02-Gray Scale Control TTF. A TTF tells us how an imaging device relates the gray level of the input to the gray level of the output. P L Luminance, L.

02-Gray Scale Control

17 July 2008 Thursday Afternoon

1:00- 1:30 01-Exposure, Stops, and Photo-Effects

1:30-2:00 Lab 1 - Practice Shoot with D50

2:00-3:30 02-TTF & Gray Scale Control

3:30-4:15 Lab 2 - ImageJ Brightness/Contrast

4:15-5:00 03-Photo Composition

Overnight Lab 3 Take Photos

18 July 2008 Friday Morning

8:30-10:00 04-Video System TTFs

10:00-10:30 Lab 3- Continued - Photo Presentation & Critique

10:30-12:00 05-Jones Plot

17 July 2008 Thursday Afternoon

1:00- 1:30 01-Exposure, Stops, and Photo-Effects

1:30-2:00 Lab 1 - Practice Shoot with D50

2:00-3:30 02-TTF & Gray Scale Control

3:30-4:15 Lab 2 - ImageJ Brightness/Contrast

4:15-5:00 03-Photo Composition

Overnight Lab 3 Take Photos

18 July 2008 Friday Morning

8:30-10:00 04-Video System TTFs

10:00-10:30 Lab 3- Continued - Photo Presentation & Critique

10:30-12:00 05-Jones Plot

TTF

A TTF tells us how an imaging devicerelates the gray level of the inputto the gray level of the output.

P

L

Luminance, L

pixel value, P

Luminance, L

pixel value, P

3c3

2c2c10 LaLaLaaP

The TTF may be in the formof a graph, equation, or Look-Up-Table (LUT).

P

L

L

01020..

100110120

.

.300

P

001..

100110120

.

.255

becomes

pixel value, P(in the camera& sent to monitor)

Original Luminance, Lo

An Imaging System involves Multiple imaging devices (TTFs) and Multiple kinds of images (types of gray)

Luminance &Reflectance

Irradiance, I(at the sensor)

Luminance

Note: We can't see a digital image. we see a copy of the digital image displayed on a monitor or printed on a printer.

TTF(P vs Lo)(camera)

TTF(L vs P)(monitor)

Luminance, L

pixel value, P

P

L

TTFs have many alternative namesDLogH curveCharacteristic curveProfile Tone curveI/O function……etc.

A successful imaging device must be designed with an appropriate TTF.

To understand the TTF of an imaging device, we first need to understand the gray scale properties of images.

x

y

y

x

gray level

A printed, black & white image has gray valuesdescribed as reflectance, R, decimal fractionsfrom 0…1.

A digital image has gray values describedas pixel values, P, typically integers from 0…255.

Luminance, L

pixel value, P

Luminance, L

pixel value, P

Consider a hard copy image with gray values R (reflectance factor) from 0 to 1.Each location in the image (x,y) has a gray value R.

x

y

Gray Value: R = 0.653

Gray ScaleR = 1 is white

R = 0 is black

Gray levels, R, can be represented in a 3D graph.

x

y

y

x

R

However, this 3D graph isn't of much use.

0 1

Number of pixels

R

sort

remove

a

b c d

0.2 0.4 0.6 0.8

So, we re-organize the gray values as follows.

We call this graph a gray level Histogram.

The histogram tells us the properties of the gray level image.

0 1

Number of pixels

R

0 1R

0

1

0

1R R

R too low R too highBalance atR=0.47

For example, the point where the histogram balances isthe "average" gray level of the image.

has an average gray value of R=0.47.

N

Average R = 0.2 Average R = 0.47 Average R = 0.78

0 1

N

0 1 0 1RR R

The average value tells us the lightness/darkness of the image.

Bright ImageDark Image

The width of the histogram tells us the contrast of the image.

Lightness and Contrast are the two most common descriptionsof the gray characteristics of an image.

HighContrast

LowContrast

R

N

0 1 R

N

0 1R

N

0 1

Digital images are described the same way.

Lightness and Contrast are the two most common descriptionsof the gray characteristics of any image.

