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Joshua Barczak CMSC435 UMBC
Antialiasing Joshua Barczak CMSC435 UMBC *Some material borrowed from Dr. Olano (without asking)
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Joshua Barczak CMSC435 UMBC
PIXELS SUCK! Joshua Barczak CMSC435 UMBC This slide NOT borrowed from Dr. Olano (if you’re offended, its all my fault)
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Why Pixels Suck Original Scene Luminosity
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Why Pixels Suck Pixel Sampling Samples 4
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Why Pixels Suck Displayed Image Luminosity 5
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Why Pixels Suck Jaggy Lines 6
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Why Pixels Suck Jaggy Edges 7
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Why Pixels Suck Missed Detail
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Strobing/Popping 9
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Frequency Aliasing
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Aliasing Pixels cause a wide range of visual errors Jagged edges
Missed detail Strobing and popping Frequency aliasing All collectively called “aliasing” Though that’s somewhat incorrect…
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Adding More… Reference Image.
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Adding More… 2x Resolution (Cropped)
Problem #1: They stop fitting on the slide…
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Adding More… 4x Resolution (Cropped)
Problem #2: It doesn’t solve the underlying problem… The pixels themselves are the problem, not the lack thereof…
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Image Blurring Simplest Blur: Smear away the problem…
Average over NxN pixel neighborhood Smear away the problem…
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Blurring the Image? Reference Image.
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Blurring the Image? 3x3 Blur
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Blurring the Image? 5x5 Blur
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Blurring the Image? 7x7 Blur Now its too blurry…
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Super-Sampling 3/9 Multiple “sub-samples” per pixel Estimates fraction of pixel covered by edge
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Super-Sampling 6/16 6/16 6/16 Adding more samples gets us closer (4x4) 0.375
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Super-Sampling 10/25 10/25 10/25 Adding more samples gets us closer (5x5) 0.4
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Super-Sampling 15/36 15/36 15/36 Adding more samples gets us closer (6x6) 0.41
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Super-Sampling 21/49 21/49 21/49 Adding more samples gets us closer (7x7) 0.42 Albeit painfully slowly…
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Super-Sampling Adding more samples gets us closer (128x128) 0.496
8128/16384 8128/16384 8128/16384 Adding more samples gets us closer (128x128) 0.496
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Original
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3x3 SuperSample
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7x7 SuperSample
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Adaptive Super-Sampling
Super-sample pixels which differ sharply from their neighbors Example: Max absolute difference in normalized RGB Thresholded at 0.1
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Aliased
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Adaptive
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Sources of Aliasing Geometric Aliasing Shader Aliasing
Small primitives Edges Shader Aliasing Noisy textures Bumpy/Shiny
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Multi-sampling (MSAA)
SuperSampling Multi-Sampling Interpolate and shade at centroid of covered samples, store same result at each sample Interpolate and shade 3 times, store 3 results Geometric Geometric Shader Shader More on this later…
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Analytic Antialiasing: Lines
Draw band of pixels straddling line Weight pixels by distance to line Wikipedia
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Analytic Antialiasing: Polygons
Compute exact area of overlap region, weight accordingly Complicated Not as effective as you think Stay tuned
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Behold! Your Nemesis! The Infamous Oblique Checkerboard!
The worst possible case for antialiasing Every possible sampling problem all in one image
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2x2 (4 SPP)
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4x4 (16 SPP) What’s that?
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Moiree Patterns Interference pattern due to misaligned grids
Regular grids are a terrible sampling pattern…
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Irregular Sampling “Jitter” sample locations
Random offset within each cell Aliasing is replaced by noise Still wrong, but its less obviously wrong… Jittered Grid
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4x4 Regular
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4x4 Jittered
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8x8 Jittered
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16x16 Jittered
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32x32 Jittered (1024 samples!) And the ringing still doesn’t stop…
What gives?
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Why Pixels Suck Pixel Sampling Samples 46
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Aliasing Undersampled: Reconstructed wave has lower frequency
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Sampling Sampling a function multiplies by an “impulse train”
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* Reconstruction Applying a filter reconstructs a continuous function
Original Better filter, better reconstruction…
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Reconstruction Discrete convolution: Shifted Filter Kernel si xi
Weighted average of samples that overlap filter’s support g()
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“A Pixel Is Not a Little Square”
It is a little shifted reconstruction filter convolved with a continuous 2D signal Sample within pixel Sample within support of reconstruction filter Averaging samples Box reconstruction filter g(x)=1 g(x)=0 X=-0.5 X=0.5
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“A Pixel Is Not a Little Square”
It is a little shifted reconstruction filter convolved with a continuous 2D signal Sample within pixel Sample within support of reconstruction filter What if we used a different filter? g(x)=1 g(x)=0 X=-1 X=1 Yes, pixels overlap…
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The Fourier Transform A periodic function can be represented as a weighted sum of an arbitrarily large number of cosine waves Frequency domain (weights): Spatial domain (signal):
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Fourier Transform: Examples
High band limit These are called “frequency spectra” Low band limit X axis Frequency Y axis Scaling factor
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Sampling Sampling does strange and terrible things to the frequency spectrum “Base” spectrum “Alias” spectrum
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Nyquist-Shannon Sampling Theorem
A signal may be exactly reconstructed from samples if the sampling rate is more than twice the band limit Nyquist Limit
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Aliasing Raise sample rate Shift Alias spectra Aliasing -Frequency
No Aliasing Nyquist limit Band limit Sampling rate
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Guess the band limit… Why is a raven like a writing desk…?
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Guess the band limit… “To infinity and beyond!”
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Box filter Fourier Transform Oscillates into infinity (and beyond…)
“Leaking” alias spectra Base signal is nice and crisp…
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Gaussian filter Fourier Transform Approaches zero very fast
“Leaking” alias spectra are imperceptibly small… Base signal gets blurred a bit…
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32x32 Box Average pixel samples…
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32x32 Gaussian Gaussian weighting (and overlap neighboring pixels)
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