Subject: LV378D Digital Image Processing Lesson 1: What is a digital image? Main objectives: This lesson gives an introduction to how a digital image is defined, how it can be generated and stored. You will be introduced to some basic concepts and some image

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-

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Subject
:

LV378D Digital
Image Processing


Lesson

1:

What is a digital image
?

Main

objectives
:

Th
is

lesson gives an introduction to how a digital image is
defined, how it can be generated and stored. You will be
introduced t
o some basic concepts and some image
examples
.

Author
:

Jan H. Nilsen

Published
:

6 November 2013




Course lessons are the property of the author
.
As a course participant, you can freely use the lessons
for your own personal u
se. Course participants who would like to use the lessons for example to teach
or for course
-
related purposes, must contact the author to reach a more specific agreement.


Copyright: Jan H. Nilsen/TISIP


1.
WHAT IS A DIGITAL I
MAGE

?
(
CHAPTER

1
IN THE COMPENDIUM
,
CHAPTER
1
IN
GONZALEZ
AND

WOODS)

1.1.1

I
NTRODUCTION

................................
................................
................................
................................
...............


2

1.1.2

USEFUL LINKS

................................
................................
................................
................................
..................

2

1.2

H
OW A DIGITAL IMAGE I
S CONSTRUCTED

................................
................................
................................
.............

2

1.3

H
OW A DIGITAL IMAGE I
S GENERATED

................................
................................
................................
................

5

1.4

H
OW TO STORE A DIGITA
L IMAGE

................................
................................
................................
.......................


8

1.5

I
NSTALL
ATION INSTRU
CTION FOR ADOBE PHOT
OSHOP TRYOUT

VERSION

................................
...........................

12

1.6

EXERCISE
1

................................
................................
................................
................................
........................

13



Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

2

What is a digital image
?

(
C
hapter 1 in the compendium
)

1.1

Introduction

This less
on gives a short introduction
to how a digital image is constructed, how it is generated and how
it is
stored
. As

part of the
exercise
s

presented in this lesson, you shall download and install Adobe Photoshop
(AdobeP) tryout version
.
You shall use AdobeP to import, enhance and generate new images.

The tryout version
of
AdobeP
may be downloaded for free from

the web p
age

http://www.adobe.com/products/tryadobe/main.html

.

Th
e AdobeP tryout

version is
somewhat limited, and does

not allow
that the analysed and enhanced images are
printed, exported or store
d.

Of course, this is
an impossible situation when you are working with images and want
to present and further analyse and store the images you have been working on.

PaintShopPro (Psp)

is an
alternative image processing program. The program may be download
ed from this web page
:
http://www.visitorinfo.com/software/paint.htm

.
You may use this downloaded version for a limited period of 30
days.
Psp
can export files which you have made.
If wanted


it is possible to use Psp instead of Adobe
P

in this
course.


The reason why the tryout version of
AdobeP
is introduced
,

is to let you
experience

for free probably the most
advanced and user
-
friendly image processing/editing/
manipulation software

package a
vailable
on

the market
today. However, in this course the complete version will not be needed
,

when you work with the exercises.


In addition to
AdobeP

the image processing software package
DynamicImager (DI)

will be used
.
Together with a

large library of
very well documented

image analysis/image processing routines, this software package allows
you to develop your own routines. This software package will be available in the course, and it allows both
export and import of image files. The
program

will be ma
de available to the course participants for free

during
the course period.


In lesson 4 we will give an introduction in how to use
DF.

T
he exercise
s

included in th
at

lesson

make use of this

software package. This will also to some extent be used in the re
maining lessons.

Digital image processing is a subject in which practice is
important;

it is not possible to learn only by reading.
Practical exercises are

emphasized
.


1.1.1

Useful links
:

Adobe Photoshop,
downloading a tryout version
:

http://www.adobe.com/products/tryadobe/main.html


Basic concepts in image processing, Dutch


”course” (in English)
:




http://www.ph.tn.tude
lft.nl//Courses/FIP/frames/fip.html


Short and easy courses on equipment and digital

image processing
:




http://www.shortcourses.com/


Downloading of

PaintShopPro:




http://www.visitorinfo.com/software/paint.htm


Definitions of
different standards:



http://www.diffuse.org/alpha.html


Contact
Tapir bokhandel Trondheim
to order

textbooks
:





kalvskinnet@tapir.no


1.2

How a digital image is constructed

Usually we think of images as drawings, paintings or paper copies of photographs. The images, both the paintings

and the photographs, are used
to
express cer
tain visual expressions which the painter or photographer want
s

to
share with us
.



Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

3






a)






b)

Fig.

1.2.1 Edvard Munch, 1863
-
1944 a) Edvard Munch.
Self
-
portrait with a
cigarette
. (1896)
and

b)
a
photography of th
e painter and some of his more
recent

images at
E
kely
,
Schøyen
, in
Oslo. (Fokus 98)


Analog images
:

While the painter may use and mix the paint rather freely to recreate ”reality”, the photographer is normally less
free.
What put color on

his
canvas, which traditionally has been photo
graphic film, is light sent from
objects/scenes which he want
s to present
.
The film/photo
paper
is exposed
to

the

light which reaches it, and
thereafter stores

the amount of li
ght analogically, by
exposing

each grain

o
n the film/phot
o paper proportionately

to the light intensity
reaching each grain on the film
.


D
igital images
:

According to the compendium a digital image is a collection of
small image elements

with a
given
position and a
value describing the grey level or color of the
image element
.
The sma
llest image element that the image consists
of is called a pixel.
The

value of each
p
ixel is
associated with

an image

coordinate

in a
n

image
coordinate system
,

where the
origin usually
is
put in the upper left corner of the image,
the
x
-
axis vertically
dow
nwar
d
s

and y
-
ax
is
horizontally rightward
s
, see F
ig.
2.
The n
ormal size of a digital image may bee

512 * 512
pixels, i.e.
512
horizontal row
s with 512 pixels in each
row
. Consequently, the pixel in the upper left corner of the image will
have the coordinate
/position
(0,0),
while the lower right corner will have the coordinate
(511,511).

Each pixel in an image has a certai
n grey level

value.

Often this value will be within the interval
0
-
255,
i.e. it may
have

2**8 = 256
unique values
.
The value
0 =
black
,
whi
le the value

255 =
white
.
Consequently, grey
level

values with these digital values
(0
-
255)
can be stored in one
byte.
An image

512 * 512
w
ith pixel elements of
grey level

values
0
-
255
may be stored by using

512 * 512 * 1 Byte = 262 144 Byte.

The number o
f pixels the image is divided into
,

defines

the resolution

of the digital image.

Modern digita
l
cameras can
generate digital images with more than
3 million
pixels, and
are almost

as good as analog cameras

for most purposes. It is usually stated that the
r
esolution
of

a
n

analog camera/film
(
image size

= 36 mm * 24 mm)
corresponds to

approximately

5 million

pixels
.
When we enlarge a digital image to a certain extent each pixel
will show, see
Fig
.

3
in the compendium
.
This will also be the result when an anal
og image (photo) is enlarged to
a certain extent. In the end we will be able to see each silver
grain

in the film
.

Different authors define the
concept digital imag
e

differently
:

According to
Gonzalez
and

Woods,
2002,
chapter
1.1,
a monochromatic

(black/
white) image (
monochrome
image)
,

or just an image
,
refers
to a two

dimensional light intensity function

f(x,y ),

where

x
and

y
are spatial

Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

4

coordinates. The value of f in a random point
( x,y )
is proportional with the
intensity

(
grey level)

of the image in

that specific point.

This is mainly the same definition
as
used in the compendium

(Bø, 2002 ),
page
6.





In the book by

Watt
and
Policarpo
, 1999
,

page 2,
the definition

is
:


What
is a data generated image?

It is a two

dimensional array of numbers. Each number represents the light intensity or color

of

a visible image
element/pixel. The number of pixels in an image and the
accuracy of each st
ored pixel (for instance 8, 16 or 24)
depend

on what kind of hardware which has been used.

You must rea
d the pages
5
-
9
in the compendium
.
Open the image in
Fig
. 2
,
page
6
,

in the compendium, in
AdobeP
and enlarge it until you get an image similar to
Fig
.
3

in the compendium
.
Find the pixel coordinates for
the center of the wom
a
n’s left eye in both image cuts, and thereafter try to find the same pixels in both images.
You
will find the

pixel coordinates in the lower left of the AdobeP window.
Ensure that you

really understand
Fig
.
1.2.2.







