Photogrammetry
Photogrammetry is the science and technology of taking spatial measurements from
photographs and preparing geometrically reliable derivative products.
The techniques are based on the geometry of perspective scenes and on the principles of
stereovision.
Two kinds of photographs used in photogrammetry: aerial and terrestrial.
Aerial photographs are usually acquired from aircraft but can also come from satellites, hot air
balloons or even kites. Terrestrial photographs come from cameras based on the ground, and
generally are used in different applications from aerial.
There are two main data extraction methods used for analysing these photographs:
a. Quantitative: that is size, length, shape, height, area, etc.
b. Qualitative: geology, vegetation, drainage, land use, etc.
Historically, the most common use of photogrammetry was to produce hardcopy topographic
maps, now it is used to produce a range of GIS data products such as DEMs, accurate raster
images backdrops for vector data
Aerial photographs
- Vertical
- Oblique
Vertical photographs most commonly used, but
true vertical photographs are rare because of the
angular attitude of the aircraft at the time of
photography.
This results in slight (1-3º) unintended
inclination of the optic axis of the camera,
resulting in titled photographs.
However, for most practical applications, such
photographs can be considered vertical
photographs.
Aerial
photographs
Aerial
photographs
Aerial photographs: Some terminology
Fiducial marks
Fiducial
axis
Fiducial marks - Index marks, usually 4, at the center point
of each side of an air negative or photo. These are rigidly
connected with the camera lens through the camera body—
which forms images on the negative. Usually are a hairline, a
cross, or a half-arrowhead.
Edge of format
Lens
Nadir
Principal Point - optical or geometric center of the
photograph - the intersection between the projection of the
optical axis (i.e., the perpendicular to the center of the lens)
and the ground. Can be located by the intersection of lines
between opposite side/corner fiducial marks.
Plumb
line
Nadir - The nadir, also called vertical point or plumb point,
is the image of the intersection between the plumb line
Y axis
Principal point directly beneath the camera center at the time of exposure
and the ground. The nadir is important because relief
displacement is radial from this point and is a function of the
distance of the displaced image from it. Unlike the principal
point, there are no marks on the photograph that permit to
X axis
locate the nadir.
Isocenter
Isocenter - The point on the photo that falls on a line halfway between the principal point and the Nadir point.
Aerial
photographs
Determination of nadir in oblique photos
Relief displacement is radial from nadir, and is a
function of the distance of the displaced image
from it.
Nadir
Isocentre
Principal
point
Unlike the principal point, there are no marks on
the photograph that permit to locate the nadir.
However, in areas where tall and perfectly vertical
objects (e.g., towers, smokestacks, electric poles,
tall buildings, etc.) are clearly located on the
photograph, the nadir point may be determined by
projecting lines along the displaced edges of these
buildings
Aerial
photographs
Principal
point
Nadir
Flightline of Vertical Aerial Photography
Flightline of Aerial Photog raphy
Direction of Flight
Exposure station
#1
#2
#3
lens
altitude
above
ground
level, H
60% overlap
s tereo scopic model
Coverage of photograph
terrain recorded on three
successive photographs
Jensen, 2000
Block of Vertical Aerial Photography
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
Jensen, 2000
Block of Vertical Aerial
Photography Compiled into
Photomosaic
Columbia, SC
Original scale = 1:6,000
Focal length = 6” (152.82 mm)
March 30, 1993
Jensen, 2000
Line of flight
x-axis
x-axis
Principal
Principal
Point of
Photo #1
PP
Principal
Point of
Photo #1
PP
P hoto 2
P hoto 2
y - axis
Fiducial
mark
y - axis
Line of flight
P hoto 1
P hoto 1
Fiducial
mark
Geometry of
Overlapping Vertical
Aerial Photographs
Principal Point of
Point of Photo #2
PP
Photo #2
2
PP
1
2
1
a.
b.
P hoto 2
b.
P hoto 2
P hoto 1
P hoto 1
a.
PP1
PP1
PP 2
CPP 2
CPP 1
CPP 2
PP 2
line of flight
CPP
1
line of flight
Principal Point of
Principal Po int o f
Photo #1 equals
Ph oto #2 equ als
Conjugate Principal
Con jug ate Prin cip al
Principal Point of
Principal Po int o f
Point of Photo #2
Po int of Pho to # 1
Photo #1 equals
Conjugate Principal
Point of Photo #2
c.
Ph oto #2 equ als
Con jug ate Prin cip al
Po int of Pho to # 160% overlap
stereoscopic model
Conjugate principal point: The point in the
