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CS148: Introduction to Computer Graphics and Imaging Final Review Session PowerPoint Presentation
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CS148: Introduction to Computer Graphics and Imaging Final Review Session. Outline. Final Info Review of Topics Displays Exposure & Tone Reproduction Mattes & Compositing Filtering Sampling Compression Digital Video Modeling. Final Exam Info.

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Presentation Transcript
outline
Outline
  • Final Info
  • Review of Topics
  • Displays
  • Exposure & Tone Reproduction
  • Mattes & Compositing
  • Filtering
  • Sampling
  • Compression
  • Digital Video
  • Modeling
final exam info
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
displays
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)
displays1
Displays
  • CRT – electron beam + phosphors
  • Plasma – ionized gas forms plasma
  • LCD – twisted nematic cells
  • DLP – fast twitching micromirrors
  • Laser Projection
  • OLED
  • Electronic Ink
exposure tonemapping
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

exposure tonemapping2
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)
mattes compositing
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

mattes compositing1
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
convolution
Convolution
  • Convolution – integration/summation of translated filter with signal
fourier transform
Fourier Transform
  • Expresses any signal as sum of sin and cos functions
fourier transform1
Fourier Transform

Fourier

Transform

Spatial Domain

f(x,y)

Frequency Domain

F(ωx, ωy)

Inverse

Fourier

Transform

Convolution Multiplication

Multiplication Convolution

Sinc Box

sampling
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)
nyquist frequency
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
compression
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!)
bases
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

lossy image compression jpeg
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.

wavelet transform
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
wavelet transform1

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

video
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
modeling
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
subdivision surfaces
Subdivision Surfaces
  • Loop subdivision algorithm
  • Extraordinary points
  • Semi-regular meshes