Fig
. 1.2.2
The
most common

definition of digital image

coordinate systems
.
Origin is in the upper left corner of
the image, the x
-
axis vertically downward
s

and the y
-
axis horizontally. The size of the image i
s

ca. 425

*
366

pixels/image elements
. Bø, 2002.


Fig
.

1.2.3
shows in a way similar to
Fig
.
1.2.2 how an analog/continuous image can be digitalized and divided
into horizontal rows and vertical columns of small image elements
.
The upper left corner in each

image
element/pixel defines the pixel coordinate for each pixel.



The value of each pixel in a monochrom
e

or grey level

image,

a(x,y) (f(x,y) i
n
Fig
.
1.2.2),
is
the mean light
intensity

sent out from

an object
, and
is observed

by
the specific pixel/image

element on the CCD chip
.
Usually
the object we take a picture of is three

dimensional (x,y,z)
. T
he light it sends out
,

will consist of many different
colors/wavelength
s
,


and

the picture may have been taken
at

di
fferent
time
s
,

t. a
or

f
will

therefore

be

defined as
a(x,y,z,

,t)
or

f(x,y,z,

,t).


X
-
axis

f(x,y)

Origin

f(0,0)

Y
-
axis


f(
425
,
366
)

f(0,511)

f(425,0)

f(511,0)
xis

Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

5

Fig
.
1.2.3
the image
is divided into
16
rows

and
16
columns or
256
pixels
.
Usually

the

resolution
/
number of
pixels in digital images will be much larger.

Within each square there are smaller visible details, and
thus there
ought to be more pixel elements to
be able to
resolve

th
e information available in the analog image in
Fig
. 1.2.3
.
Consequently, the matrix is only an illustration showing how an image is divided into individual image elements.
Today commercial
digital cameras may have chips generating more than
3 million pixel
s
.



Fig
.

1.2.3
.

Digit
alization
of

a continuous image
.

The image is divided into
16 (
horizontal
) rows
and

16 (verti
cal
)
columns, i.e.
256 pixel
s or image elements
.
The value of the b
rightn
ess
in each image element is given at
a(x,y,z,

,t)
which is equal to the amount of light sent out by the three

dimensional object
,

reaching

the image
sensor
element

(x,y,z,
with color
,



and at a given

time
,t).

http://www.ph.tn.tudelft.nl//Courses/FIP/frames/fip.html



1.3
How a digital image is generated

In the last few y
ears digital cameras have become quite advanced. Instead of photogra
p
hic film as
a
sensor and
media for storage
,

t
hese digital cameras use
CCD

chips

(Charge Coupled Device),
which consist of a great
number of
very
small photosensitive

rechargeable

cells/sensors
.


1.3.
1
Photosensitive

image sensor and analog
-
to
-
digital converter


To capture

a digital image two units mu
st be available.

Firstly, a physical unit must be available, wh
ich is
sensitive to a given
part

of the light/electromagnetic spectrum, for instance to ultraviolet, visible or infrared
radiation/light
.
The unit must produce an analog, electrical signal
,

whi
ch is
proportional
to

the radiation energy
reaching
it
.
Today r
egular video cameras and digital still frame cameras
are equipped with CCD chips
(Charge
Coupled Device),
which register the light reaching the cameras
, se
e

Fig
.

1.3.1.


Fig
.

1.3.1.
The
figur
e shows a CCD chip upon an enlarged matrix of small image sensors, which is an
enlargement of the photosensitive
dark grey part in the middle of the chip.

Chips in digital cam
eras sold today
may have up to

3 million of these small image sensors.

The chips
are small.

This chip which is in one of Sony’s

Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

6

digital video cameras has the size

0.625 cm * 0.625 cm
and consists of

1152 * 864
photosensitive cells
.

I
.e.
approximately 1 million cells are being activated when the
camera is in a still frame mode
.

Dennis
P.
Curtin
http://www.shortcourses.com/


The light intensity

which

reaches

each individual cell registers/produces an electrical charge
/voltage

within
each
cell, proportiona
l

to the
incoming light intensity
.
In

Fig.

