Computer Graphics. Course SS 2007 Antialiasing. computer graphics & visualization

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1 Computer Graphics Course SS 2007 Antialiasing

2 How to avoid spatial aliasing caused by an undersampling of the signal, i.e. the sampling frequency is not high enough to cover all details Supersampling - increase sampling frequency Prefiltering - filter the signal before sampling Postfiltering filtering after reconstruction

3 How to avoid spatial aliasing caused by an undersampling of the signal Supersampling - increase sampling frequency Use more rays per pixel, i.e. virtually increase resolution of pixel raster e.g. use 4x4 rays per pixel and compute average of all 16 colors as final pixel color OK, but doesn t eliminate aliasing because sharp edges contain infinitely high frequencies

4 Supersampling Uses several samples from the scene Virtually increases image resolution Then, down-filter the high resolution image to the original size Use different kinds of filters for down-filtering Regular supersampling Nyquist frequency for aliasing only shifted Use irregular sampling patterns

5 Filtering: average weighted samples

6 Filtering example

7 Filtering - jittered instead of regular sampling

8 Regular sampling Visibility of aliases is due to regular sampling grid Human visual system: Sensitive against regular structures But rather insensitive against high frequency noise Stochastic supersampling Place samples randomly within pixel Can result in sample clusters Alias frequencies are converted to noise

9 Poisson-disk sampling Minimal distance between samples Random generation of samples Jittered sampling Random jittering from regular grid points Stratified random sampling Regular partitioning of pixel region One random sample per partition

10 Comparison Regular, 1x1 Regular 3x3 Regular, 7x7 Jittered, 3x3 Jittered, 7x7 10

11 Adaptive supersampling Performs supersampling in regions of high frequencies Edges, shadows etc. Has to weight contributions appropriately

12 Example: 12

13 Example: 13

14 Example: 14

15 Example: 15

16 How to avoid spatial aliasing caused by an undersampling of the signal Prefiltering Antialiasing before sampling Filtering (smoothing) of the signal to remove details below the sampling frequency Ideally eliminates aliasing completely Area weighted sampling per pixel Combine the color contributions under a pixel to determine the final color

17 Prefiltering Smoothing the image removes high frequencies

18 Prefiltering

19 Prefiltering How can we perform the smoothing of an image Think about the respective operation in the frequency domain set all frequencies higher than a particular frequency to zero (low-pass filtering) This can be achieved by multiplication of the fourier transform with a box function

20 Prefiltering Multiplication of the fourier transform with a box function corresponds to convolution of the signal with a sinc-function (sin(x)/x) s(x) S(f) 1 - /2 0 /2 x FT IFT 0 sinc-function f

21 Antialiasing by prefiltering Ideal reconstruction Convolution with a sinc Spreads colors across neighbors In reality, i.e. on a monitor, convolution is rather with box or sphere 21

22 Prefiltering by area weighted sampling Treat a pixel as an area rather than a point Determine the color of all objects seen under this area Weight color contributions relative to coverd area and use as the pixel color

23 Prefiltering combines color contributions into a pixel

24 Example

25 Example Without and with prefiltering

26 Texture mip-mapping is a prefiltering method A texture is stored in different resolutions i.e. with decreasing frequency limit At each resolution values from next finer resolution levels are averaged At rendering time, at every rendered object point the appropriate averages with respect to the actual sampling frequency are used

27 Mip-mapping is a prefiltering method

28 Nearest Neighbor Linear texture interpolation

29 without MipMapping with MipMapping

30 How to avoid spatial aliasing caused by an undersampling of the signal Postfiltering (low-pass filter) after reconstruction No, just blurres the image

31 Summary Quality of rendering strongly depends on antialiasing algorithms used Typically, supersampling in combination with prefiltering is used Supersampling of both textures and geometry And now, we are ready to implement a high quality and efficient ray tracing algorithm What comes next is an alternative (and more efficient!!!) rendering technique

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