CS 775: Advanced Computer Graphics. Lecture 12 : Antialiasing

Transcription

1 CS 775: Advanced Computer Graphics Lecture 12 : Antialiasing

2 Antialiasing How to prevent aliasing? Prefiltering Analytic Approximate Postfiltering Supersampling Stochastic Supersampling Antialiasing Textures Other forms of aliasing and antialiasing Colour Time

3 Antialiasing Prefiltering f x Prefilter Prefilter or smoothen the image so that the high-frequency components are removed before sampling. I ' x R w This is infeasible in a CG context (why?)

4 Antialiasing Prefiltering Prefiltering is infeasible in a CG context because discrete sampling is inherent in a pixel-based image model. Sampling and reconstrucion in CG is calculating a value at the centre of a pixel and then assigning that value to the entire spatial extent of that pixel So we cannot filter before sampling as we can do with convential continuous signals.

5 Antialiasing Prefiltering A1 A3 I = I1A1+I2A2+I3A3+IBAB Analytic solution Convolve with a filter at every pixel. A2 AB We can do subpixel sampling. Practical solution -This can be incorporated in the scanline rasterization process using the Abuffer (antialiased, area-averaged accumulation buffer). Make polygon masks, approximate and accumulate coverage.

6 Antialiasing Prefiltering That said, digital cameras can include optical filters to prefilter the image before capturing it on a CCD sensor. This can help bandlimit the analog optical intensity function captured by the camera and prevent some aliasing. More on this if you study computer vision/image processing.

7 Antialiasing Supersampling (or Postfilterng) reducing x here Supersampling increases the sampling rate and thus removes aliasing. increases 1/ x here R w Does this always work? What changes when we are working with images?

8 Fourier Theory Fourier Transforms in 2D Since images can be treated as 2D signals With the intensity being the signal value at a particular (x, y) pixel location. i 2 ux uy F u, v = f x, y e dxdy But images are also discrete samples of the continuous world and hence we use a discrete form of the Fourier transform to work with images. N 1 N 1 1 F u, v = 2 N x=0 i 2 f x, y e ux uy N N y=0

9 Fourier Theory Fourier Transform in 2D Remember that Fourier Spectra plots are Magnitude plots M = F u, v = R 2 u, v I 2 u, v 1/ 2

10 Fourier Theory Fourier Transform in 2D - Filters

11 Antialiasing Supersampling For supersampling, we assumed a bandlimited signal. What if the original signal has infinite support? There is no way to bandlimit frequencies that can appear in an image.

12 Antialiasing Supersampling In reality, there is no way to restrict the frequencies that may appear in an image during formation. Consider a square image made of nxn pixels of side Δx. Then the Nyquist limit of the pixel is 1/(2Δx). Frequencies higher than one cycle every two pixels will cause aliasing

13 Antialiasing Supersampling

14 Antialiasing Supersampling Create a higher resolution image and combine samples I pixel = w s. I s s Instead of one sample per pixel Take more samples per pixel Then combine the sample to calculate the intensity at the pixel

15 Antialiasing Supersampling This pushes aliasing to higher frequencies. nxn pixels of side x fmax=1/2 x 2nx2n pixels of side x/2 fmax=1/ x

16 Antialiasing Supersampling Supersampling reduces (but does not remove) anti-aliasing in images. Often create a higher resolution image, lowpass filter (i.e., blur) and then downsample.

17 Antialiasing Stochastic Supersampling Regular super sampling Adaptive super sampling Jitterred super sampling Types of Noise patterns that can be used for sampling Poisson, Poisson Disk and Jitterred. Watt, A. and Watt, M Advanced Animation and Rendering Techniques

18 Antialiasing Stochastic Supersampling Stochastic sampling is considered better as the eye is less sensitive to the presence of high frequency noise than aliases. Intuition: Yellot, 1983 Distribution of photoreceptors in the eye is like a poisson disk. Yellott, J. I. Jr (1983). Spectral consequences of photoreceptor sampling in the rhesus retina. Science, 221,

19 Antialiasing - FSAA Full scene antialiasing is common in modern graphics cards. Controlled by the display driver. Supersampling can also be controlled by the application. For e.g., while playing a game the game engine may increase or decrease the levels of antialiasing.

20 Antialiasing in Half-Life 2