Digital image & linear stretching

REMOTE SENSING
SCALE
The shape of the earth is geoid (three-dimensional) and a globe represents it the best way. While
a map is a simplified depiction of whole or part of the earth on a piece of paper (two-dimensional).
To show the 3-D earth on the 2-D surface we use a system of map projections. As it is impossible
to represent all the features of the earth’s surface in their actual size and form, a map is drawn at a
reduced scale.
Systems of Measurements
There are two different systems of measurement of the distances used in different countries of the
world.
A. Metric System of measurement (in use in India)
B. English System of measurement
Metric System of Measurement
1 km = 1000 Metres
1 Metre = 100 Centimetres
1 Centimetre = 10 Millimetres
English System of Measurement
1 Mile = 8 Furlongs
1 Furlong = 220 Yards
1 Yard = 3 feet
1 Foot = 12 Inches
Scale: It’s the first step in map making. It shows the ratio between the distances of two points on
the map, image or photograph and the actual distance between the same two points on the ground.
The scale of a map sets limits of information contents and the degree of reality with which it can
be delineated on the map.
Photograph scale: It is the ratio between the distance on the aerial photograph or map and the
actual distance on the ground or the land surface. There are two types of scale:
a) Large Scale Photo: A map or photo which depicts a small territory is referred to as a large-
scale map. This is because the area of land being represented by the map has been scaled
down or in other words, the scale is larger. It only shows a small area, but in great detail.
b) Small Scale Photo: A map or photo depicting a large area, such as an entire country is
considered a small-scale map. In order to show the entire country, the map must be scaled
down until it is much smaller. A small-scale photograph similarly shows more territory,
but it is less detailed.
There are at least three methods of representation of scale:
1. Statement of Scale
2. Representative Fraction (R. F.)
3. Graphical Scale
Statement of Scale: It is the simplest of the three methods. Indicated in the form of a written
statement. For example, “1 cm represents 10 km” means that on that map 1 cm equals 10 km on
the ground. It may also be expressed in any other system of measurement i.e. 1 inch represents 10
miles
Limitations:

• The people who are familiar with one system may not understand the statement of scale in
another system of measurement.
• If the map is reduced or enlarged, the scale will become superfluous and a new scale is to
be worked out.
Graphical or Bar Scale: This scale shows map distances and the corresponding ground distances
using a line bar with primary and secondary divisions marked on it. Unlike the statement of the
scale method, the graphical scale stands valid even when the map is reduced or enlarged.
Representative Fraction (R. F.): The most versatile method representing the relationship between
the map distance and the corresponding ground distance in units of length. It is generally shown
in fraction because it shows how much the real world is reduced to fit on the map. For example, a
fraction of 1: 25,000 shows that one unit of length on the map represents 25,000 of the same units
on the ground. It may, however, be noted that while converting the fraction of units into Metric
or English systems, units in centimeter or inch are normally used by convention. This quality of
expressing scale in units in R. F. makes it a universally acceptable and usable method.
Relationship Between Photo Distance and Map Distance
Photo scale: Map scale = Photo distance: Map distance
Focal Length (f): Flying Height(H) = Photo distance (PD): Ground distance (GD)
Formulae
𝑷𝒉𝒐𝒕𝒐 𝑺𝒄𝒂𝒍𝒆 =
𝒇𝒐𝒄𝒂𝒍 𝒍𝒆𝒏𝒈𝒕𝒉
𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒂𝒊𝒓𝒄𝒓𝒂𝒇𝒕
[𝑷. 𝑺. =
𝒇
𝑯
]
𝑷𝒉𝒐𝒕𝒐 𝑺𝒄𝒂𝒍𝒆
=
𝒇𝒐𝒄𝒂𝒍 𝒍𝒆𝒏𝒈𝒕𝒉
𝑯𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒉𝒆 𝒂𝒊𝒓𝒄𝒓𝒂𝒇𝒕 − 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒕𝒆𝒓𝒓𝒂𝒊𝒏
[𝑷. 𝑺. =
𝒇
𝑯 − 𝒉
]
𝑷𝒉𝒐𝒕𝒐 𝑺𝒄𝒂𝒍𝒆 =
𝑷𝒉𝒐𝒕𝒐 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝑮𝒓𝒐𝒖𝒏𝒅 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝑴𝒂𝒑 𝑺𝒄𝒂𝒍𝒆 =
𝑴𝒂𝒑 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝑮𝒓𝒐𝒖𝒏𝒅 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝑮𝒓𝒐𝒖𝒏𝒅 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 =
𝑷𝒉𝒐𝒕𝒐 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝑷𝒉𝒐𝒕𝒐 𝑺𝒄𝒂𝒍𝒆

