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

Announcements
Photoshop help sessions for project 1
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Thursday at 6pm (228)
Demo sessions next Thursday 12-2:30
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Image Scaling

Image sub-sampling

Even worse for synthetic images

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

Subsampling with Gaussian pre-filtering

Some times we want many resolutions

Gaussian pyramid construction

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?

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?

Image resampling
So what to do if we don’t know

Resampling filters
What does the 2D version of this hat function look like?

Subsampling with bilinear pre-filtering

Bilinear interpolation
A common method for resampling images

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