HighContrast

LowContrast

P

N

0 255 P

N

0 255P

N

0 255

There are many metrics for image contrast. Most are based on the maximum and minimum values in the histogram.There are two ways to show the range between Pmax and Pmin.

N NN

P0 255 P0 255P0 255

Pmin Pmax

(1) The contrast ratio: C = Pmax/Pmin

(2) The contrast difference: P = Pmax - Pmin (also called the "window")

window

Printed images can be described in terms of Reflectance or Density.

Io I

printed image

R ≡ Io/I

and

D ≡ -Log(R)

A Rule of Thumb for Contrast Metrics: A ratio is used for describing things proportional to power. A difference is used for describing things proportional to Log(power)

I is proportional to power.

Printed images can be described in terms of Reflectance or Density.

Io I

printed image

I is proportional to power.

Note that D ≡ Dmax - Dmin = [-Log(Rmin) ] - [-Log(Rmax) ] = Log(Rmax) - Log(Rmin)= Log(Rmax/Rmin)= Log(C)

Two ways to describe image contrast:(1) C = Rmax/Rmin

(2) D = Dmax - Dmin

R ≡ Io/I (R is proportional to power)

and

D ≡ -Log(R) (D is proportional to Log(power) )

"Dynamic Range": Printed Image

Io I

printed imageTwo ways to describe image contrast:

(1) C = Rmax/Rmin

(2) D = Dmax - Dmin

R ≡ Io/I (R is proportional to power)

and

D ≡ -Log(R) (D is proportional to Log(power)

(1) C is often called the "Contrast Ratio"

(2) D is often called the "Dynamic Range" (Dr = D)

L ≡ luminance in cd/m2

Lmax and Lmin

Image contrast is in terms of the maximumand the minimum luminance in the image.

Contrast Ratio: C=Lmax/Lmin

Dynamic Range: Dr = Log(C)

"Dynamic Range": Monitor (soft) Image

Hard Copy Soft CopyOriginal Scene

Contrast metrics of the Scene/Image

Lmax Lmin

Lmax LminDmax

Rmin

Dmin

Rmax

"Image Contrast Ratio" C = Lmax/Lmin or C = Rmax/Rmin

"Image Dynamic Range" Dr = Log(C)

Note: These are contrast metrics of the Images, not the imaging devices that produced them. (See later)

Caution:

There are many other metrics in common use todescribe the gray scale properties of images.Many are industry or profession specific.Many are only loosely defined.

For example, professional photographers often use the term "Key" of an image.

High "Key"Low "Key"

"Key is a characteristic of a "PROPERTLY" exposed image (subjective). Lightness is adjusted until a "PROPER" image is obtained.Then Key can be expressed in terms of the average gray level.

Low "Key"

High "Key"

High "Key"NOT low "Key", but anunder exposed image.

Learn the language of your customers!!Don't tell them they are "wrong" if their favorite metric is subjective.

Tone Characteristics of an Imaging Device


An imaging device changes one imageinto another.

original L

copy, P

The tone characteristic of theimaging device is described by the TTF

P

L

TTF of a cameratransforms thethe original histogram intothe copy histogram.

L

N

00

P

N

00

Tone Characteristics of an Imaging DeviceJust as the tone characteristics of an image are fully described bythe histogram……………

original L

copy, P

…the tone characteristicsof the imaging device are fully described by the TTF.

P

L

L

N

00

P

N

00

Tone Characteristics of an Imaging DeviceJust as the tone characteristics of an image arepartially described by metrics extracted from the histogram(contrast ratio, dynamic range, etc.)…

original L

copy, P

…the tone characteristicof the imaging device partially described by metrics extractedfrom the TTF.

P

L

L

N

00

P

N

00


original L

copy, P

L

N

00

P

N

00

Metrics of the TTFare defined differently forthe three major types of imaging devices:

(1) Image Capture Devices(camera, scanner, etc.)

(2) Digital Image Processor(computers and chips)

(3) Display Devices(printers, monitors, etc.)

Original Image

Copy Image

A computer is a commonly used DIP. It transformsone digital image intoanother digital image.

