AERIAL PHOTOGRAMMETRY

Aerial Photograph: The science of taking a photograph from

a point in the air for the purpose of making some type of
study of the surface of the earth.
Photogrammetry The science of making measurements on
photographs
Categories:
Metric / Quantitative: determination of ground positions,
distances, elevations, areas, volumes
Interpretive or quantitative ( Photographic interpretation
/ Photomensuration) is an art of examining these
photographic images for the purpose of identifying
objects

Unique Perspective of Aerial photographs

Human vision provides vertical perspective ground level view
Aerial platforms provide horizontal perspective synoptic view

Aerial Platforms for Cameras

Balloons/Blimps
Pigeons
Kites
Airplanes

Aerial Platforms - U-2 and SR-71

Developed for the military to carry high resolution aerial
camera systems for intelligence gathering have been in
continuous operation since the 1950s

Types of Photographs used in Photogrammetry

Terrestrial Photographs photos taken from a fixed and
usually known position on or near the ground with the
camera
axis
horizontal
or
nearly
so
using
phototheodolites.
Aerial Photographs Camera station in air with camera
axis vertical of near vertical
Close range Photographs camera close to object being
observed. Most often used when direct measurement is
impractical.

PHOTOTHEODOLITES
Combination of camera and theodolite.
Any camera equipped for orienting its optical axis in
known directions with respect to a base line is called
Phototheodolite.
Generally mounted on Tripods, centered over a desired
station by means of plumb bob.
Camera axis can be set in any desired azimuth with
respect to a base line.

Types of Aerial Photograph: On the basis of attitude of the camera axis, lens
systems, types of camera and Types of films and filters, aerial photography may
be classified
1 According to orientation of A) Vertical photography
camera axis
B) Low oblique Photography
C) High oblique Photography
2 According to lens system

A) Single lens photography

B) Three lens photography
(Trimetrogon photography)
C) Four lens photography
D) Nine lens photography
E) Continuous strip photography

3 According
to
special A) Black and white photography
properties of films, filters B) Infra-red photography
or
photographic C) Colour photography
equipment
D) Colour infra-red photography
E) Thermal infra-red imagery
F) Radar imagery
G) Spectrazonal photography
4 Digital aerial photographs Digital data
(Instead of films, using
the CCD arrays

According to orientation of camera axis

A)A Vertical photography is one taken with the axis of the

camera as vertical as possible at the time of exposure. It is
virtually impossible to take absolutely vertical photographs.
Deviation of the optic axis from the vertical, which rarely
exceeds 1 to 2 degree, results the tilted photographs.

B) An oblique photograph is taken with the axis of the

camera intentionally tilted from the vertical.

i) Low oblique photography:

In this type of photography, the camera axis is tilted
intentionally to a certain low angle, such that the horizon
is not photographed. (Max. angle of tilt is 35o)

ii) High oblique photography:

Here the camera axis is tilted intentionally to certain
greater angle such that horizon is seen on low resulted
photograph (max. angle of tilt > 35o). Such photographs
are of importance in military purposes where scenery has
to be appreciated with out stereo vision

Advantages of vertical over oblique aerial photographs

1.Vertical photographs present approximately uniform scale
throughout the photo.
2.Because of a constant scale throughout a vertical photograph,
the determination of directions (i.e., bearing or azimuth) can be
performed in the same manner as a map.
3.Because of a constant scale, vertical photographs are easier to
interpret than oblique photographs. Furthermore, tall objects
(e.g., buildings, trees, hills, etc.) will not mask other objects as
much as they would on oblique photos.
4.Vertical photographs are simple to use photogrammetrically as
a minimum of mathematical correction is required.

5.Stereoscopic study is also more effective on vertical than on

oblique photographs.

Advantages of oblique over vertical aerial photographs

1.An oblique photograph covers much more ground area than a
vertical photo taken from the same altitude and with the same focal
length.

