1	Image Filtering, Part 2: Resampling Today’s readings Forsyth & Ponce, chapters 8.1-8.2 http://www.cs.washington.edu/education/courses/490cv/02wi/readings/book-7-revised-a-indx.pdf
2	Announcements Photoshop help sessions for project 1 Today after class (228) Thursday at 6pm (228) Demo sessions next Thursday 12-2:30 signup online
3	Image Scaling
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 Demo applet http://www.cs.brown.edu/exploratories/freeSoftware/repository/edu/brown/cs/exploratories/applets/nyquist/nyquist_limit_java_plugin.html occurs when your sampling rate is not high enough to capture the amount of detail in your image 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 i.e., need more than two samples per period This minimum sampling rate is called the Nyquist rate
7	Subsampling with Gaussian pre-filtering
8	Some times we want many resolutions
9	Gaussian pyramid construction
10	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?
11	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?
12	Image resampling So what to do if we don’t know
13	Resampling filters What does the 2D version of this hat function look like?
14	Subsampling with bilinear pre-filtering
15	Bilinear interpolation A common method for resampling images
16	Things to take away from this lecture Things to take away from this 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