Pc0 255

0 255Po

Pc

Po

Po

Pc

(2) Digital Image Processor(DIP)

Original Image

Copy Image

Po

Pc

A B C D

OriginalIncrease

in contrast, tool A

Increasein lightness,

tool C

DIPs Commonly providesimple controls for(1) Brightness and(2) contrast

A B C D

OriginalIncrease

in contrast, tool A


tool C

A B C D

OriginalIncrease

in contrast, tool A


tool C

A B C D

OriginalIncrease

in contrast, tool A


tool C

= Brightness = Lightness/Darkness = Level

A B C D

OriginalIncrease

in contrast, tool A


tool C

= Contrast = Window

The most common TTF that isprovided in DIPs such as ImageJ and PhotoShop is a simplestraight line.

Pc = ∙Po + i or Pc = ∙(Po - j) + 128

Original Image

Copy Image

Po

Pc

0 255Po

0 255Pc

Po

Pc

0 2550

255

Slope andintercept, i

Po

Pc

0 2550

255

Slope andcenter location, j

A B C D

OriginalIncrease

in contrast, tool A


tool C

Po

Pc

0 2550

255

Shifting the curve tothe left is a brightness increase.

The left/right location is called either "brightness", "lightness", or "level".

A B C D

OriginalIncrease

in contrast, tool A


tool C

A B C D

OriginalIncrease

in contrast, tool A


tool C

Original Image

Copy Image

Po

Pc

0 255Po

0 255Pc

Shifting the curve to the left is equivalent toincreasing the intercept.

Po

Pc

0 2550

255

A B C D

OriginalIncrease

in contrast, tool A


tool C

A B C D

OriginalIncrease

in contrast, tool A


tool C

Original Image

Copy Image

Po

Pc

0 1Po

0 1Pc Shifting the curve tothe right is a brightness decrease.

A B C D

OriginalIncrease

in contrast, tool A


tool C

The left/right location is called either "brightness", "lightness", or "level".

Po

Pc

0 2550

255

> 1 is a contrast increase.

A B C D

OriginalIncrease

in contrast, tool A


tool C

Original Image

Copy Image

Po

Pc

0 1Po

0 1Pc

window

Pc = ∙Po + i or Pc = ∙(Po - j) + 128

The slope is called either "contrast", "window", or "gamma".

A B C D

OriginalIncrease

in contrast, tool A


tool C

The common digital TTF is a simplestraight line.

P0 = ∙Pc + i

Po

Pc

0 2550

255

< 1 is a contrast decrease

A B C D

OriginalIncrease

in contrast, tool A


tool C

Original Image

Copy Image

Po

Pc

0 1Po

0 1Pc

window

A B C D

OriginalIncrease

in contrast, tool A


tool C

The Digital TTF

Also called tone curve, profile, and LUT (look-up-table), point process

Often, a much more complex TTF is needed. In that case,the TTF is not well described by two simple metrics.

A B C D

OriginalIncrease

in contrast, tool A


tool C

A B C D

OriginalIncrease

in contrast, tool A


tool C

The Digital TTF

In "Threshold" Mode


original L

copy, P

L

N

00

P

N

00





Original Image

Copy Image

A printer converts pixel values, P,into reflection image density, D.

D0 3

0 255Po

P

D = -Log(R)


Generate P=0,1,2,3……255 (all possible P values)

D

Use a densitometerto measure all possibleoutput density valuesthe printer can make.

The printer TTF

D

P0 255

Dmin

Dmax

printer convention

monitor convention

P=0,1,2,3……………… 255

The printer TTF

D

P0 255

Dmin

Dmax

Printer Dynamic Range = D = Dmax - Dmin (Looks like an image dynamic range!! But it is NOT the same.)

Note that the printer dynamic range is expressed in terms of the density it CAN produce (Dmin and Dmax).

An image dynamic range is expressed in terms of its individual Dmin and Dmax.

Original Image

Copy Image

A monitor converts pixel values, P,into screen Luminance, L.

L

0 255Po

P

L


Generate P=0,1,2,3……255 (all possible P values)

Measure all possibleoutput Luminance values themonitor can make.