2.If an area is frequently covered by cloud layer, it may be too low

and/or impossible to take vertical photographs, but there may be
enough clearance for oblique coverage.
3.Oblique photos have a more natural view because we are
accustomed to seeing the ground features obliquely.
4.Objects that are under trees or under other tall objects may not be
visible on vertical photos if they are viewed from above. Also some
objects, such as ridges, cliffs, caves, etc., may not show on a vertical
photograph if they are directly beneath the camera.
5.Determination of feature elevations is more accurate using oblique
photograph than vertical aerial photographs.

Geomentry of Aerial Photograph

Exposure Station : Point in the air occupied by the front nodal point of the
camera lens at the instant of exposure
Perspective projection: The straight rays radiate from a common or
selected point and pass through points on the sphere to the plane of
projection
Perspective centre: Real or imaginary point of the origin of bundle of
prespective rays.
Flying Height: Elevation of exposure station above mean sea level
Incoming light rays from objects on the ground pass through the camera
lens before they are imaged on the film in the focal plane.
Focal length: The distance between the lens and the focal plane is termed
Field of View The region which is collected in the photograph is often
referred to as the camera systems field of view (FOV

Fiducial mark

Marks in the camera

image plane located
either in the middle or
corners

Used as reference for

measurement
of
image coordinates or
distance
Fiducial Line: line
joining
opposite
fiducial mark
Centre of Collimation:
Intersection
of
fiducial lines

The most of the aerial photographs are not perfectly

vertical
There are three different photo centers: the principal
point, the nadir, and the Iso-center.

Each one of these centers plays a specific role and is of

great importance to the photogrammetrist because
different types of distortion and displacement radiate
from each of these points.
If an aerial photograph is perfectly vertical, the three
centers coincide at one point (i.e., the principal point),

Principal point
The principal point is the optical or geometric center of the photograph.
It is the intersection point between the projection of the optical axis (i.e.,
the perpendicular to the center of the lens) and the ground.
We can locate the principal point (PP) on a single photo by the intersection
of lines drawn between opposite side or corner fiducial marks.

This PP is then transferred stereoscopically onto the adjacent (left and right)
photographs of the same flight line

Photo 2

Fiducial
mark

y - axis

Photo 1

These transferred points are called transferred principal points or conjugate

principal points (CPP). The line segment joining the principal points and the
conjugate principal points constitute the flight line of the aircraft, also called base line
or air base

Line of flight

x-axis
Principal
Point of
Photo #2
PP2

Principal
Point of
Photo #1
PP1

b.

Photo 2

Photo 1

a.

PP1
CPP2

PP2
CPP1

line of flight
Principal Point of
Photo #1 equals
Conjugate Principal
Point of Photo #2

c.

Principal Point of
Photo #2 equals
Conjugate Principal
Point of Photo #1

60% overlap
stereoscopic model

Nadir Point

The nadir point is also called vertical point or

plumb point

It is the intersection point between the

plumb line directly beneath the camera
center at the time of exposure and the
ground.
The nadir is important because
displacement is radial from this point

relief

Unlike the principal point, there are no marks

on the photograph to locate the nadir point.
Locating the nadir requires sophisticated
stereoscopic plotting techniques involving
expensive instruments and ground control
information.
However, can be located as follows: The
nadir point is at the intersection of lines
extended from the top to bottom of tall and
perfectly vertical objects.

Isocentre
The isocenter is the point halfway
between the principal point and the
nadir and on the line segment
joining these two points on the
photograph.
It is a point intersected by the
bisector of the angle between the
plumb line and the optical axis.
The isocentre is the point from
which tilt displacement radiates.