SAMPLE QUESTION & ANSWERS
Question 1: If the focal length of the camera is 151.8mm and the aircraft is at 2000meters, with
the given terrain height of 500m. Find the photo scale of the aerial photograph.
Solution:
Given: Focal length = 151.8 mm.~ 0.1518 m. (∵ 1m=1000mm.)
Height of the aircraft =2000m
Terrain height =500m
To find: Photo scale
𝑃. 𝑆. =
𝑓
𝐻 − ℎ
=
0.1518
2000 − 500
=
0.1518
1500
=
1
9881.42
~
1
10,000
∴ P.S.= 1:10,000
Question 2. Find the scale of the aerial photograph, if focal length of the camera is 151.8mm and
height of the flying aircraft 600 ft.
Solution:
Given: Focal length = 151.8mm ~ 0.1518 m. (∵ 1m=1000mm.)
Height of the aircraft (H)= 600ft. ~ 181.81 (∵ 1m=3.3 ft.)
To Find: Photo scale (P.S.)
𝑃𝑆. =
𝑓𝑜𝑐𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑚𝑒𝑟𝑎
𝐹𝑙𝑦𝑖𝑛𝑔 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑖𝑟𝑐𝑟𝑎𝑓𝑡
[𝑃. 𝑆. =
𝑓
𝐻
]
=
0.1518
181.81
=
1
1197.7
∴ P.S.= 1:1200

QUESTIONS WITH RF 1:25,000
Question 3. On a topographical map with RF= 1:25,000, the distance between two points was found to be
7 cms. and the distance between the same points on an aerial photograph was found to be 1cms. Calculate
scale of aerial photograph.
Solution:
Given: Map scale = 1: 25,000
Map distance = 7cm
Photo distance = 1cm
𝑃ℎ𝑜𝑡𝑜 𝑠𝑐𝑎𝑙𝑒 =
𝑃ℎ𝑜𝑡𝑜 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐺𝑟𝑜𝑢𝑛𝑑 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒
Map scale =
Map Distance
Ground Distance
⇒ 𝐺𝑟𝑜𝑢𝑛𝑑 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 =
Map Distance
Map Scale
=
7
1
25000
= 7 ×
25000
1
G.D. = 1,75,000 cm.
1
175000
∴ P.S.= 1:1,75,000
Solution:
Map distance = 5cm
Map scale =
Map Distance
Ground Distance
Map Distance
Map Scale
=
5
1
25000
= 5 ×
25000
1
G.D. = 1,25,000 cm.
2
125000
⇒
1
62500

∴ P.S.= 1:62,500
Question 5. The scale of the aerial photograph is 1: 25,000, ground distance is 3.5 km. Find the photo
distance.
Solution:
Given: Photo scale (P.S.) = 1:25,000
Ground distance (G.D.) = 3.5 km~ 3,50,000 cms. (∵ 1km. = 1000 m.= 1,00,000 cm.)
To find: Photo distance (P.D.)
⇒ 𝑃ℎ𝑜𝑡𝑜 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑃ℎ𝑜𝑡𝑜 𝑆𝑐𝑎𝑙𝑒 × 𝐺𝑟𝑜𝑢𝑛𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
=
1
25000
× 350000
∴ P.S. = 14cms. ~ 0.14m.
QUESTIONS WITH RF 1:50,000
Solution:
Map distance = 5cm
Map scale =
Map Distance
Ground Distance
Map Distance
Map Scale
=
5
1
50000
= 5 ×
50000
1
G.D. = 2,50,000 cm.
2
250000
⇒
1
125000
∴ P.S.= 1:1,25,000

Question 7. The scale of the aerial photograph is 1: 50,000, ground distance is 3.5 km. Find the photo
distance.
Solution:
Given: Photo scale (P.S.) = 1:50,000
Ground distance (G.D.) = 3.5 km~ 3,50,000 cms. (∵ 1km. = 1000 m.= 1,00,000 cm.)
To find: Photo distance (P.D.)
⇒ 𝑃ℎ𝑜𝑡𝑜 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑃ℎ𝑜𝑡𝑜 𝑆𝑐𝑎𝑙𝑒 × 𝐺𝑟𝑜𝑢𝑛𝑑 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
=
1
50000
× 350000
∴ P.S. = 7 cms. ~ 0.07m.
Solution:
Map distance = 7cm
Map scale =
Map Distance
Ground Distance
Map Distance
Map Scale
=
7
1
50000
= 7 ×
50000
1
G.D. = 3,50,000 cm.
1
350000
∴ P.S.= 1:3,50,000

