Shrinking the aperture

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Cameras

Digital Visual Effects, Spring 2006 Yung-Yu Chuang

2006/3/1

with slides by Fedro Durand, Brian Curless, Steve Seitz and Alexei Efros

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Outline

• Pinhole camera

• Film camera

• Digital camera

• Video camera

• High dynamic range imaging

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Camera trial #1

scene film

Put a piece of film in front of an object.

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Pinhole camera

scene film

Add a barrier to block off most of the rays.

• It reduces blurring

• The pinhole is known as the aperture

• The image is inverted

barrier

pinhole camera

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Shrinking the aperture

Why not making the aperture as small as possible?

• Less light gets through

• Diffraction effect

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Shrinking the aperture

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High-end commercial pinhole cameras

$200~$700

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Adding a lens

scene lens film

“circle of confusion”

A lens focuses light onto the film

• There is a specific distance at which objects are “in focus”

• other points project to a “circle of confusion” in the image

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Lenses

• Any object point satisfying this equation is in focus

• Thin lens applet:

http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html

Thin lens equation:

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Exposure = aperture + shutter speed

• Aperture of diameter D restricts the range of rays (aperture may be on either side of the lens)

• Shutter speed is the amount of time that light is allowed to pass through the aperture

F

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Exposure

• Two main parameters:

– Aperture (in f stop)

– Shutter speed (in fraction of a second)

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Effect of shutter speed

• Longer shutter speed => more light, but more motion blur

• Faster shutter speed freezes motion

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Aperture

• Aperture is the diameter of the lens opening,

usually specified by f-stop, f/D, a fraction of the focal length.

– f/2.0 on a 50mm means that the aperture is 25mm – f/2.0 on a 100mm means that the aperture is 50mm

• When a change in f-stop occurs, the light is either doubled or cut in half.

• Lower f-stop, more light (larger lens opening)

• Higher f-stop, less light (smaller lens opening)

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Depth of field

Changing the aperture size affects depth of field.

A smaller aperture increases the range in which the object is approximately in focus

See http://www.photonhead.com/simcam/

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Exposure & metering

• The camera metering system measures how bright the scene is

• In Aperture priority mode, the photographer sets the aperture, the camera sets the shutter speed

• In Shutter-speed priority mode, the

photographers sets the shutter speed and the camera deduces the aperture

• In Program mode, the camera decides both

exposure and shutter speed (middle value more or less)

• In Manual mode, the user decides everything (but can get feedback)

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Pros and cons of various modes

• Aperture priority

– Direct depth of field control

– Cons: can require impossible shutter speed (e.g. with f/1.4 for a bright scene)

• Shutter speed priority

– Direct motion blur control

– Cons: can require impossible aperture (e.g. when requesting a 1/1000 speed for a dark scene)

• Note that aperture is somewhat more restricted

• Program

– Almost no control, but no need for neurons

• Manual

– Full control, but takes more time and thinking

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Distortion

• Radial distortion of the image

– Caused by imperfect lenses

– Deviations are most noticeable for rays that pass through the edge of the lens

No distortion Pin cushion Barrel

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Correcting radial distortion

from Helmut Dersch

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Film camera

scene lens & film

motor

aperture

& shutter

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Digital camera

scene sensor

array lens &

motor

aperture

& shutter

• A digital camera replaces film with a sensor array

• Each cell in the array is a light-sensitive diode that converts photons to electrons

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CCD v.s. CMOS

• CCD is less susceptible to noise (special process, higher fill factor)

• CMOS is more flexible, less expensive (standard process), less power consumption

CCD CMOS

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Sensor noise

• Blooming

• Diffusion

• Dark current

• Photon shot noise

• Amplifier readout noise

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SLR (Single-Lens Reflex)

• Reflex (R in SLR) means that we see through the same lens used to take the image.

• Not the case for compact cameras

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SLR view finder

lens

Mirror

(when viewing) Mirror

(flipped for exposure)

Film/sensor Prism

Your eye

Light from scene

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Color

So far, we’ve only talked about monochrome

sensors. Color imaging has been implemented in a number of ways:

• Field sequential

• Multi-chip

• Color filter array

• X3 sensor

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Field sequential

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Field sequential

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Field sequential

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Prokudin-Gorskii (early 1900’s)

Lantern projector

http://www.loc.gov/exhibits/empire/

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Prokudin-Gorskii (early 1990’s)

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Multi-chip

wavelength dependent

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Embedded color filters

Color filters can be manufactured directly onto the photodetectors.

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Color filter array

Color filter arrays (CFAs)/color filter mosaics Kodak DCS620x

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Color filter array

Color filter arrays (CFAs)/color filter mosaics Bayer pattern

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Bayer’s pattern

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Demosaicking CFA’s

bilinear interpolation

original input linear interpolation

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Demosaicking CFA’s

Constant hue-based interpolation (Cok)

Hue:

Interpolate G first

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Demosaicking CFA’s

Median-based interpolation (Freeman)

1. Linear interpolation 2. Median filter on color

differences

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Demosaicking CFA’s

Median-based interpolation (Freeman)

original input linear interpolation

color difference median filter reconstruction

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Demosaicking CFA’s

Gradient-based interpolation (LaRoche-Prescott)

1. Interpolation on G

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Demosaicking CFA’s

Gradient-based interpolation (LaRoche-Prescott)

2. Interpolation of color differences

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Demosaicking CFA’s

bilinear Cok Freeman LaRoche

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Demosaicking CFA’s

Generally, Freeman’s is the best, especially for natural images.