overlapping photo that is equivalent to the
principal point of adjacent photograph
Negative
(Reversal of
tone and
geometry
Focal
length (f)
Exposure station
Camera lens
Altitude
ASL (H)
Positive print/
transparency
Geometry of A Vertical
Aerial Photograph
Obtained Over
Flat Terrain
Ground points are denoted in capitals,
the corresponding points on the image
are denoted in small letters.
- X axis along the flight direction
-Y axis perpendicular to X
- Principal point - Origin
Elevation
ASL (h)
SEA LEVEL
Geometry of A Vertical Aerial Photograph Collected Over Flat Terrain
Photographic scale
Scale (S) = Photo
distance/ground distance = d/D
56.0’
0.112”
6’
0.012”
Scale (S) = f/H′
Or
Scale (S) = f/(H – h)
Scale is dependent on the
flying height ~ terrain
clearance ~ terrain elevation
Geometry of A Vertical
Aerial Photograph
Collected Over Variable
Relief Terrain:
Geometric distortion
Variation in the terrane elevation
would result in scale variations across
the photograph
Scale (S) = f/(H – h)
 Generally the average scale based
on average height is given
Map vs Photograph
- On a map we see a top view of objects in their
true horizontal (planimetric) positions
(Orthographic projection)
- On a photograph they are displaced from their
true map positions due to geometric distortions
(perspective projection)
• Objects at higher elevations (closer to
the camera) appear larger than the
corresponding objects at lower elevations
• Tops of the objects are displaced from
their bases (relief displacement), which
causes any object standing above the
terrain to “lean” away from the principal
point.
Map – Orthographic
projection – No relief
displacement
Photo – Perspective projection
– Varied scale - Relief
displacement
Measurement of Object Height From A Single
Aerial Photograph Based on Relief Displacement
Principal point
r
d
Given that the flying height is H
Measurement of Object Height From A Single
Aerial Photograph Based on Relief Displacement
h = dH/r
d –relief displacement on the
photograph
r – radial distance from the principal
point to the displaced image point
h – height above datum of the object
point
H – flying height above the same
datum chosen to reference h
ΔLOB′ ~ ΔBAB′
D/R = h/H
or, on the scale of the photograph
d/r = h/H
d = rh/H
b’ a’
Exposu re statio n
h
=
H
h
=
o’
Neg ative
f
Principal point
,L
d
d
r
r
Positive
d x H
o
r
a d
b
r
r = 2.23 in .
d = 0.129 in.
H = 2978.5 ft ab ov e lo cal datum
h = 172 ft
local datum
H
H
B
hh
OPP
A
D
R
B′
Measurement of Object Height From A
Single
Aerial Photograph Based on
Measurement of the Height of
Shadow
on Level Terrain
Objects
BasedLength
on Shadow Length
tan a =
opposite
Su
n 's
adjacent
=
heigh t, h
shadow, L
ra y
s
h
a
h = L x tan a
shadow
L
0.119”
0.119”
59.1’
59.1’
Object Height
Determined by
Shadow Length
0.241”
0.241”
119.65’
119.65’
Image parallax
Apparent change in relative positions of stationary objects caused by a change in viewing position
Objects closer to the viewing position appear to move with respect to the objects farther away
Eye base
Distance to
the object
Parallax
angle
Parallax
Parallax: Look at apparent motion of
object against distant background from
two vantage points; knowing baseline
allows calculation of distance:
distance (in parsecs) =
1/parallax (in arc seconds)
1 parsec ~ 3.3 ly
Image parallax
Objects closer to the aircraft-mounted camera (that is, at higher elevation) would appear to move with respect
to objects at lower elevation when the position of the air craft changes in successive exposures.
These relative displacements or parallax form the basis of stereo viewing (depth perception)
Parallax = a –b
PP2
PP1
a
b
Parallax on overlapping vertical photos
Parallax displacement occurs parallel to the line-of- flight
In theory the line-of-flight should be parallel to the fiducial
x axis. In reality, there is a slight offset - the true flight
direction is along the line joining the principal point and the
conjugate principal point.
The line-of-flight for a stereopair defines the photocoordinate
x axis. Line drawn through the principal point perpendicular
to the flight line defines photocoordinate y axis.
Parallax of a point (Pa) = xa – x′a ,
where
xa is the measured x coordinate of the image point a on the
left photo of the stereopair
x′a is the measured x coordinate of the image point a on the
right photo of the stereopair
L
L
a
L′
L′
a′
f
+
o
a′x
o
o′
hA
L
H
a′x
o
AX
hA
O
o′
f
A
XA
a′x
==>
ax
ax
ax
Parallex = Pa = xa - x′a
L
M
L′
a′
f
Parallex = Pa = a′xax = xa - x′a
Lo = Focal length = f
LL’ = Air base = B
L
a
a′x
o
o′
ax
f
a′x
A
hA
XA
Δa′xLax is similar to the ΔLL′AX
Therefore,
H
a x a x
LL
AX
hA
O
ax
o

