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

CS148: Introduction to Computer Graphics and Imaging

Final Review Session

CS148 Midterm Review Pat Hanrahan, Winter 2007

Outline

Final InfoReview of Topics

DisplaysExposure & Tone ReproductionMattes & CompositingFilteringSamplingCompressionDigital VideoModeling


Final Exam Info

Time: Wed, Mar 21st at 12:15pmLocation: Building 300, Rm 300Duration: 2 hours

Closed bookConsists of a few (4 or 5) multi-part questionsAll material through modeling lecture

Emphasis: second half of classStrongly emphasized: material on assignmentsFocus on: material from lecturesAlso covered: material from readings

This review covers the second half, see the midterm review for the first half of the material


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)


Displays

CRT – electron beam + phosphorsPlasma – ionized gas forms plasmaLCD – twisted nematic cellsDLP – fast twitching micromirrorsLaser ProjectionOLEDElectronic Ink


Exposure & Tonemapping

Contrast: Max:MinWorld:

Possible 100,000,000,000:1Typical 100,000:1

People: 100:1Media:

Printed Page: 10:1Displays: 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



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 rangeLinear mapRemap through response/gammaLog L – L / (1+L)More complicated techniques (separate luminance/color)


Mattes & Compositing

Combine foreground and background objectsα = 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 & Compositing

Blue screen matte extraction

Given:C – Observed colorCB – 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 – integration/summation of translated filter with signal

n

nmgnfmgf )()())(*(


Fourier Transform

Expresses any signal as sum of sin and cos functions


Fourier Transform

Spatial Domainf(x,y)

Frequency DomainF(ωx, ωy)

Fourier Transform

InverseFourier

Transform

Convolution Multiplication

Multiplication Convolution

Sinc Box


Fourier Transform


Fourier Transform – Low Pass


Fourier Transform – High Pass


Fourier Transform – Band Pass


Sampling

Imagers sample continuous functionssensors integrate over their area

Examples of imagersretina photoreceptorsdigital camera CCD or CMOS array

Digitally – record value of signal periodically (samples)


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


Sampling – Spatial Domain


Sampling – Frequency Domain


Undersampling – Frequency Domain


Reconstruction – Frequency Domain


Reconstruction – Spatial Domain


Compression

Kolmogorov Complexity – smallest program to generate data

Lossless CodingRun length coding – exploit obvious redundancyHuffman 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

e1

e2

b1b2

a*e1 + b*e2

(a,b) in this basis

m*b1 + n*b2

(m,n) in this basis

Any vector can be expressed as linear combination of either basis (pair of vectors)


Lossy Image Compression (JPEG)

Image

DiscreteCosine

TransformTransformed

Image

Quantization

(Lossy Step)

Reorder+

Coding CompressedData 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

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 Transform

6 8 5 9 5 5 6 6

6.25 0 -1 -2 0 0

Full Transform

High Resolution DetailsMedium Resolution DetailsLow Resolution DetailsAverage Value

-.5.75


Video

Raster scan – convert 2D signal to 1DSynchronize vertical refresh to swap buffers

Television – Amplitude modulation (next)Color TV – use amplitude modulation to place

luminance and chrominance signals at different frequenciesLess responsive to high frequencies in color

CompressionI-Frames – JPEG CompressionP,B-Frames – Motion predictions + encode difference


Amplitude Modulation


Modeling

RepresentationsDense Polygonal MeshesBicubic surfacesSubdivision Surfaces

OperationsInstancingTransformation – linear and non-linearCompression, simplificationDeform, skin, morph, animateSmoothSet operations


Bezier Curve


Subdivision Surfaces

Loop subdivision algorithmExtraordinary pointsSemi-regular meshes

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

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