The Monitor TTF

L

P0 255

Lmin

Lmax

L

printer convention

monitor convention

P=0,1,2,3……………… 255

Monitor Contrast Ratio C = Lmax - Lmin

Monitor Dynamic Range = Log(C)(Looks like an image dynamic range!! But it is NOT the same.)

Note that the monitor dynamic range is expressed in terms of the luminance it CAN produce (Lmin and Lmax).

An image dynamic range is expressed in terms of its individual Lmin and Lmax.

The Monitor TTF

L

P0 255

Lmin

Lmax


original L

copy, P

L

N

00

P

N

00





(1) Image Capture Device(camera, scanner, etc.)

Illuminanceat sensor, I

pixel value, P

The TTF of the camera/scannercan be expressed in many ways:P vs RP vs LP vs I P vs H, where H=I∙tP vs Log(H)

object Rreflected L

R, L, I, H

P

It depends on the type of device and the specifications one wants to express.

(1) Image Capture Device(camera, scanner, etc.)

Illuminanceat sensor, I

pixel value, P

Or in terms of exposure, H = I∙tP vs RP vs LP vs I P vs H

object Rreflected L

R, L, or I

P

Film Camera:

D

Log(H)

Dmax

Dmin

Log(Hmin) Log(Hmax)

Output Density Dynamic Range: D = Dmax - Dmin

Input Detection Contrast Ratio: C = Hmax/Hmin

Input Detection Dynamic Range: Log(C) = Log(Hmax) - Log(Hmin)

exposure, H = I∙t

The definition of Dynamic Range depends on definingDmax, Dmin, Hmax, and Hmin. This means defining appropriatemetrics of system noise. H and D.

D

Log(H)

Dmax

Dmin

Log(Hmin) Log(Hmax)

Output Density Dynamic Range: D = Dmax - Dmin



Hmax, and Hmin

are the limiting values that are "meaningful" beyondthe level of the noise.

Dmax and Dmin

are limitingD the film can make.

Digital Video Camera:

P

L

Pmax = 255

Pmin = 0Lmin Lmax

Output Pixel Range: = Pmax + 1 (number of discrete levels)Bit Depth = Log2(N)

Input Detection Contrast Ratio: C = Lmax/Lmin

Input Detection Dynamic Range: Log(C) = Log(Lmax) - Log(Lmin)

Note: Bit Depth ≠ Camera Dynamic Range

For a digital video camerathe TTF is typically describedas P vs L.

Noise is a part of definingLmin and Lmax.

Digital Still Camera:

P

H

Pmax = 255

Pmin = 0Hmin Hmax

Output Pixel Range: = Pmax + 1 (number of discrete levels)Bit Depth = Log2(N)



For a digital still cameraexposure is H=I∙t, and the TTF is often describedas P vs H.

Noise is a part of definingHmin and Hmax.

Exposure: H=I∙t

Contrast Ratio, C = Wmax/Wmin

Input Detection Dynamic Range: Log(C)

But what kind of Logarithm do you use?

Log is the"Common Logarithm"

Dynamic Range is defined using Logarithms of different bases, K.

recall that LogK(C) = Log(C)/log(K)

Log(C) = the regular base 10 logarithm of x.

ln(C) = Log(C)/Log(e), called the natural log.

Lg2(C) = Log(C)/Log(2)

Db(C) = Log(C)/Log(100.1) called the decibel

Db(C) = 10∙Log(C) (another way to calculate Db)

D(R) = log(R)/Log(0.1)

D(R) = -1∙log(R) (another way to calculate D)

Common Log

Natural Log

Bits & Stops

Decibel

Decibel

Density

Density

10

e=2.718…

2

100.1=1.259…

100.1=1.259…

1/10 = 0.1

1/10 = 0.1

Name How to Calculate The base, K

End

02-Gray Scale Control TTF. A TTF tells us how an imaging device relates the gray level of the input to the gray level of the output. P L Luminance, L.

Documents

image contrast

gray level image

image x

gray characteristics

gray level histogram

gray value r

gray levels

hard copy image