1.3.1, 1.3.2
and 1.3.3 the sensors are red, green and blue.
Most cells are green. Each square three times three cells consists of 2 red, 5 green and 2 blue.
It follows from fig.
1.3.3 that most
of the filters are green
. This is

because the human eye
is most sensitive towards green/yellow
-
green light
.

In reality the photosensitive cells are
not
colored.
Above the cells in color cameras there are color filters which
ensure that only red, green or blue light goes through
and reaches
the

individual cell.

In addition, to increase and
to focus the light towards each individual cell
,

there is a small optical lens above each color filter
. These lenses

focus the light towards the cell
s
, se
e

Fig.

1.3.2.



Fig.

1.3.2.
A
CCD

chip illustration of the structure

-

photosensitive cell
s

at the bottom,
colour


filter
s

in the
middle and on the top lenses which focus
the incoming

light
towards

the individual cell
s
.
Dennis P. Curtin
http://www.shortcourses.com/

(Courtesy of
Fuji).


Because of
the
color filters each cell is only able
to
capture

either red, green or

blue light. To calculate the “real”
color and the luminosity for each cell on the chip
,

or the
corresponding

image element/pixel on the image/screen,
an interpolati
on/mix of the values for each cell
based on

the nearest eight cells
,

is implemented
, se
e

Fig.

1.3.3.
These are extensive calculations taking place in the micro processor in the digital camera.
It is t
hese values

that
are stored and then shown on the
camera

screen.
It also exist

color video cameras

which separate the incoming
light into red, green and blue
spectral bands.

The light from each band is captured by a separate chip,

i.e. there
are three chips in the camera.


Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

7



Fig.

1.3.3
The color
of

the pixel i
n the middle is calculated by interpolation between the color values in the eight
neighboring

pixels
.


In
photographic

images the colors are usually based on the three primary colors red, green and blue
(RGB).
This
is
called
the additive color
model
,

becau
se when equal values
of R
, G
and

B
are mixed together
,

white
light is
produced,
se
e

Fig.

1.3.4.




Fig.

1.3.4.
The primary colors red, gree
n

and blue and the mix
ture

of these colors
.
Equal parts of all these three
color
s

mixed together produce
s

white ligh
t.
Dennis P. Curtin
http://www.shortcourses.com/



1.3.2
Analog
-
to
-
digital
converter (A/D converter)


In addition to the
photosensitive
recorder

unit
,

a converter is needed which
converts the

transmitted elect
rical

signals into numbers/digital information
.
With one
8
-
bit/1Byte
representation
,

the charge
/voltage

may have
digital values b
etween
0
-
255.

In a

m
onochrom
e

or
a
black/white
recording
,

0

is
usually equal to 0
charge
,
i.e.
completely bl
a
ck
, and

255
to
max
imum brightness
, or completely white.


Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

8

1.4

How to store a digital image

In digital cameras the image is
captured

as
photo electric
charge
s
,
analog/proportional

to

the light intensity
which
reaches

each of the cells on the CCD chip
.
Before a new image can be
ca
ptured

the chip must
be
discharged,
and
the
charge
s

must be store
d

on another
device
.

All the cells on the CCD chip in a
digital
video camera
are
discharge
d

every
1/30
second
according to
American
Television
standard

(National Television Sandard Com
mitee,

NTSC’s standard RS
-
170), or every
1/25
second
Europan standard

(Comite Consultatif International des Radiocommunications, CCIR’s standard PAL (Phase
Alternating Line).
Lesson 3 focuses on hardware, and will explain how the transmission of information fro
m the
chip to
a storage device
functions.

1.4.1


Data
storage
media
:

In digital still frame cameras the analog signal on the chip is converted into a digital signal via an analog
-
to
-
digital converter inside the camera
,
thereafter it is stored on a data
medium

i
n the camera.

