Image Filtering, Part
2: Resampling
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Today’s readings |
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Forsyth & Ponce, chapters 8.1-8.2 |
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http://www.cs.washington.edu/education/courses/490cv/02wi/readings/book-7-revised-a-indx.pdf |
Announcements
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Photoshop help sessions for project 1 |
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Today after class (228) |
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Thursday at 6pm (228) |
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Demo sessions next Thursday 12-2:30 |
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signup online |
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Image Scaling
Image sub-sampling
Even worse for synthetic
images
Sampling and the Nyquist
rate
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Aliasing can arise when you sample a
continuous signal or image |
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Demo applet http://www.cs.brown.edu/exploratories/freeSoftware/repository/edu/brown/cs/exploratories/applets/nyquist/nyquist_limit_java_plugin.html |
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occurs when your sampling rate is not
high enough to capture the amount of detail in your image |
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formally, the image contains structure
at different scales |
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called “frequencies” in the Fourier
domain |
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the sampling rate must be high enough
to capture the highest frequency in the image |
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To avoid aliasing: |
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sampling rate > 2 * max frequency in
the image |
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i.e., need more than two samples per
period |
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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
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So far, we considered only power-of-two
subsampling |
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What about arbitrary scale reduction? |
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How can we increase the size of the
image? |
Image resampling
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So far, we considered only power-of-two
subsampling |
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What about arbitrary scale reduction? |
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How can we increase the size of the
image? |
Image resampling
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So what to do if we don’t know |
Resampling filters
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What does the 2D version of this hat
function look like? |
Subsampling with bilinear
pre-filtering
Bilinear interpolation
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A common method for resampling images |
Things to take away from
this lecture
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Things to take away from this lecture |
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An image as a function |
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Digital vs. continuous images |
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Image transformation: range vs. domain |
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Types of noise |
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LSI filters |
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cross-correlation and convolution |
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properties of LSI filters |
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mean, Gaussian, bilinear filters |
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Median filtering |
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Image scaling |
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Image resampling |
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Aliasing |
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Gaussian pyramids |
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Bilinear interpolation |
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