Kashtan, Gerald, "A Tone reproduction study of a digital image processing system" (1980). Thesis. Rochester Institute of Technology.

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A Tone reproduction study of a digital image processing system

A Tone reproduction study of a digital image processing system

Gerald Kashtan

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A TONE REPRODUCTION STUDY OF A

DIGITAL IMAGE PROCESSING SYSTEM

by

Gerald L. Kashtan

A thesis submitted in partial fulfillment

of the requirements for the degree of

Bachelor of Science in the School of

Photographic Arts and Sciences in the

College of Graphic Arts and Photography

of the Rochester Institute of Technology

May, 1980

Signature of the Author .

Photographic Science

and Instrumentation

Certif ied by .

Thesis Advisor

Accepted by _ .

Supervisor, Undergraduate Research

A TONE REPRODUCTION STUDY OF A

DIGITAL IMAGE PROCESSING SYSTEM

by

Gerald L. Kashtan

Submitted to the

Photographic Science and Instrumentation Division in partial fulfillment of the requirements

for the Bachelor of Science degree

at the Rochester Institute of

_Technology

ABSTRACT

Photographic tone reproduction analysis was applied

to a digital image _processing system

_(DIPS)

. The problem

was to calculate computer _mapping functions for the DIPS

that would cause input scenes to be reproduced

_having

Clark's tone reproduction characteristics.

_Using

the graph

ical method of a Jones

_Diagram,

unique computer _mapping

functions were constructed for four images ^processed

_by

the DIPS. After _processing the

_imagery

in the _computer, the

pixels were reconstructed into photographic transparencies for projection in a _specially designed projection area.

The results of this work concluded that tone reproduction

analysis is useful in _studying the macro effect of luminance

transfer through a DIPS_, and that tone reproduction charac

teristics _may be modified

_digitally

_using pre-determined computer _mapping functions.

ii

ACKNOWLEDGMENTS

The author extends his thanks and appreciation to

Mr. Thomas Lianza and Mr.

_Andy

Masia of the Eikonix Cor

poration, ^{and to Mr. Mohamed Abouelata of the Defense}

Mapping

Agency. Appreciation and thanks also goes out to the

Eikonix Corporation who supplied the equipment for the

digital image _{processing system,} and to the United States

Central Intelligence

_Agency

for

_funding

this work. Special acknowledgment _is given to Mr. James J. Jakubowski of the

Xerox Corporation whose _advisory role in this thesis pro

ject was _greatly appreciated.

111

TABLE OF CONTENTS

List of Tables ^v

List of Figures vi

Introduction 1

Statement of the Problem 7

Discussion 7

Data Acquisition Subsystem 13

Data Reconstruction Subsystem 20

Jones Diagram 22

Experimental 23

Data Acquisition Subsystem 23

Data Reconstruction Subsystem 26

Jones Diagram 29

Results 32

Data Acquisition Subsystem 32

Data Reconstruction Subsystem 33

Jones Diagram 34

Summary

^and Conclusions 41

List of References 43

Bibliography

⁴⁵

Appendix 1 46

Appendix 2 51

iv

LIST OF TABLES

1. Experimental Steps taken to _quantify the DIPS

2. Coefficients of the Cubic Equations of

the Computer

_Mapping

Functions ³¹

v

LIST OF FIGURES

1. Clark's Tone Reproduction Curve 3

2. Jones _Diagram of the Digital Image

_Processing

System

_(DIPS)

4

3. Flow Diagram

_Showing

Major Steps. of this

Project 6

4. Black Box Example 8

5. Data Acquisition Subsystem 10

6. Data Reconstruction Subsystem 11

7. Jones Diagram 12

8. Eikonix Linear

_Array

Digitizer Bench

Layout 15

9. Quantization and

_Log

Transformation of

_Analog

Image Signals 16

10. Random

_Grey

Test

_(RGT)

Target 19

11. Sketch of Slide Projection Area 21

12. Time-Development Curves for Kodak Contrast

Process Ortho 4x5 Film 50

13. Time-Gamma Curve for Kodak Contrast Process

Ortho 4x5 Film ₅₀

14. Block Diagram of the Eikonix Digitizer

Functions ₅₂

15. Typical Response Curve for a Photodiode

Detector in the Detector

_Array

53

VI

INTRODUCTION

Two dimensional picture _processing of photographic

images _using digital computers has been used successfully

to correct degraded images , ^{perform pattern} recognition

and classification2, ^and subjectively ^{enhance recorded}

scenes3.

_Early

work in the applications of digital ^com

puters to picture _processing gave emphasis to algorithm de

sign to minimize computer time and _resources, and to output

images that resembled the input scene ^. Current applications

research is _underway to _study image _quality of

_digitally

processed _images^. Much of this work takes the form of

_dig

ital filtration functions in the spatial

_frequency

domain to fit models of the human visual system. Investigation of

spatial luminance transfer and image _quality in an image

processing ^{system should also be} considered. A type of

spatial luminance analysis well developed and documented is known in the photographic _community as tone reproduction.

