CS 445 / CS 645TodaySamplesSampling ErrorsSupersamplingUnweighted Area SamplingWeighted Area SamplingHow is this done today? Full Screen AntialiasingGeForce3GeForce3 - MultisamplingSlide 11Slide 12PowerPoint PresentationSignal TheorySlide 15Fourier AnalysisFourier TransformNyquist RateFlaws with Nyquist RateSlide 20Sampling in the Frequency DomainConvolutionFilteringSinc FilterBilinear FilterSampling PipelineCS 445 / CS 645AntialiasingToday•Final Exam–Thursday, December 13th at 7:00•Project 4-1 Out•MoviesSamples•Some objects missed entirely, others poorly sampledSampling ErrorsSupersampling•Take more than one sample for each pixel and combine them•Do you actually render more pixels?•Can you combine the few pixels you have?•How many samples is enough?•How do we know no features are lost?Unweighted Area Sampling•Average supersampled points•All points are weighted equallyWeighted Area Sampling•Points in pixel are weighted differently–Flickering occurs as object movesacross display•Overlapping regions eliminates flickerHow is this done today?Full Screen Antialiasing•Nvidia GeForce2–OpenGL: scale image 400% and supersample–Direct3D: scale image 400% - 1600%•3Dfx Multisampling–2- or 4-frame shift and average•Nvidia GeForce3–Multisampling but with fancy overlaps•ATI SmoothVision–Programmer selects samping patternGeForce3•Multisampling–After each pixel is rendered, write pixel value to two different places in frame bufferGeForce3 - Multisampling•After rendering two copies of entire frame–Shift pixels of Sample #2 left and up by ½ pixel–Imagine laying Sample #2 (red) over Sample #1 (black)GeForce3 - Multisampling•Resolve the two samples into one image by computing average between each pixel from Sample 1 (black) and the four pixels from Sample 2 (red) that are 1/ sqrt(2) pixels awayGeForce3 - Multisampling•No AA MultisamplingGeForce3 - Multisampling•4x Supersample MultisamplingSignal Theory•Convert spatial signal to frequency domainSignal Theory•Represent spatial signal as sum of sine waves (varying amplitude and phase shift)Fourier Analysis•Convert spatial domain to frequency domain–U is a complex number representing amplitude and phase shift–i = sqrt (-1)Fourier Transform•Examples of spatial and frequency domainsNyquist Rate•The lower bound on the sampling rate equals twice the highest frequency component in the image’s spectrum•This lower bound is the Nyquist RateFlaws with Nyquist Rate•Samples may not align with peaksFlaws with Nyquist Rate•When sampling below Nyquist Rate, resulting signal looks like a lower-frequency oneSampling in the Frequency Domain•Remember, sampling was defined as multiplying a grid of delta functions by the continuous image•This is called a convolution in frequency domainThe sampling gridThe function beingsampledConvolution•This amounts to accumulating copies of the function’s spectrum sampled at the delta functions of the sampling gridFiltering•To lower Nyquist rate, remove high frequencies from image: low-pass filter–Only low frequencies remain•Sinc function is common filter:–sinc(x) = sin (x)/xSpatial DomainFrequency DomainSinc Filter•Slide filter along spatial domain and compute new pixel value that results from convolutionBilinear Filter•Sometimes called a tent filter•Easy to compute–just linearly interpolate between samples•Finite extent and no negative values•Still has artifactsSampling
View Full Document
Unlocking...