Flightline of Aerial Photography

Direction of Flight
Exposure station
#1
#2

Flightline of Aerial Photography

#3

lens
altitude
above
ground
level, H

60% overlap
stereoscopic model
Coverage of photograph
terrain recorded on three
successive photographs

Block of Aerial Photography

Flightline #1

oblique photography may be

acquired at the end of a
flightline as the aircraft
banks to turn

Flightline #2

20 30%
sidelap
Flightline #3

Effective Area
Central portion of a vertical photograph, delimited by
bisecting the overlap areas of neighboring photographs
Objects in effective area have less displacement than the
same objects in neighboring photographs
Delineates areas to avoid duplication
interpretation effort between photos

or

gaps

in

Relationship between aircraft altitude and ground coverage

Changing the focal length of the
camera lens will alter the angular
coverage of the system as the focal
length
gets
smaller, the angular
coverage increases
As the angular cover increases (focal
length decreases), the FOV increases
Changing the aircraft altitude will alter
the ground coverage of the system

MAP SCALE & SCALE OF AERIAL PHOTOGRAPH

Map Scale is the ratio between the map distance and
the corresponding distance on the ground.
Similarly, the Scale of an Aerial Photograph is the ratio
of a distance on the photo to that same distance on the
ground.
On a map, scale is uniform everywhere because of its
orthographic projection.
An photos scale changes as the distance from the
exposure to the ground changes due to perspective
projection

Example
Two football fields at two elevations will not have the same length on an aerial
photo.
Similarly, a ground based exposure of two six foot tall people different
distances from the exposure will be of different length

But on the aerial photograph, since it is a perspective

projection, scale varies with terrain elevations.
Expressed in 3 ways,

1) Unit equivalents : 1 in. = 1,000 ft.

2) Dimensionless representative fractions : 1/10,000
3) Dimensionless ratio : 1: 10,000

The photo scale can be determined in 3 ways

By establishing the selection between the photo

distance and ground distance
By establishing the relation between photo
distance and Map distance

By establishing the relation between the focal

length of the camera and flying height

By establishing the selection between the photo

distance and ground distance

This method is usually adopted when the focal

length and flying height of the camera are not
known.
The scale is calculated by comparing the photo
distance and ground distance
Scale

Photo distance :

Ground distance

or Scale = Photo distance / Ground distance

For example,
The distance between points A
and D in ground = 6 km and in
air photo = 10 cm
6 km = 6 x 1000 x 100 cm
=

6,00,000

= 6 lakhs cm

10/6,00,000 = 1/60,000

Therefore, 1 cm in aerial photograph is equal to 60,000 cm in ground.

 By establishing the relation between photo distance and Map

distance Using Topographic map sheet

Minimum of four points with wider separations is preferable

The scale of the topographic sheet is used, e.g. 1: 50,000.

If an aerial photo can be assumed to be

vertical, similar triangles can be used to
solve.

The scale may be expressed in

terms of camera focal length (f),
and flying height above ground
(H) by equating the similar
triangles Lab and LAB,

i.e., the scale of a vertical photo is directly proportional to camera focal length
(image distance) and inversely proportional to flying height above ground (object
distance).

THE SCALE EQUATION

ab
f
S = ----- = ------AB
H'
where
S = scale
ab = photo distance
AB = ground distance (horizontal)
f = focal length (6 inches for most film based aerial
cameras)
H' = flying height above line AB
Note:
H = H h
Where
H = flying height above datum (usually sea level)
h = elevation above datum

The scale equation can be rewritten many ways.

ab
f
----- = ------AB
H

Flying height: Let's assume a relatively flat area is on a

photo. By Measuring a photographic distance of a known
ground horizontal distance, flying height is
AB
H' = f * ---ab
Ground Distance: Once a flying height is determined other
photo distances can be measured and one can solve for a
ground distance.
H' * ab
AB = ------f

Example:
I. A football field (goal line to goal line) measures 0.6
in. on an aerial photo. What is the flying height?
H = AB * f / ab = 300 ft. * 6 in. / 0.6 in.
H = 3000 ft.
II. At a flying height of 1200 ft., a building edge
measures 0.15 in. on an aerial photo. What is its
ground length?
AB = H * ab /f = 1200 ft. * 0.15 in. / 6 in.
AB = 30 ft

Scale of A Vertical Aerial

Photograph Over Variable Terrain
Photo scale, increases with
increasing terrain elevation
and
decreases
with
decreasing terrain elevation.
Photo Scale at different
points can be calculated
using the following equation

S =
H n
Average Photo Scale
Calculate the average terrain elevation as below:
Average Object Height
havg = (h1 + h2 + h3 + h4 + .hn ) / n
Then, calculate Average Flying Height H = H - havg

Average photo scale can be calculated.