There are different
types of
data media
.
Today the most usual is
relocatable

media, which can be overwritten, for instance

magnetic
disks and ”flash memory” cards
.
There is one significant difference between these two. Magnetic disks have
mov
eable
parts, while the ”flash memory” cards do not. “Flash memory” cards are lighter, smaller and less
exposed to damage
, but they are more expensive and currently they
cannot store as much data as the
magnetic
disks. Today a number of “flash memory” card
s are available on the market.
Often the camera
manufacturer

has
its own special card which
cannot be used in devices

produced by other manufacturers
.
Fig.

1.4.1
illustrates a

Memory Stick
card mad
e

by
Sony.




Figur
e

1.4.1 Sony Memory Stick
for
data
st
or
age

in

digital
cameras
.

Notice the size approximately

5 cm * 2 cm *
0.3 cm.
These small cards made by
Sony
can store up to

128 M
B
. Dennis P. Curtin

http://www.shortcourses.com/

There are a number of different

data
storage
media, as mentioned earlier. These will not be covered in this lesson.
A summary is available on this web page
:
http://www.shortcourses.com/choosing/storage/06.htm#


1.4.
2
Image compression

Non
-
compressed digital

image
files easily become

very large
,
occupying

too much of the
storage capacity
.
Currently d
igital

still frame cameras

might
have more than 3 million pixels

(resolution)
.
Consequently, an image
of which each pixe
l is stored using
24 bit
or

3 byte
,

will need
9 MB

of storage capacity
,
if not compressed before
storing it. Image compression is an important part of d
igital image processing
, which will be in focus in lessons
later on.


Image compression may be divided i
nto two main
categories



lossless compression and lossy compression
.
In
lossless compression the compression is such that the code used to code/compress the original image is
reversible,
making it possible to decode/decompress

the coded/compressed/packed
image
, thus getting
back
the
Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

9

original image.

From l
ossy compress
ed images it is not possible by decoding/decompressing to reconstruct the
original image
.

1.4.3 Still

image

file
formats
:


Most digital cameras compress image files to reduce the size of the i
mage files, thus making
space

for more
image files on the
storage device

in the digital camera
.
The most usual file
formats

are
:

Non
-
compressed images
:

RAW,
no reduction of the original size of the image

Lossless compression
:

GIF
and

TIFF,
reduces t
he size of the original image to approximately

1/2
-
1/10

Lossy compression
:


JPEG,
reduces the size of the original image to approximately

1/10
to

1/40

JPEG (Joint Photographic Expert Group)
used in

JFIF file
s

(JPEG File Interchange Format)
is the curre
nt ISO
standard for loss
y

image compression
.
Some cameras offer the possibility to choose level of compression before
storing the image file.

The higher the level of compression
used
the more information is
lost
,
and the images get
more blurred and degrade
d
.
Fig.

1.4.2
consists of an enlarged
part

of a

JPEG

image stored with the
lowest
level
of compression
a),
and the
highest

level of compression

b).







1.4.2 a)







1.4.2 b)

Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

10

Figur
e

1.4.1
Enlarged part

of a
JPEG
image
. a)
lowest level of compression
, b)
highest level of compression
.

Dennis P. Curtin
http://www.shortcourses.com/

Image
b)
is clearly ”worse” than

a).
Further,
b)
is divided into squares consisting of

8 * 8
single pixels. This
because the im
age compression is done
based on

blocks

of
8

* 8
pixels, and these blocks are visible when
enlarging the image
significantly
.


Warning
:

Sometimes when storing a
JPEG
image as a
JPEG
image
a second time
,

the compressed image may be
compressed once more
/a th
ird time
.
Consequently, the quality
/
resolution

of the image will be reduced further.
By
repeating this storing process a certain number of times the image will become completely degraded.
Consequently, i
f you work with a
JPEG image you need to store severa
l times before finishing, then use a GIF or
TIFF format for
intermediate storing
.


1.4.4
Video im
age format
s

MPEG (Motion Pictures Expert Group) is a compressed sound/video format. MPEG
-
1 is developed for systems
which use non
-
interlaced display screens. N
on
-
interlaced screens are screens in which the horizontal rows in the
entire image are scanned sequentially one by one, i.e. first row number 1, then row number 2 etc. In some
cameras this format is u
sed to store short
video sequences
.
The image quality wh
en using
MPEG
-
1

is not as good
as the
VHS

format.