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Foveon X3 sensor

• light penetrates to different depths for different wavelengths

• multilayer CMOS sensor gets 3 different spectral sensitivities

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Color filter array

red green blue output

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X3 technology

red green blue output

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Foveon X3 sensor

X3 sensor Bayer CFA

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Cameras with X3

Sigma SD10, SD9 Polaroid X530

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Sigma SD9 vs Canon D30

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Color processing

• After color values are recorded, more color processing usually happens:

– White balance

– Non-linearity to approximate film response or match TV monitor gamma

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White Balance

automatic white balance warmer +3

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Manual white balance

white balance with the white book

white balance with the red book

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Autofocus

• Active

– Sonar – Infrared

• Passive

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Digital camera review website

• http://www.dpreview.com/

• A cool video of digital camera illustration

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Camcorder

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Interlacing

with interlacing without interlacing

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Deinterlacing

blend weave

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Deinterlacing

Discard

(even field only or odd filed only)

Progressive scan

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Hard cases

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High dynamic range imaging

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Camera pipeline

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High dynamic range image

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Short exposure

10

^-6

10

⁶

10

^-6

10

⁶

Real world radiance

Picture intensity

dynamic range

Pixel value 0 to 255

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Long exposure

10

^-6

10

⁶

10

^-6

10

⁶

Real world radiance

Picture intensity

dynamic range

Pixel value 0 to 255

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Real-world response functions

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Camera calibration

• Geometric

– How pixel coordinates relate to directions in the world

• Photometric

– How pixel values relate to radiance amounts in the world

•• GeometricGeometric

–– How pixelHow pixel coordinatescoordinates relate to directionsrelate to directions in the in the world

world

•• PhotometricPhotometric

–– How pixelHow pixel valuesvalues relate to radiancerelate to radiance amounts in the amounts in the world

world

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Camera is not a photometer

• Limited dynamic range

⇒ Perhaps use multiple exposures?

• Unknown, nonlinear response

⇒ Not possible to convert pixel values to radiance

• Solution:

– Recover response curve from multiple exposures, then reconstruct the radiance map

•• Limited dynamic rangeLimited dynamic range

⇒⇒ Perhaps use multiple exposures?Perhaps use multiple exposures?

•• Unknown, nonlinear response Unknown, nonlinear response

⇒⇒ Not possible to convert pixel values to radianceNot possible to convert pixel values to radiance

•• Solution:Solution:

–– Recover response curve from multiple exposures, Recover response curve from multiple exposures, then reconstruct the

then reconstruct the radiance mapradiance map

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Varying exposure

• Ways to change exposure

– Shutter speed – Aperture

– Natural density filters

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Shutter speed

• Note: shutter times usually obey a power series – each “stop” is a factor of 2

• ¼, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000 sec

Usually really is:

¼, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024 sec

• Note: shutter times usually obey a power series – each “stop” is a factor of 2

• ¼, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, 1/500, 1/1000 sec

Usually really is:

¼, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, 1/512, 1/1024 sec

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Varying shutter speeds

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Math for recovering response curve

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Idea behind the math

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Idea behind the math

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Idea behind the math

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Recovering response curve

• The solution can be only up to a scale, add a constraint

• Add a hat weighting function

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Recovering response curve

• We want

If P=11, N~50

• We want selected pixels well distributed and sampled from constant region. They pick points by hand.

• It is an overdetermined system of linear equations and can be solved using SVD

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Matlab code

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Matlab code

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Matlab code

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Recovered response function

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Constructing HDR radiance map

combine pixels to reduce noise and obtain a more reliable estimation

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Reconstructed radiance map

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What is this for?

• Human perception

• Vision/graphics applications

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Easier HDR reconstruction

raw image =

12-bit CCD snapshot

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Easier HDR reconstruction

exposure=radiance* ΔΔtt

exposure

ΔtΔt

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• 12 bytes per pixel, 4 for each channel

sign exponent mantissa

PF

768 512 1

<binary image data>

Floating Point TIFF similar

Text header similar to Jeff Poskanzer’s .ppm image format:

Portable floatMap (.pfm)

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(145, 215, 87, 149) =

(145, 215, 87) * 2^(149-128) = (1190000, 1760000, 713000)

Red Green Blue Exponent

32 bits / pixel 32 bits / pixel

(145, 215, 87, 103) =

(145, 215, 87) * 2^(103-128) =

(0.00000432, 0.00000641, 0.00000259)

Ward, Greg. "Real Pixels," in Graphics Gems IV, edited by James Arvo, Academic Press, 1994

Radiance format (.pic, .hdr, .rad)

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ILM’s OpenEXR (.exr)

• 6 bytes per pixel, 2 for each channel, compressed

sign exponent mantissa

• Several lossless compression options, 2:1 typical

• Compatible with the “half” datatype in NVidia's Cg

• Supported natively on GeForce FX and Quadro FX

• Available at http://www.openexr.net/

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Radiometric self calibration

• Assume that any response function can be modeled as a high-order polynomial

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Space of response curves

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Space of response curves

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Assorted pixel

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Assorted pixel

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Assorted pixel

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Assignment #1 HDR image assemble

• It you have not subscribed the mailing list, please do so.

• Will be announced around Friday through the mailing list

• You will use a tripod to take multiple photos with different shutter speeds. Write a program to recover the response curve and radiance

map. We will provide image I/O library.

Furthermore, apply some tone mapping operation on your photograph.

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References

• http://www.howstuffworks.com/digital-camera.htm

• http://electronics.howstuffworks.com/autofocus.htm

• Ramanath, Snyder, Bilbro, and Sander. Demosaicking Methods for Bayer Color Arrays, Journal of Electronic Imaging, 11(3), pp306-315.

• Paul E. Debevec, Jitendra Malik, Recovering High Dynamic Range Radiance Maps from Photographs, SIGGRAPH 1997.

• http://www.worldatwar.org/photos/whitebalance/ind ex.mhtml

• http://www.100fps.com/