DISTORTION AND DISPLACEMENT

Distortion in aerial photography is defined as any shift in the position

of an image on a photograph that alters the perspective characteristics
of the image and

Displacement is any shift in the position of an image on a photograph

that does not alter the perspective characteristics of the photograph.
Displacement results mainly from the perspective viewing of the
camera resulting in a perspective or central projection on the
photograph. In contrast, a map is the product of an orthographic
projection.

Relief Displacement on a vertical aerial photograph

Relief displacement is the shift or displacement in
the photographic position of an image caused by the
relief of the object

Relief displacement:

Caused by the terrain undulations.

Objects at edges of the photo will appear
to lean away from the principal point

There is a mathematical relationship

between object heights and the amount
of displacement, which allows us to
determine the heights of objects
The amount of displacement depends on
the height of the object and the radial
distance of the object from the image
nadir.

Relief displacement increases with

increase of radial distance from principle point (R) and Increase of object height
(h)
Relief displacement decreases with
increase of Flying height above the datum (H)

Relief displacement side view

h = height of vertical object
r

Relief displacement on photo

r = radial distance from principal point to top of object

d = relief displacement = photo distance between bottom
to top of object
Note relief displacement is along a radial line.

By similar triangles
d/h = r/H Or h = d*H/r

h = actual height of object

H = flying height above bottom of object
If flying height is given, we can measure
d and r on a vertical photo

b a

Easily an objects height can be

determined
Note the equation can also
d= h*r/H or
r=d*H/h
H=h*r/d

beh
H

d
written
=
r

h =

dxH
r

Negative

Principal point

Exposure station, L

d
r

Positive

o a

or

r = 2.23 in.
d = 0.129 in.
H = 2978.5 ft above local datum
h = 172 ft
local datum

B
h
PP

(1) A building edges top is 3.5 in. from the center of a

photo and its vertical edge measures 0.05 in. on the
photo. If the flying height of the photo is 3000 ft. what is
the height of the building?
h = dH/r = 0.05 in. * 3000 ft. / 3.5 in.
h= 43 ft.

(2) The flying height is 1200 ft. If ones measuring

ability on a photo is 0.01 in., and once desires to
measure vertical objects to a resolution of 5 ft., how far
does the top of the object need to be displaced from
the center of the photo?
r=d*H/h = 0.01 in. * 1200 ft. / 5 ft.
r = 2.4 in

Two towers were identified on a perfectly vertical photograph taken from 2500 m
above the datum. The distances from the base of the towers to the photo center are
equal and are measured to be 8.35 cm. If the height of tower1 is 120 m and that of
tower2 is 85 m above the datum, find the relief displacement of the summit of these
towers on the photograph? Conclude.
Where h = height above datum of the object point
whose image is displaced
d = relief displacement
r = radial distance on the photograph from the
principal point to the displaced image (the units of
d and r must be the same).
H = flying height above the datum selected for
measurement of h

rh
D = ------H

Conclusion: Relief displacement varies directly as the height of the object.

Because tower1 is higher than tower2, its image is displaced more.

A vertical photograph taken from an elevation of 535 m above MSL contains the
image of a tall vertical radio tower. The elevation at the base of the tower is 259 m
above MSL. The relief displacement d of the tower was measured as 54.1mm,
and the radial distance to the top of the tower from photo centre was 121.7 mm.
What is the height of the tower?.