A great deal of literature has been found

_dealing

with tone reproduction and image _quality of photographic

processes .

_Early

work

_{by Jones', dealing}

with tone repro duction made it possible to determine graphically ^{the rel}

ative relationships between input scene luminances and re

produced output luminances. Jones defined the objective of

the photographic process as

_being

the one to one reproduc tion of relative luminances8. Later work

_{by Clark^,}

_showed

that _Jones ^' s criterion was not an adequate method for repro

ducing

^scene

^luminances

^when visually evaluating ^{a photo}

graphed _{scene. Clark found that optimum}

(preferred)

, ^image

quality ^{could be determined through subjective} methods, ^and the results included _into an objective tone reproduction

system.

Clark's method to obtain data _relating scene lumin

ance reproduction _to subjective visual requirements was

_by

conducting psychological _scaling experiments of photographic

images on groups of observers. The results pointed out that

there exists a preferred print or

transparency

^{(the prints}

were viewed in a bright _surround, and the transparencies

projected in a dark surround) ^{. Of} both the prints and trans

parencies, ^{it was found that the preferred tone} reproduction

curves were independent of scene type and

_lighting

(night

and _very dark scenes were excluded from the

_imagery

set

Clark _tested) . A further examination of the transparencies

viewed in a dark surround showed that the preferred mean

density

^{level of the image is dependent on screen luminance}

Work

_by

Bartleson12

and ^Breneman1 _, demonstrated the

need to characterize and include the human visual and per

ception system as a part of a tone reproduction study. An

important outcome of their work is that optimum tone repro

duction will be ^obtained for _any photographic reproduction

process and _{any viewing} condition when the reproduction of

brightnesses proportional to white is made14. When this work

was compared to Clark's _research, where the relationships

between,

^stimulus characteristics and image _quality were

15 measured, ^the independent results agreed .

It is the aim of this experiment to _apply tone ^re

production analysis to a digital image _processing ^system

(DIPS),

^{for black and white imagery. Clark's preferred tone}

reproduction curve for projected positive images in a dark

surround (figure

₁₎

, ^{will be used as the} relationship ^between

log

^{scene luminances and projection}

density (log

^reproduced

scene

luminances)

^.

"

CO ^{> *}

CM

*

m

m

"12

3 4

LOG SCENE LUMINANCE

Clark's Tone Reproduction Curve (figure

₁₎

This curve will be ^inserted into quadrant VIII of the Jones

Diagram (figure

₂₎

^. The computer _mapping functions (quad

rant _{IV) ,} ^will be the variables left to be determined after

the other quadrants are known. An overall pictorial

_descrip

tion of the physical steps to this process are given in

KEY _{TO QUADRANTS}

Q

^I

Q

^II Q ^III

Q

^IV

Q

^V

Q

^VI

Q

^VII

Q

^VIII

Flare Curve

Panatomic-X film curve

_(D-log-H

_curve) Eikonix Image _{Digitizer Curve}

Computer

_Mapping

_{Function Curve} Tektronix Video Monitor Curve Contrast Process _{Ortho Film Curve}

Viewing

^{Conditions Curve}

Clark's Tone Reproduction Curve

(figure ₁₎

Jones Diagram of the Digital Image

_Processing

_System

_(DIPS)

Figure 2

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figure 3. The experimental steps used to _quantify the DIPS

is shown in table 1.

STATEMENT OF THE PROBLEM

The problem _is to calculate computer _mapping func

tions for the DIPS

(figure 2)

, ^{that will cause input scenes}

to be reproduced

_having

_{Clark's tone} reproduction character istics16

(figure

₁₎

^. The method of analysis will be to use

the graphical approach of a Jones Diagram.

DISCUSSION

A part of Jones^' s

_theory

of tone reproduction applies

the principle of superposition to find a relationship ^be

tween input and output

_log

luminances. Superposition is a method applied to linear systems analysis that states the

overall responses to linear combinations of stimuli _is

simply ^{the same linear} combinations of the individual ^re- 17

sponses-1-

',

^i.e.,

f

_(x)

+ _g(x) ⁼ 0 f

_(x)

+ 0

_jg(x)l

g(x)

₍₁₎

The coefficients of equation

₍₁₎

are taken as _unity in this

example. The photographic process _is made _up of ^stimuli-

response components which are conventionally ^{expressed as}

common logarithms (base

10)

^. The result of

_log transforming

each term of the right hand side of _equation

_{(1) is,}

log

^0(f

_(xj) ^>L log _0(g(x5)

⁼⁼

_log 0(f(x)).0(g(x)) ⁽²⁾

The right hand side of

₍₂₎

says that in

_log

_space, the in dividual responses are multiplied

_(cascaded)

_, onto each

other. The

justification

for _using superposition with tone

reproduction is that the error involved in _using a linear

approximation to characterize the photographic system is

small18.