Digital image & linear stretching

ANNOTATIOOM OF SATELLITE IMAGERY
The data recorded/captured by the satellite sensors is used for information derivation related to the
forms, and patterns of the area, objects and phenomena of the earth’s surface. The derivation of
both qualitative and quantitative properties of the features is carried out either through visual
interpretation methods or digital image processing techniques. The visual interpretation involves
observation of the images of objects for their identification. On the other hand, digital images
require a combination of hardware and software to extract the information.
Annotation is a note which provides background information and baseline data of the time at
which the imagery was captured. It is used foe explanatory purpose and to indicate items or areas
of spatial importance.
Annotation Table
SL. No. Parameter Description
1 Satellite name IRS-1B
2 Country India
3 Date of Acquisition 14 October 1996
4 Date of Processing 24 September 1997
5 Date of Printing 29 September 1997
6 Projection POL
7 Sampling Method CC (cubic consultation)
8 Sensor LISS-1
9 Product type SD (Standard)
10 Bands B-2 (Green), 3 (Red), 4(Near Infrared)
11 Path number PO28
12 Row number R46
13 Format centre FN 30°25’N & 78°53’E
14 Latitudinal Extent 29°30’N & 34°00’N
15 Longitudinal Extent 78°00’E & 79°30’E
16 Generation Agency ISRO-NRSA/NRSC
17 Exposure Time 5:48 AM
18 Colour Scale YES
19 Grain Setting 63
20 Station XT
21 Negative number XT:85705
22 Project Type NA
23 Colour Scheme LGLUT (Linear OpenGL Utility Toolkit)
24 Imagery number 026138

VISUAL INTERPRETATION OF SATELLITE IMAGERY
Elements of Visual Interpretation
In our day-to-day life we use the form, size, location of the objects and their relationships with the
surrounding objects to identify them. These characteristics of objects are termed as elements of visual
interpretation.
Tone or Colour: The reflected amount of the EMR energy that is received and recorded by the sensor in
tones of grey, or hues of colour in black and white, and colour images depending upon the orientation of
incoming radiations, surface properties and the composition of the objects. Smooth and dry object surfaces
reflect more energy in comparison to the rough and moist surfaces. For example, healthy vegetation reflects
strongly in the infrared region because of the multiple-layered leaf structure and appears in a light tone or
bright red colour in standard false colour composite and the scrubs appear in greyish red colour). Similarly,
a fresh water body absorbs much of the radiations received by it and appears in dark tone or black colour,
whereas the turbid water body appears in light tone or light bluish colour.
Texture: The texture refers to the minor variations in tones of grey or hues of colour. These variations are
primarily caused by an aggregation of smaller unit features such as high density (fine texture) and low
density (coarse texture) of features. The textural differences in the images of certain objects vary from
smooth to coarse textures.
Size: The size of an object as observed from the resolution or scale of an image is another important
characteristic of the features. It helps in distinctively identifying the similar features.
Shape: The general form and configuration or an outline of a feature provides important clues in the
interpretation of remote sensing images. The shape of some of the objects is so distinctive that make them
easy to identify. For example, religious places, a railway line can be readily distinguished from a road due
to its long continuous linearity in shape with gradual change in its course.
Shadow: Shadow of an object is a function of the sun’s radiance angle and the height of the object itself.
Shadow also adversely affects the identifiability of the objects by producing a dark tone, which dominates
the original tone or colour of the features lying under the shadow of tall buildings. The shadow as an element
of image interpretation is of less use in
satellite images. However, it serves a useful purpose in large-scale aerial photography.
Site: The position on the landscape with reference to direction as well as the latitudinal and longitudinal
values enabling to locate the exact location of the feature.
Pattern: The spatial arrangements of natural and man–made features show repetitions of form and
relationship. The arrangements can easily be identified from the images through the utilization of the pattern
they form. For example, planned residential areas with the same size and layout in an urban area can easily
be identified; same goes for orchards and plantations, drainage system etc.
Resolution: Photographic resolution is the maximum number of line-pairs per mm that can be distinguished
on a film when taken from a resolution target. It describes the distance between distinguishable patterns or
objects in an image that can be separated from each other. Resolution depends mainly on granularity.
Stereoscopic Resolution: Distinguishable pattern of the shadows formed by any feature on the surface
with a particular height.

