CS148: Introduction to Computer Graphics and Imaging Final Review Session

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

2. Outline • Final Info • Review of Topics • Displays • Exposure & Tone Reproduction • Mattes & Compositing • Filtering • Sampling • Compression • Digital Video • Modeling

3. 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. 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. Displays • CRT – electron beam + phosphors • Plasma – ionized gas forms plasma • LCD – twisted nematic cells • DLP – fast twitching micromirrors • Laser Projection • OLED • Electronic Ink

6. 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 Sun Moon Stars 10000 1000 100 10 1 .1 .01 .001 .0001 candela/m2 100 Eye 1

7. Exposure & Tonemapping

8. 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. Mattes & Compositing • Combine foreground and background objects • α = Coverage • = Area • = Opacity • = 1 – Transparency • CF – foreground color, CB – background color • C = α * CF + (1 – α) * CB • Premultiplied α: C’ = αC = (αr, αg, αb, α) • “Pulling a matte” – blue screen, image processing α

10. Mattes & Compositing • Blue screen matte extraction • Given: • C – Observed color • CB – Backing color (possibly per pixel) • Compute: • CF = (αFRF, αFGF, αFBF, αF) • Matte Equation: • C = CF + (1 – αF)CB • 3 Equations, 4 Unknowns – must make some assumptions

11. Convolution • Convolution – integration/summation of translated filter with signal

12. Fourier Transform • Expresses any signal as sum of sin and cos functions

13. Fourier Transform Fourier Transform Spatial Domain f(x,y) Frequency Domain F(ωx, ωy) Inverse Fourier Transform Convolution Multiplication Multiplication Convolution Sinc Box

14. Fourier Transform

15. Fourier Transform – Low Pass

16. Fourier Transform – High Pass

17. Fourier Transform – Band Pass

18. 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. 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. Sampling – Spatial Domain

21. Sampling – Frequency Domain

22. Undersampling – Frequency Domain

23. Reconstruction – Frequency Domain

24. Reconstruction – Spatial Domain

25. 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. Bases e1 e2 a*e1 + b*e2 (a,b) in this basis Any vector can be expressed as linear combination of either basis (pair of vectors) b2 b1 m*b1 + n*b2 (m,n) in this basis

27. Lossy Image Compression (JPEG) Discrete Cosine Transform Quantization (Lossy Step) Image Transformed Image 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. 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. 6 8 5 9 5 5 6 6 0 -1 -2 0 0 -.5 .75 Wavelet Transform Full Transform 6.25 High Resolution Details Medium Resolution Details Low Resolution Details Average Value

30. 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. Amplitude Modulation

32. 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. Bezier Curve

34. Subdivision Surfaces • Loop subdivision algorithm • Extraordinary points • Semi-regular meshes