Additionally,

^{the predicted values of a tone re}

production _study correlate well with observed physical re

sponse. Superposition thus allows a photographic system to

be constructed

by identifying,

quantifying, ^and cascading ^its

system components together. The net result is a relationship between input signals and the system output responses.

In this experiment,

_key

^{components of the} DIPS

_(fig

ure

₂₎

_, are measured for their characteristic responses _using

"black ^box" analysis. This technique is useful in

determining

the input-output relationship ^{of a system or subsystem with}

out the need to know the internal details of the box (figure

₄₎

f ^{(x)' f}

(x)

Black Box Example

(figure ₄₎

The DIPS (figure

2)

, ^{is assembled} into eight black

boxes (each black box was determined

_by

_this experimenter

to be a

_key

component of the

_DIPS)

. _{The analysis} required

the separation of figure 2 into three smaller four quadrant

diagrams

(figures _{5, 6,}

and

_7),

in which five and six _rep resent a component system

(or

_{subsystem) ,} and seven is the

simplified version of the DIPS. The three diagrams show

the Data Acquisition Subsystem

(figure 5)

, ^{the Data Recon}

struction Subsystem (figure

6)

, and the Jones Diagram

_(fig

ure

_7),

of the DIPS. The subdivision of figure 2 was per

formed because major DIPS components were in themselves a

system that could be characterized _separately from figure

2. It must be pointed out that although figures 5 and 6

look and act similar to a Jones

_{Diagram, they}

should not

be called a Jones Diagram. This is because a Jones Diagram

relates input to output

_log

luminances of a photographic system.

The Data Acquisition Subsystem (figure

₅₎

_, consists

of the flare _curve, the film characteristic _curve, and the

characteristic curve of the Eikonix Image Digitizer. The

fourth quadrant of this figure contains the Data Acquisition

curve found

_by

_cascading the other quadrants. _Quadrant IV is descriptive of the events _occuring when

transforming _log

scene luminances into discrete picture elements

_(pixels)

_,

for computer processing.

The Data Reconstruction Subsystem

_{(figure 6)}

, ^consists

of the Tektronix video ^monitor curve, ^the negative film

characteristic curve used to make a positive

transparency

10

11

01

>

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13

from the monitor

_image,

and _{the curve} of the _viewing con

ditions ^when _projecting these transparencies. The resultant

of _this diagram is the Data Reconstruction curve of quadrant

IV. This curve graphically ^{shows the} relationship ^between

log

^{pixel code to projection}

_density

^{of the reproduced}

images.

The Jones Diagram of figure 7 is the tone reproduc

tion diagram of the DIPS. This simplified version of figure

2 uses quadrant IV of figures 5 and 6 (quadrants I and III

respectively), ^{Clark's tone} reproduction curve from figure 1

(quadrant

_VIII) , ^and the computer _mapping function in

quadrant II

(these

are to be discussed

_later)

_, to show the

effects of tonal

(luminance)

^{transfer through} the DIPS. The

following

^{sections will discuss in greater detail the two}

subsystems and the simplified DIPS Jones Diagram _previously

mentioned.

Data Acquisition Subsystem

Quadrant I of the Data Acquisition subsystem

(figure

5)

, ^{is the flare curve. This curve represents the} mapping

of scene luminances into illuminances incident on the _neg

ative film in the camera. ^These illuminances on the film

over time become the exposures that correspond to the scene

luminances. The measurement of flare was included in the

DIPS because the author ^feels that it has a significant effect

on the photographed ^imagery- The amount and effect is dependent

on such factors as the

14

camera-lens-film combination, ^the

directionality

^{and position}

of scene

illumination,

^{and the}

intensities

of the luminances in the scene19.

Quadrant II is the characteristic curve _{(D-log-H curve)}

of _Kodak Panatomic-X 35mm film. This curve describes the

effects of

_log

exposure

(corresponding

^to

log

^{scene lumin}

ances) , to the developed _densities. A complete description

of _the sensitometry ^{used to evaluate the film is located in}

Appendix 1.

Quadrant III is the characteristic curve for the

Eikonix Linear

_Array

Image Digitizer (figure

8)

^{. This in}

strument uses a linear _array of 1,024 photodiode detectors

to measure incident transmitted _energy from an illuminated

negative. Two dimensional digitization results from _stepping

the detector _assembly 1,024 times across the imagery. The

output of the digitizer is an _array of pixels which are

encoded into eight bits. The number of discrete codes _rep

resenting grey ^{levels range from 2^ to 2%, with the shadows}

of the scene

_taking

on high pixel _codes, and the scene high

lights

_becoming

low codes. The modulated _energy transmitted from the negative to the detector generates a proportional

analog ^{voltage which is corrected for photodiode} non-uniform

ities and artifacts. The _analog ^signal is digitized _into a

numerical integer code

_by

the _analog to digital

_(A/D)

convert er, ^{and stored on a computer compatible tape}

^(CCT)

^.