COMPARISON
The Codrington port is located at 17°38′N 61°50′W in the Caribbean sea. As evident the ‘after’
image of the port, Barbuda gives a stark contrast to the ‘before’ image. The before image provides
a sunny image of the area, the sinuous and well-connected roads form trellis and dendritic pattern
as a river basin, the settlements are spread across the whole area and vegetation has grown in close
proximity. The port is in the central western part on the shore, a strip of vegetation cover parallels
the coastline, the concentration of settlement and vegetation increases as one moves towards the
east. In the ‘after image’ the area has been ransacked by the Irma cyclone, most of the road network
and settlements have been destroyed and all that which is left is just the debris. The port has been
ransacked, most part of the image is not clear due to the presence of clouds/cyclonic wind.
CODRINGTON PORT, BARBUDA
LOCATION: 17°38′N 61°50′W
Before After

CODRINGTON PORT, BARBUDA (BEFORE)

VISUAL INTERPRETATION
Sl.
No
.
ROADS SETTLEMENT WATER PORT
1 Image
2 Location Spread all
over the
area except
the Western
part.
Spread all
over the area
excluding the
Western part
with increase
in
concentration
as one moves
towards East
Spread all
over the area
except the
water covered
western part
Western part:
broader
towards NW
direction and
tapered
towards the
SW part
West central
part of the
image along
the coast
3 Recognitio
n
Form a
elongated
network
with well
connectivity
Proximity to
the
settlements,
lush and deep
green colour.
Polygonal
with different
shades, spread
all over the
area except
the ocean.
Spread over a
large area
with
dominant
bluish colour.
Located at the
shore.
4 Shape Elongated
and curvy
Spotty,
Circular
Patches
Polygonal as
well as
irregular
Irregularly
enclosed
Rectangular
and elongated
5 Size Elongated
with
variable
width.
Medium-
Small size as
discerned
from the tree
crowns.
Small
compared to
one large one
to the north-
eastern of the
port
Comparativel
y larger than
all other
features
Longer than
any other
settlements
extended into
the ocean.
6 Tone Mostly grey
and a little
of white
tone
Dark Green Varying from
Grey to cream
Deep Blue Cream
7 Shadow No Yes Yes No Yes, on the
ocean surface
8 Pattern Dendritic Heterogeneou
s
Heterogeneou
s
Homogeneou
s
Homogeneous
9 Texture Rugged Rough Rough blocks Smooth Smooth on the
roof but rough
VEGETATION

at the
outstretches
10 Resolution High High High Medium Medium
11 Stereoscop
ic
Appearanc
e
No Yes Yes No Yes
12 Feature
Remark
Road:
Because
elongated,
curvy and
connected
Vegetation:
because are
of similar
shape and
deep green
colour
Settlement:
Spread all
over the area
with rough
polygonal
roof as seen
from top.
Water body:
includes
Shore and
port
Port: Location
along the water
body

CODRINGTON PORT, BARBUDA (AFTER)

VISUAL INTERPRETATION
Sl.
No
.
ROADS
VEGETATION SETTLEMENT
CLOUDS/
CYCLONI
C WIND
PORT
1 Image
2 Location Spread all
over the
area
except the
Western
part.
Spread all
over the area
excluding the
Western part
with increase
in
concentration
as one moves
towards East
Spread all
over the area
except the
water covered
western part
South-
Western,
South-
Central
and
Eastern
part
West central
part of the
image along
the coast
3 Recognitio
n
Form a
elongated
network
with well
connectivit
y
Proximity to
the
settlements,
lush and deep
green colour.
Polygonal with
different
shades, spread
all over the
area except the
ocean.
Appears
smoky/
feather like
Located at
the shore.
4 Shape Elongated
and curvy
Spotty,
Circular
Patches
Polygonal as
well as
irregular
Irreguular Rectangular
and
elongated
5 Size Elongated
with
variable
width.
Medium-
Small size as
discerned
from the tree
crowns.
Small
compared to
one large one
to the north-
eastern of the
port
Comparativ
ely larger
than all
other
features
(Covering
almost half
of the area)
Longer than
any other
settlements
extended into
the ocean.
6 Tone Mostly
grey and a
little of
white tone
Dark Green Varying from
Grey to cream
Light ash Cream
7 Shadow No No Yes No Yes, on the
ocean
surface
8 Pattern Dendritic Heterogeneou
s
Heterogeneous Homogeneo
us
Homogeneou
s