MPEG
-
2
is developed for
screen
s

using interlaced scanning
,
i.e. row 1 on the top of the screen is scanned first,
then row
3, 5 , 7
etc
.
When the first 50 per cent is scanned, then rows with even numbers ar
e scanned, row
2, 4, 6
etc.

These two
”half

images”
are then interlaced
.

Each
”semi image”

is then scanned within
1/60
of a second
,
NTSC standard,
or
1/50
second

(PAL

standard)
, while the whole image
is updated every

1/30
second
(1/25
se
cond

PAL,
European
standard).
This
method allows

a faster update of the visible image on the screen
;

the
perceived
image sequences

does not flicker and are therefore “better”

than non
-
interlaced
scanning.
Do

also see
the web page

http://www.diffuse.org/alpha.html

for more in
-
depth information on the different standards.



Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

11

1.5

Installa
tion instruction

for Adobe Photoshop Tryout

Version

See
the
attached file for
complete coverage
:

NedlastinstallveiledprvAdobePhS60.doc
Downloading and installation guide for test version of Adobe Photoshop 6.0


Note
: The installation is tested for the operating systems W
indows 98, 2000 and NT.
For
W98
it
is
easily installed by double
-
clicking the downloaded file AdobePS6Tryout.exe.
In W 2
000 and NT it
is
necessary in Explorer to drag the file AdobePS6Tryout.exe into
the catalog you choose to view the files
in, and thereby ensure that all the files in the
packed file are viewable
. Setup.exe is one of these files. When you double
-
click on th
e
file in Explorer the program will be installed. Other
wise
, please follow the instruction
below.



Enter the web page:
http://www.adobe.com/products/tryadobe/main.html



The web page will
be shown as below if you use Netscape. Similarly in MS
-
Internet
Explorer.




Fig. 1
The Adobe web page for free downloading of software.


Copyright:
Jan H.

Nilsen
/TISIP


Programming


Develop a small program

12

1.6
Exercise

1

You must read the pages
5
-
9
in the compendium and chapter 1 in
Gonzalez
and

Woods.

1a)
Install
Adobe Photoshop, AdobeP,
on your local
PC.
Follow the installation instructions in Attachment 1,
and
then

use the attached p
rogram installation information
.

In addition to image material, there shall be text explaining each image and subtasks in the Word document

you
return.

1b)
Import

the image in
Fig.

1.2.2
into
AdobeP.
Then
put the image on the
clipboard

while you simultane
ously
press the buttons
Ctrl + Alt + PrintScrn
on the keyboard
.
Then import the

image into a Word document
.

1c
)
I
mport
a copy of
the

same image in a new
sub
window in
AdobeP.
Enlarge this image in the new window

until you get an image showing
only
the wom
an’s eye, as in
Fig.

3
in the compendium
.
Read the pixel coordinates
of

the center of the
woman’s left eye in both
image
sub
windows
, and thereafter check if you are able to find the
same pixel in both
sub windows
.
You can
read the pixel coordinates
i
n the

navigator menu window in the
upper
right in the AdobeP window. Do also put this soft copy on the
clipboard
,
and then

import it

in

the same Word
document
.

Make sure that you understand the figure on page
6
in the compendium
/
Fig.

1.2.2
in the lesson
.

1d)
B
ecome familiar with
AdobeP
by testing the various functions
.
Import Munch’s self
-
portrait
,
Fig.

1.2.1 a),
into

AdobeP.
Change for instance the
brightness
and the colors on the image
.
Extract

3
different
color
combinations

from

this image, then paste them i
nto a Word document
.
Write down which
of the available
functions in the menu you use
d

to complete
the

image manipulation.

1e)
Convert
Fig.

1.2.1 a)
to a grey level

image, then paste it

to the word document
.

The images generated in
1a)

1e)
shall be sent in

as
an
answer
to

exercise
1.
If

you want to, you may zip

the file
before sending it
.
Thereafter, become
more
familiar with
AdobeP
by testing

the program
,
and do

use the
help
menu

in

AdobeP when
you practice.



Deadline for sending in the exercise
: 2002
-
09
-
13.

Send the exercises to the course

teacher
, janhn@aitel.hist.no

State the

subject number
,
your name and
the
exercise number
.
E.g.
: lv378dolanormannoving1