sampling-13apr10-150dpi-med

sampling-13apr10-150dpi-med - Sampling and pixels CS 178,...

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Sampling and pixels CS 178, Spring 2010 Marc Levoy Computer Science Department Stanford University
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! Marc Levoy Outline ! sampling and aliasing ! solutions to aliasing raise the sampling rate preflter using convolution ! sampling and human perception the “sampling rates” oF typical display media the acuity oF the human visual system the right way to compute circle oF conFusion ( C ) ! prefltering versus postfltering versus reconstruction ! display and printing technologies 2
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! Marc Levoy Point sampling a scene 3 (Classic Media) (original image is 1976 ! 1240 pixels)
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! Marc Levoy Point sampling a scene 4 (Classic Media) sample every 4 th pixel in x and y (original image is 1976 ! 1240 pixels)
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! Marc Levoy Point sampling a scene 5 every 4 th pixel in x and y
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! Marc Levoy Point sampling a scene 6
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! Marc Levoy Point sampling a scene ! point sampling means sampling at widely separated positions without frst prefltering (smoothing) ! in the presence oF high Frequencies in the original, this oFten produces aliasing (jaggies, moiré) 7
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! Marc Levoy Point sampling a different scene 8 (Natasha Gelfand)
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! Marc Levoy Point sampling a different scene 9 (Natasha Gelfand) sample every 4 th pixel in x and y (original image is 1024 ! 683 pixels)
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! Marc Levoy Point sampling a different scene 10 every 4 th pixel in x and y
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! Marc Levoy Point sampling a different scene ! sharp boundaries exhibit aliasing, but smooth features don’t ! i.e. high frequencies alias easily, but low frequencies don’t 11
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! Marc Levoy Aliasing of sine waves ! aliasing is high frequencies masquerading as low frequencies due to insufFciently closely spaced samples 12 abstract function (http://ptolemy.eecs.berkeley.edu/eecs20/week13/moire.html) spatial aliasing in images
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! Marc Levoy Aliasing of sine waves 13 abstract function (http://ptolemy.eecs.berkeley.edu/eecs20/week13/moire.html) spatial aliasing in images (http://ptolemy.eecs.berkeley.edu/eecs20/week13/aliasing.html) temporal aliasing in audio ( http://www.michaelbach.de/ot/mot_wagonWheel/index.html) temporal aliasing The demo of wagon wheels below is fun to play with but a bit confusing. What I believe the author is doing is drawing point samples regularly in time (always at 24 samples per second) of a continuously spinning wagon wheel, then presenting these images to us as a movie. What the slider controls is not the number of samples taken per second - it’s always 24 - but rather the amount the wheel has rotated between samples. One thing that makes it confusing is that computer displays don’t update at 24 frames per second (fps), but rather 60, or 75, or something else, depending on the display. There is probably some interaction between the 24fps and 60fps that the author is not describing, and we may be seeing. That’s why I punted in class and started drawing wagon wheels on the whiteboard.
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! Marc Levoy Combinations of sine waves ! a sum of sine waves, each of different wavelength (
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sampling-13apr10-150dpi-med - Sampling and pixels CS 178,...

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