9 Texture Rugged Rough Rough blocks Smooth Smooth on
the roof but
rough at the
outstretches
10 Resolution High High High Medium Medium
11 Stereoscopi
c
Appearanc
e
No Yes Yes No Yes
12 Feature
Remark
Road:
Because
elongated,
curvy and
connected
Vegetation:
because are
of similar
shape and
deep green
colour
Settlement:
Spread all over
the area with
rough
polygonal roof
as seen from
top.
Cloud/
cyclonic
wind: due to
the smoky
and feather
like
appearance
Port:
Location
along the
water body

AERIAL PHOTOGRAPH
The photographs taken of ground from an elevated position from an aircraft or any other flying
object using a precision camera are termed aerial photographs. Aerial photographs are used in
topographical mapping and interpretation.
History of Aerial Photography in India
Aerial photography in India goes back to 1920 when large-scale aerial photographs of Agra city
were obtained. Subsequently, several similar surveys were carried out and advanced methods of
mapping from aerial photographs were used. Today, aerial photography in India is carried out
under the supervision of the Directorate of Air Survey (Survey of India) New Delhi. Three flying
agencies, i.e. Indian Air Force, Air Survey Company, Kolkata and
National Remote Sensing Agency (NRSA), Hyderabad have been officially authorized to take
aerial photographs in India.
Difference between Maps and Aerial Photographs
Aerial Photograph Map
1 It is a central Projection. It is an orthogonal Projection.
2 An aerial photograph is geometrically
incorrect. The distortion in the geometry
minimum at the centre and
increases towards the edges of the
photographs.
A map is a geometrically correct representation
of the part of the earth is projected.
3 The scale of the photograph is not uniform. The scale of the map is uniform throughout the
map extent.
4 Enlargement/reduction does not change the
contents of the photographs and can easily
be carried out.
Enlargement/reduction of the maps involves
redrawing it afresh.
5 Aerial photography holds good for
inaccessible and inhospitable areas.
The mapping of inaccessible and inhospitable
areas
is very difficult and
sometimes it becomes impossible.

ANNOTATION OF AERIAL PHOTOGRAPH
Annotations are preliminary information about an aerial photograph. The aim is to improve
information content of the image description. Annotations can add information that can't be easily
included in descriptions. These generally highlight features, details, or points of interest within an
imagery.
Need of Annotation:
• Provides crucial prerequisite information on the imagery.
• Identifies places/objects/locations in panoramic/aerial photographs.
• Highlighting important hard-to-notice details of the image.
• Identify the various elements of a composition of physical earth.
• Transcribing inscriptions, signs, or words in the image for better understanding.
SL. No. Parameter Description
1 Size of the Photograph 23 x 23 cm
2 Photograph Number 1296 − 𝐵
𝐴3 − 3
3 Negative Number 0700
4 Secret Yes
5 Kodak Safety Film No
6 Instrument Number UAg479
7 Focal length 151.80
8 Watch 1:55:48 pm
9 Resolution 3000m
10 Fiducial Marks 04

VISUAL INTERPRETATION OF AERIAL PHOTOGRAPHY
Image Interpretation: An act of identifying the images of the objects and judging their relative
significance. The principles of image interpretation are applied to obtain qualitative information
from the aerial photographs such as land use/land cover, topographical forms, soil types, etc.
Sl. No. ROADS VEGETATION SETTLEMENT
1 Image
2 Location A major road passes through
the centre of the section and
smaller roads are connected
to it
Located along the roads and
near the settlements.
Located along the roads.
3 Recognition Form an elongated network
with well connectivity.
Proximity to the settlements
and roads, lush and deep
green colour.
Polygonal with different shades,
sizes located along the road.
4 Shape Elongated, sinuous and
curvy
Spotty, Amorphous Patches Polygonal as well as irregular
5 Size Elongated with variable
width.
Medium- Small size as
discerned from the tree
crowns.
Varying from small to long
rectangular to large cubicle.
6 Tone Light ash/dusty (Middle
shade)
Dark Green Mostly dark grey
7 Shadow No Yes Yes
8 Pattern Trellis Heterogeneous Heterogeneous
9 Texture Rugged Rough Rough blocks
10 Resolution High High High
11 Stereoscopic
Appearance
No Yes Yes
12 Feature Remark Road: Because elongated,
curvy and connected
Vegetation: because are of
similar shape and deep green
colour
Settlement: Spread along the road
with rough polygonal roof as seen
from top.

