling with Gaussian pre-filtering
10	Compare with...
11
12	Some times we want many resolutions
13	Gaussian pyramid construction
14	Image resampling So far, we considered only power-of-two subsampling What about arbitrary scale reduction? How can we increase the size of the image?
15	Image resampling So far, we considered only power-of-two subsampling What about arbitrary scale reduction? How can we increase the size of the image?
16	Image resampling So what to do if we don’t know
17	Resampling filters What does the 2D version of this hat function look like?
18	Bilinear interpolation A simple method for resampling images
19	Things to take away from this lecture Things to take away from image processing lecture An image as a function Digital vs. continuous images Image transformation: range vs. domain Types of noise LSI filters cross-correlation and convolution properties of LSI filters mean, Gaussian, bilinear filters Median filtering Image scaling Image resampling Aliasing Gaussian pyramids Bilinear interpolation