1. CS148: Introduction to Computer Graphics and Imaging Final Review Session

2. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Outline Final Info Review of Topics Displays Exposure & Tone Reproduction Mattes & Compositing Filtering Sampling Compression Digital Video Modeling

3. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Final Exam Info Time: Wed, Mar 21st at 12:15pm Location: Building 300, Rm 300 Duration: 2 hours Closed book Consists of a few (4 or 5) multi-part questions All material through modeling lecture Emphasis: second half of class Strongly emphasized: material on assignments Focus on: material from lectures Also covered: material from readings This review covers the second half, see the midterm review for the first half of the material

4. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Displays Resolution - Spatial, temporal, and color/intensity Interlaced vs. Non-Interlaced (Progressive scan) Calibration – not all displays have the same colors, calibrate to match standard (e.g. sRGB)

5. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Displays CRT – electron beam + phosphors Plasma – ionized gas forms plasma LCD – twisted nematic cells DLP – fast twitching micromirrors Laser Projection OLED Electronic Ink

6. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Exposure & Tonemapping Contrast: Max:Min World: Possible 100,000,000,000:1 Typical 100,000:1 People:100:1 Media: Printed Page:10:1 Displays:80:1 (400:1) Typical Viewing:5:1 10000 1000 100 10 1.1.01.001.0001 candela/m2 100 Eye 1 Sun Moon Stars

7. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Exposure & Tonemapping

8. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Exposure & Tonemapping Create HDR Image – Weighted log-average based on input images, shutter speeds, and response curve Gamma – display intensity is non-linear response to voltage (monitor gamma ~ 2.5) Perception – non-linear as well ( ~ 1/3) Tone Reproduction – map HDR to displayable range Linear map Remap through response/gamma Log L – L / (1+L) More complicated techniques (separate luminance/color)

9. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Mattes & Compositing Combine foreground and background objects α = Coverage = Area = Opacity = 1 – Transparency C F – foreground color, C B – background color C = α * C F + (1 – α) * C B Premultiplied α: C’ = αC = (αr, αg, αb, α) “Pulling a matte” – blue screen, image processing α

10. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Mattes & Compositing Blue screen matte extraction Given: C – Observed color C B – Backing color (possibly per pixel) Compute: C F = (α F R F, α F G F, α F B F, α F ) Matte Equation: C = C F + (1 – α F )C B 3 Equations, 4 Unknowns – must make some assumptions

11. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Convolution Convolution – integration/summation of translated filter with signal

12. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform Expresses any signal as sum of sin and cos functions

13. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform Spatial Domain f(x,y) Frequency Domain F(ω x, ω y ) Fourier Transform Inverse Fourier Transform ConvolutionMultiplication MultiplicationConvolution SincBox

14. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform

15. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform – Low Pass

16. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform – High Pass

17. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Fourier Transform – Band Pass

18. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Sampling Imagers sample continuous functions sensors integrate over their area Examples of imagers retina  photoreceptors digital camera  CCD or CMOS array Digitally – record value of signal periodically (samples)

19. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Nyquist Frequency Nyquist Frequency – ½ the sampling frequency A periodic signal with a frequency above the Nyquist frequency cannot be distinguished from a periodic signal below the Nyquist frequency These indistinguishable signals are called aliases

20. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Sampling – Spatial Domain

21. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Sampling – Frequency Domain

22. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Undersampling – Frequency Domain

23. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Reconstruction – Frequency Domain

24. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Reconstruction – Spatial Domain

25. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Compression Kolmogorov Complexity – smallest program to generate data Lossless Coding Run length coding – exploit obvious redundancy Huffman Coding – variable length code, highly probable characters -> shorter codes Transform Coding – perform invertible transform on data to make it more amenable to compression (applies to lossless and lossy!)

26. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Bases e1e1 e2e2 b1b1 b2b2 a*e 1 + b*e 2 (a,b) in this basis m*b 1 + n*b 2 (m,n) in this basis Any vector can be expressed as linear combination of either basis (pair of vectors)

27. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Lossy Image Compression (JPEG) Image Discrete Cosine Transform Transformed Image Quantization (Lossy Step) Reorder + Coding Compressed Data Stream JPEG2000 is similar but uses the wavelet transform. Exploit human perception – quantize high frequencies more heavily since we are less sensitive to them.

28. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Wavelet Transform Just another invertible transform (expresses signal in different basis) Generated in steps by calculating smoothed (approximate) values and detail (corrective) values Resulting basis functions have compact support – they are only non-zero over a limited range – error in coefficient causes localized error

29. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Wavelet Transform 68595566 6.250-200 Full Transform High Resolution Details Medium Resolution Details Low Resolution Details Average Value -.5.75

30. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Video Raster scan – convert 2D signal to 1D Synchronize vertical refresh to swap buffers Television – Amplitude modulation (next) Color TV – use amplitude modulation to place luminance and chrominance signals at different frequencies Less responsive to high frequencies in color Compression I-Frames – JPEG Compression P,B-Frames – Motion predictions + encode difference

31. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Amplitude Modulation

32. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Modeling Representations Dense Polygonal Meshes Bicubic surfaces Subdivision Surfaces Operations Instancing Transformation – linear and non-linear Compression, simplification Deform, skin, morph, animate Smooth Set operations

33. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Bezier Curve

34. CS148 Midterm ReviewPat Hanrahan, Winter 2007 Subdivision Surfaces Loop subdivision algorithm Extraordinary points Semi-regular meshes