DIGITAL IMAGE & LINEAR STRETCHING
The electromagnetic energy may be detected either photographically or electronically. The
photographic process uses light sensitive film to detect and record energy variations. On
the other hand, a scanning device obtains images in digital mode. It is important to distinguish
between the terms images and photographs. An image refers to pictorial representation, regardless
of what regions of energy have been used to detect and record it. A photograph refers specifically
to images that have been recorded on photographic film.
Hence, it can be said that all photographs are images, but all images are not photographs.
Based upon the mechanism used in detecting and recording, the remotely sensed data products
may be broadly classified into two types:
• Photographic Images
• Digital Images
Photographic Images: Photographs are acquired in the optical regions of electromagnetic
spectrum, i.e. 0.3 – 0.9 µm. In aerial photography black and white film is normally used.
Photographs may be enlarged to any extent without losing information contents or the contrast.
Digital Images: A digital image consists of discrete picture elements called pixels. Pixels are the
smallest size of picture element on an image. Each pixel in an image represents an intensity value
and an address in form of rows and columns in two-dimensional image space. A digital number
(DN) represents the average intensity value of a pixel. It is determined by the electromagnetic
energy received by the sensor and the intensity levels used to describe its range. The details in the
images of the features are governed by the size of the pixel. However, zooming of the digital image
beyond certain extent produces loss of information and the appearance of pixels only. Basically,

Digital image are an array of digital numbers (DN) arranged in rows and columns, having the
property of an intensity value and their locations.
Formula:
Perform the linear stretch of the following 5X5 matrix of an 8-bit system
8-Bit system matrix (5X5)
31 38 45 49 89
73 75 85 89 100
95 95 93 89 110
110 111 93 89 150
110 111 93 89 150
DN (Maximum)=150
DN (Minimum)=31
DN (Input) Frequency
31 1
38 1
45 1
49 1
73 1
75 1
85 1
89 5
93 3
95 2
100 1
110 3
111 2
150 2
DN (Output) = [
𝐷𝑁 (𝐼𝑛𝑝𝑢𝑡) − 𝐷𝑁(𝑀𝑖𝑛𝑖𝑚𝑢𝑚)
𝐷𝑁 (𝑀𝑎𝑥𝑖𝑚𝑢𝑚) − 𝐷𝑁 (𝑀𝑖𝑛𝑖𝑚𝑢𝑚)
] × 255

DN input
Calculation
[𝐷𝑁 𝑜𝑢𝑡𝑝𝑢𝑡 =
𝐷𝑁 (𝑖𝑛𝑝𝑢𝑡) − 𝐷𝑁 (𝑚𝑖𝑛𝑖𝑚𝑢𝑚)
𝐷𝑁 (𝑚𝑎𝑥𝑖𝑚𝑢𝑚) − 𝐷𝑁 (𝑚𝑖𝑛𝑖𝑚𝑢𝑚)
× 255]
DN output
31 31 − 31
150 − 31
× 255
0
38 38 − 31
150 − 31
× 255
15
45 45 − 31
150 − 31
× 255
30
49 49 − 31
150 − 31
× 255
39
73 73 − 31
150 − 31
× 255
90
75 75 − 31
150 − 31
× 255
94
1 1 1 1 1 1 1
5
3
2
1
3
2 2
0
1
2
3
4
5
6
31 38 45 49 73 75 85 89 93 95 100 110 111 150 255
FREQUENCY
DN (Input)
DIGITAL NUMBER (INPUT)

85 85 − 31
150 − 31
× 255
116
89 89 − 31
150 − 31
× 255
124
93 93 − 31
150 − 31
× 255
133
95 95 − 31
150 − 31
× 255
137
100 100 − 31
150 − 31
× 255
148
110 110 − 31
150 − 31
× 255
169
111 111 − 31
150 − 31
× 255
171
150 150 − 31
150 − 31
× 255
255
DN (Output)
0 15 30 39 124
94 94 116 124 148
137 137 133 124 169
169 171 133 124 255
169 171 133 124 255
DN (Maximum)=255
DN (Minimum)=0
DN (Output)
DN output Frequency
0 1
15 1
30 1
39 1
90 1
94 1
116 1
124 5
133 3
137 2
148 1
169 3
171 2
255 2

1 1 1 1 1 1 1
5
3
2
1
3
2 2
0
1
2
3
4
5
6
0 15 30 39 90 94 116 124 133 137 148 169 171 255
FREQUENCY
DN (Output)
DIGITAL NUMBER (OUTPUT)

Digital image & linear stretching

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