Pa
B

LO
MA X

f
H  hA
 H  hA 
Bf
 hA  H 
Bf
Pa
Pa
L
M
Parallex = Pa = a′xax = xa - x′a
Lo = Focal length = f
LL = Air base = B
a
L′
a′
f
a′x
o
Now ΔLoax is similar to the ΔLOAAX
o′
ax
f
Therefore,
oa x
A
hA
YA
OA
XA
Lo

O A AX
LO A
xa
f

X

H  hA
A
H
 X
A

xa ( H  hA )
f
AX
hA
 X
A
 B
O
 YA  B
xa
Pa
ya
Pa
xa (

Bf
Pa
f
)
L
M
Parallax Equations
a
L′
a′
f
hA  H 
a′x
o
o′
ax
f
X
 B
H
h 
pa
xa
pa
YA  B
A
hA
A
Bf
ya
pa
pH 
pa
OA XA
AX
hA
O
Where:
Δh - Difference in the elevation of
two points whose parallax
difference is Δp
H′ - Flying height above the lower
point
Pa – Parallax of the higher point
in e fro m Ph o to 4 -5
The height of the Senate Condominium in Columbia
x a ’ = - 0.270”
Flying height above the base of the building – 3000 feet
Methods of Measuring
Stereoscopic
x-parallax from
Overlapping Aerial Photographs:
• Measurement Using Fiducial Lines (a,b)
• Measurement Based on Superposition (c)
Principal point 4-5
a.
x axis
PP 4-4
PP 4-5
Ph oto 4-4
Photo 4-5
y axis
a.
Ph oto 4-4
b.
PP 4-4
Ph oto 4-5
a
c.
p x  x b  x b '   0 . 267 "  (  3 . 606 " )  3 . 339 "
b
 p  3 . 55 "  3 . 339 "  0 . 211 "
b.
p xa

0 . 211 " 3000 '
3 . 55 "
 x178
. 30 '
a = - 3.82”
c.
Ph oto 4-4
F id u cia l lin e fro m P h o to 4 -4
p x  x a  x a '   0 . 27 "  (  3 . 82 " )x b = - 33.606”
. 55 "
pH 
x a ==-3.82”
- 3.82”
X
a’
F id u cia l lin e fro m P h o to 4 -4
Xa=-0.270”
x a ’ = - 0.270”
b =-3.606”
= - 3.606”
Xx b’
F id u c ial lin e fro m Ph o to 4 -5
= - 0.267”
Xxbb’=-0.267”
h 
Principal point 4-4
h 
dH
r