The ^{Eikonix digitizer measures} transmitted light

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17

modulated

_by

the _negative, and _{outputs quantized integer} codes20. The

digitization

operation _is accomplished in

linear space. To make the linear codes compatible to the

DIPS,

^{the pixels must} be

_log

transformed. Figure 9 ^shows the steps

_involved

_in

digitizing,

quantizing, ^and

log

^trans

forming

^{the negative image. The linear} _analog ^{signal is}

quantized

by truncating

^and rounding ^{it to a discrete linear}

code

_(N)

_{, between 1 and 256. This is the pixel code that is}

stored on the CCT. To process the digitized information

through the

_DIPS,

the codes must be

functionally

^evaluated

by

^{the computer (as real data} types) , ^to their

_log

equivalent. The new

_log

pixel codes are then stored in the computer or on CCT in

_floating

point format.

Because of quantization and

_log

transformation to the linear image _signals, a modification of the negative

image occurs. Quantization lumps a pre-determined range of

continuous values into one integer code

_(i.e.,

all of the fractional signal about a certain value will become an in

teger _number) . If the quantization is ^made fine enough (as

in the Eikonix

device)

, ^{no visual} degredation is noticable

to the image upon reconstruction. This ^{assumes a} one to one

mapping ^{of pixels in the computer, and that eight bit pixels}

were output to the reconstruction device. In the Results

section, ^{itwill be pointed out how pixel} mapping ^{in the com}

puter _using the computer _mapping functions can affect the

visual appearance of the reconstructed image

_by aggrevating

18

the quantization effect.

After quantization, ^the

_log

^of the pixel values are

computed. The operation _{produces 256}

_log

_{codes that are un} equally ^{spaced on the}

_log

^axis. Small numbers are spaced

very ^{far apart} in

_log

space relative to the fine separation of _{the larger numbers. A} consequence of _working in discrete

log

^{space is that little}

sensitivity

^{to change occurs in the}

low code _{regions, and high}

sensitivity ^{to change occurs in} the high code area _(this corresponds to the compression-

expansion of

_equally

spaced linear numbers in

_log

space) ^. When the

_log

numbers are processed in the _computer, and the

values mapped to new

_log

pixel _codes, small changes in the low

sensitivity

^{area will have little or no effect on the}

image tone reproduction. On the other

_hand,

small changes

to the high end will produce the desired effects. The net

effect of _working in discrete

_log

space is that the luminance

resolution of the image in the low code region will decrease

slightly, ^{and that an} equally ^subtle processing ^{shift to}

the

_log

pixels will produce an uneven

_log

distribution to all of the discrete values.

The test target ^used to _quantify quadrants I and III

of this subsystem was a random _grey test target

(RGT

_{target) ,}

shown in figure 10. This target was photographed on ^Panatomic-

X film and developed as described in Appendix 1. The RGT

target was chosen because it was thought to simulate a lumin

ance distribution ^{found in Clark's}

_imagery

^set.

_Also,

when

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the _target was photographed full frame on the 35mm

_film,

the

individual

_grey patches could _be measured on the pro

cessed _{film with a diffuse}

density

densitometer. The RGT target consists of eleven _{grey patches ranging from} black

to white _that are

arbitrarily

^{assigned a position within}

the target _{plane. Care was made in}

assuring ^{uniform illum}

ination

and _sufficient

_lighting

_{to again}

comply ^{with Clark's}

imagery

^set.

Data Reconstruction Subsvstem

^^ ^mtm>^r^^rj^r^r^r_H_WM^>^r^r^r_I_a

Quadrant I of the Data Reconstruction Subsystem

_(fig

ure

₆₎

_, is the Tektronix raster scanned video monitor char

acteristic curve. This precision monitor was designed for

photographing ^{images off its flat screen. At} reconstruction

time,

^{the processed pixels were} anti-logged,

truncated,

^and

rounded cff to integer numbers between 1 and

_256,

and passed

off to the monitor's circuitry. A negative image of the

original scene appears on the screen as a distribution of

grey

tones,

^{and is} photographed with a 4x5 view camera. A bellows was placed between the camera lens and the monitor

screen to eliminate most of the _stray flare light. The size

of the monitor's image was reduced on the film to convention

al 35mm

_format,

^{and mounted in a standard slide holder.} Quadrant II is the characteristic curve of Kodak Con

trast Process Ortho 4x5 film. This film was _{chosen because}

it has an _extemely low base plus

_fog

level

(approximatly

^.05),