CSE168 Computer Graphics II, Rendering. Spring 2006 Matthias Zwicker

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1 CSE168 Computer Graphics II, Rendering Spring 2006 Matthias Zwicker

2 Last time Sampling and aliasing

3 Aliasing Moire patterns

4 Aliasing Sufficiently sampled Insufficiently sampled [R. Cook ]

5 Fourier analysis Periodic signals can be expressed as a summation of sinusoidal waves The Fourier transform computes the complex amplitude at each frequency Spatial domain Frequency domain, power spectrum

6 Convolution Spatial domain Convolution Frequency domain Multiplication

7 Sampling Spatial domain: multiply signal with impulse train Frequency domain: convolve signal with Fourier transform of impulse train Spatial domain

8 Sampling Theorem (Shannon 1949) A signal can be reconstructed exactly if it is sampled, at least, at twice its maximum frequency The minimum sampling frequency is called the Nyquist frequency

9 Anti-aliasing in graphics Image signals are not band-limited to half the pixel frequency in general Prefiltering Supersampling Band-limit Sample Sample Reconstruct

10 Supersampling Sampling patterns Reconstruction filters

11 Poisson Disk Sampling [Hanrahan] Spatial domain [Hanrahan] Frequency domain Random sampling with minimum distance constraint Dart throwing algorithm

12 Poisson Disk Sampling 2x2 Poisson sampling 2x2 uniform sampling [Dippe 85] [Dippe 85]

13 Today Reconstruction filtering Realistic camera models High dynamic range imaging

14 Reconstruction Reconstruction filters are weighting functions to compute a weighted average of the samples Continuous pixel Sampled pixel Sample Reconstruct

15 Box Filter Pretending pixels are little squares Take the average of samples in each pixel spatial frequency

16 Box filter Pixels are not little squares Original highresolution image Horizontal banding artifacts Down-sampled with a 5x5 box filter (uniform weights)

17 The Ideal Reconstruction Filter Unfortunately it has infinite spatial extent Every sample contributes to every interpolated point Expensive/impossible to compute Ringing (Gibbs phenomenon) Sampled signal frequency Ideal reconstruction filter spatial frequency

18 Problems with Reconstruction Filters Excessive pass-band attenuation results in blurry images Excessive high-frequency leakage can accentuate the sampling grid Filters with a small support in the spatial domain have a large support in the frequency domain frequency

19 Mitchell-Netravali Filters [1988]

20 Reconstruction from non-uniform samples Requires normalization Samples Reconstruction kernel Non-uniform positions Pixel boundary

21 Questions?

22 Realistic camera models So far: ray tracing using the pinhole model

23 Pinhole cameras

24 Pinhole cameras Problems

25 Pinhole cameras Problems Small pinhole gathers little light, requires long exposure Larger pinhole reduces sharpness

26 Lenses Gather more light Need to be focused Lens

27 Lenses Pinhole Lens 6 sec. exposure 0.01 sec exposure

28 Thin lens model Approximative model for well-behaved lenses All parallel rays converge at focal length Rays through the center are not deflected

29 Thin lens model How are arbitrary rays deflected when passing through a thin lens?

30 Thin lens model

31 Thin lens model Similar triangles

32 Thin lens model More similar triangles

33 Thin lens model Thin lens formula All rays passing through a single point on a plane at distance in front of the lens will pass through a single point at distance behind the lens

34 Thin lens model Focus at infinity: Film plane Closest focusing distance: Object

35 Thin lens model Out of focus film plane results in spherical blur Out of focus film planes Spherical blur

36 Depth of field Blurriness of out of focus objects depends on aperture size Aperture

37 Depth of field

38 Ray tracing using a thin lens model Place image plane at distance D from lens plane Generate primary rays with random origin on lens aperture Pinhole Thin lens Object in focus Primary rays Image plane Primary rays Image plane

39 Camera parameters Typical SLR lens Focal length 35mm f-number f-3.5 Aperture is (focal length)/(f-number), i.e. 10mm Depth of field effects only for very short distances distances, < 5m

40 Camera parameters Typical SLR lens Field of view depends on focusing distance Film size is 36mm x 24mm Focus at infinity, vertical field of view is

41 More realistic camera models A realistic camera model for computer graphics, Kolb, Mitchell, Hanrahan Lens distortion Exposure, motion blur [Kolb et al.] Full simulation Thick lens approximation Thin lens approximation

42 Questions?

43 HDR and tone mapping HDR: high dynamic range Dynamic range: ratio of largest over smallest intensity value in image The dynamic range of light in real environments is often larger than the range of the sensor The dynamic range of rendered images is often larger than the range of the display

44 HDR photography Acquire several images with different exposures Recover a HDR intensity for each pixel [Wikipedia]

45 HDR photography Steve Mann /index.html Paul Debevec Mitsunaga, Nayar, Grossberg ects/rad_cal/rad_cal.php

46 Tone mapping Compress dynamic range of image without losing detail [Wikipedia]

47 Tone mapping Naïve approach: map fix luminance value to white using linear scaling

48 Tone mapping Contrast preserving, non-linear scaling A contrast based scale factor for luminance display, Ward, 1994

49 Tone mapping Spatially varying non-linear scaling A tone mapping algorithm for high contrast images, Ahiskmin, 2002

50 Multi-scale methods Reduce contrast of low-frequencies Keep high frequencies

51 Multi-scale methods Halos

52 Edge-preserving filtering Do not blur across edges Non-linear filtering (not a convolution)

53 Bilateral filter Tomasi and Manduchi 1998

54 Tone mapping with the bilateral filter

55 Tone mapping with the bilateral filter Fast Bilateral Filtering for the Display of High-Dynamic-Range Images, Durand et al., 2002

56 Next time Participating media and subsurface scattering

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