0 . 247 " 3000 '
4 . 164 "pa
p b = 0.511”
 177 . 95 '
= 0.30”
dp = 0.211”
Parallax measurement
x′
x
PP1
+
+
+
d
D
Parallax = x – x′ = D - d
+PP2
Ground Control Points
A point on the surface of the earth of known horizontal and vertical location (i.e. fixed
within an established co-ordinate system and datum) which is used to geo-reference
image data sources, such as aerial photographs, remotely sensed images, and scanned
maps.
When mutually identifiable on the ground and on a photograph, GCPs are used to
establish the exact spatial position and orientation of a photograph relative to the ground
Historically GCPs have been established through ground survey techniques, now a days
GPS are more frequently used.
Accurate ground control is essential to all photogrammetric operations because
photogrammetrical measurements can only be as reliable as the ground control
FLIGHT PLANNING
Parameters:
• Focal length of the camera to be used
• The film format size
• Photoscale desired
• Size of the area to be photographed
• Average elevation of the area to be photographed
• The overlap desired
• Side-lap desired
• Ground speed of the aircraft
Based on the above parameters, mission planner decides:
• The flying height above the datum
• the location, direction, and the number of flight lines to be made
• the time interval between exposures
• the number of exposures on each flight line
• the total number of exposures for the mission
North
FLIGHT PLANNING
10 km
16 km
Area to be
photographed
Camera characteristics:
• f = 152.4 mm
• Film format = 230 mm
Photoscale: 1:25000
End-lap – 60%; side-lap 30%
Average elevation: 300m
Beginning and ending flight lines
should be along the boundaries
Aircraft speed – 160 km/hr
Direction of flight lines?
N-S
Flying Height?
H=f/s + Mean elevation = 0.23/(1/25000) = 4110 m
Ground coverage per photo?
= film format size/scale = 0.23 m/(1/25000) = 5750 m on a side
Ground separation between photos (in the flight direction)?
Advance per photo = 40% (60% overlap) = 0.40*5750 m = 2300 m
(Between photocentres)
Time between exposures?
= 2300m/160 km/hr = 51.75 s
North
FLIGHT PLANNING
10 km
16 km
Area to be
photographed
Because time can set in seconds, the number is rounded off.
Recalculate the distance between photos?
51 sec/phot * 160 km/hr = 2267 m
Number of photos?
= 16000 m per line/2267 m/photo + 1 +1 =9.1 (use 10)
Flight line separation?
Camera characteristics:
• f = 152.4 mm
• Film format = 230 mm
Photoscale: 1:25000
End-lap – 60%; side-lap 30%
Average elevation: 300m
Beginning and ending flight lines
should be along the boundaries
30% sidelap = separation of 70% of the coverage = 0.70 * 5750 m
= 4025 m between flight lines
Number of flight lines?
= 10000/4025 +1 = 3.48 (use 4)
Adjusted flight line space?
= 10000/(4-1) spaces = 3333 m
Total number of photos?
= 10 photos per line + 4 lines = 40 photos
Principles of Remote Sensing : NR –603
• History and development of remote sensing
• Electromagnetic radiation - nature and sources, interaction
with matter and atmosphere
•Atmospheric windows and effects, corrections
• Multispectral systems
• Characteristics of important remote sensing systems: LANDSAT, IRS,
ASTER, SPOT;
• High resolution sensors
• Hyperspectral sensors
• Thermal systems
• Microwave systems
• Geostationary systems (?)
• Interpretations and applications - agriculture, forestry, land-use
mapping, geology, water resources etc etc.
… and Arial Photography/Photogrammetry.