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(1)

Cameras

Digital Visual Effects Yung-Yu Chuang

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

Camera trial #1

scene film

Put a piece of film in front of an object.

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

Shrinking the aperture

Why not making the aperture as small as possible?

• Less light gets through

• Diffraction effect

(2)

Shrinking the aperture High-end commercial pinhole cameras

$200~$700

Adding a lens

scene lens film

Lenses

Thin lens equation:

(3)

Thin lens formula

f D’ D

Similar triangles everywhere!

y’

y

y’/y = D’/D

Frédo Durand’s slide

Thin lens formula

f D’ D

y’

y

y’/y = D’/D y’/y = (D’-f)/f

Frédo Durand’s slide

Similar triangles everywhere!

Thin lens formula

f D’ D

D’ D 1 1 1

+ = f

The focal length f determines the lens’s ability to bend (refract) light. It is a function of the shape and index of refraction of the lens.

Frédo Durand’s slide

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

• Thin lens applet:

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

(4)

Zoom lens

Nikon 28-200mm zoom lens.

200mm

28mm

simplified zoom lens in operation From wikipedia

Field of view vs focal length

i o

f o i

1 1 1 

Gaussian Lens Formula:

Scene

Sensor

f α

α = 2arctan(w/(2i)) w

Field of View:

Example: w = 30mm, f = 50mm => α ≈ 33.4º

≈ 2arctan(w/(2f))

Slides from Li Zhang

Focal length in practice

24mm

50mm

135mm

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

(5)

Correcting radial distortion

from Helmut Dersch

Vignetting

Vignetting

L1

L2

L3 B

A

more light from A than B !

Slides from Li Zhang

Vignetting

Vignetting

L1

L2

L3 B

A

more light from A than B !

original corrected

Goldman & Chen ICCV 2005

Slides from Li Zhang

Chromatic Aberration

Lens has different refractive indices for different wavelengths.

Special lens systems using two or more pieces  of glass with different refractive indexes can 

reduce or eliminate this problem.

http://www.dpreview.com/learn/?/Glossary/Optical/chromatic_aberration_0 1.htm

Slides from Li Zhang

(6)

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

Exposure

• Two main parameters:

– Aperture (in f stop)

– Shutter speed (in fraction of a second)

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

• Faster shutter speed freezes motion

Effects of shutter speeds

1/125 1/250 1/500 1/1000

Walking people Running people Car Fast train

From Photography, London et al.

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)

(7)

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

lens sensor

Point in focus

Object with texture Diaphragm

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

lens sensor

Point in focus

Object with texture Diaphragm

Depth of field

From Photography, London et al.

Exposure

• Two main parameters:

– Aperture (in f stop)

– Shutter speed (in fraction of a second)

• Reciprocity

The same exposure is obtained with an exposure twice as long and an aperture area half as big

– Hence square root of two progression of f stops vs. power of two progression of shutter speed

– Reciprocity can fail for very long exposures

From Photography, London et al.

(8)

Reciprocity

• Assume we know how much light we need

• We have the choice of an infinity of shutter speed/aperture pairs

• What will guide our choice of a shutter speed?

– Freeze motion vs. motion blur, camera shake

• What will guide our choice of an aperture?

– Depth of field, diffraction limit

• Often we must compromise

– Open more to enable faster speed (but shallow DoF)

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, 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)

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

Sensitivity (ISO)

• Third variable for exposure

• Linear effect (200 ISO needs half the light as 100 ISO)

• Film photography: trade sensitivity for grain

• Digital photography: trade sensitivity for noise

From dpreview.com

(9)

Summary in a picture

source hamburgerfotospots.de

Demo

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

Film camera

scene lens & film

motor

aperture

& shutter

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

(10)

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

Sensor noise

• Blooming

• Diffusion

• Dark current

• Photon shot noise

• Amplifier readout noise

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

SLR view finder

lens

Mirror (when viewing) Mirror

(flipped for exposure)

Film/sensor

Prism Your eye

Light from scene

(11)

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

Field sequential

Field sequential Field sequential

(12)

Prokudin-Gorskii (early 1900’s)

Lantern projector

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

Prokudin-Gorskii (early 1900’s)

Multi-chip

wavelength dependent

Embedded color filters

Color filters can be manufactured directly onto

the photodetectors.

(13)

Color filter array

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

CMY

Why CMY CFA might be better

Color filter array

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

Bayer’s pattern

(14)

Demosaicking CFA’s

bilinear interpolation

original input linear interpolation

Demosaicking CFA’s

Constant hue-based interpolation (Cok)

Hue:

Interpolate G first

Demosaicking CFA’s

Median-based interpolation (Freeman)

1. Linear interpolation 2. Median filter on color

differences

Demosaicking CFA’s

Median-based interpolation (Freeman)

original input linear interpolation

color difference (e.g. G-R)

median filter (kernel size 5)

Reconstruction (G=R+filtered difference)

(15)

Demosaicking CFA’s

Gradient-based interpolation (LaRoche-Prescott)

1. Interpolation on G

Demosaicking CFA’s

Gradient-based interpolation (LaRoche-Prescott)

2. Interpolation of color differences

Demosaicking CFA’s

bilinear Cok Freeman LaRoche

Demosaicking CFA’s

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

(16)

Foveon X3 sensor

• light penetrates to different depths for different wavelengths

• multilayer CMOS sensor gets 3 different spectral sensitivities

Color filter array

red green blue output

X3 technology

red green blue output

Foveon X3 sensor

X3 sensor

Bayer CFA

(17)

Cameras with X3

Sigma SD10, SD9 Polaroid X530

Sigma SD9 vs Canon D30

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

White Balance

automatic white balance warmer +3

(18)

White Balance

illumination

reflectance perception

Color constancy

What color is the dress?

Color constancy Autofocus

• Active

– Sonar – Infrared

• Passive

(19)

Digital camera review website

• A cool video of digital camera illustration

• http://www.dpreview.com/

Camcorder

Interlacing

with interlacing without interlacing

Deinterlacing

blend weave

(20)

Deinterlacing

Discard

(even field only or odd filed only)

Progressive scan

Hard cases

Computational cameras 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.

• Rajeev Ramanath, Wesley E. Snyder, Youngjun Yoo, Mark S. Drew, Color Image Processing Pipeline in Digital Still Cameras, IEEE Signal Processing Magazine Special Issue on Color Image Processing, vol. 22, no. 1, pp. 34- 43, 2005.

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

• http://www.100fps.com/

參考文獻

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