Formula Sheets: Photogrammetry | Geomatics Engineering (Surveying) - Civil Engineering (CE) PDF Download

 Page 1


GA TE CE 2026 F orm ula Sheet: Geomatics Engineering - Pho-
togrammetry
1. Photogrammetry Basics
• Scale of v ertical photograph:
S =
f
H-h
where:
– S : Scale of photograph (dimensionless)
– f : F o cal length of camera (m)
– H : Flying heigh t ab o v e datum (m)
– h : Elev ation of terrain ab o v e datum (m)
• Ground distance:
D
g
=
D
p
S
where:
– D
g
: Ground distance (m)
– D
p
: Photo distance (m)
• Area on ground:
A
g
=S
2
·A
p
where:
2. Stereoscopic P arallax
– P arallax equation:
p =x
l
-x
r
where:
* p : P arallax (mm)
* x
l
: x-co ordinate on left photo (mm)
* x
r
: x-co ordinate on righ t photo (mm)
– Heigh t of ob ject using parallax:
h =H-
fB
p
where:
* h : Heigh t of ob ject ab o v e datum (m)
* B : Air base (distance b et w een camera stations, m)
– P arallax difference for heigh t difference:
?h =
?p·f ·H
B(p+?p)
where:
* ?h : Heigh t difference b et w een t w o p oin ts (m)
* ?p : Difference in parallax (mm)
1
Page 2


GA TE CE 2026 F orm ula Sheet: Geomatics Engineering - Pho-
togrammetry
1. Photogrammetry Basics
• Scale of v ertical photograph:
S =
f
H-h
where:
– S : Scale of photograph (dimensionless)
– f : F o cal length of camera (m)
– H : Flying heigh t ab o v e datum (m)
– h : Elev ation of terrain ab o v e datum (m)
• Ground distance:
D
g
=
D
p
S
where:
– D
g
: Ground distance (m)
– D
p
: Photo distance (m)
• Area on ground:
A
g
=S
2
·A
p
where:
2. Stereoscopic P arallax
– P arallax equation:
p =x
l
-x
r
where:
* p : P arallax (mm)
* x
l
: x-co ordinate on left photo (mm)
* x
r
: x-co ordinate on righ t photo (mm)
– Heigh t of ob ject using parallax:
h =H-
fB
p
where:
* h : Heigh t of ob ject ab o v e datum (m)
* B : Air base (distance b et w een camera stations, m)
– P arallax difference for heigh t difference:
?h =
?p·f ·H
B(p+?p)
where:
* ?h : Heigh t difference b et w een t w o p oin ts (m)
* ?p : Difference in parallax (mm)
1
3. Photo Co ordinates and Relief Displacemen t
– Relief displacemen t:
d =
h·r
H
where:
* d : Relief displac emen t (mm)
* r : Radial dis tance from principal p oin t on photo (mm)
– Corrected photo co ordinate for relief:
x
c
=x-
h·x
H
, y
c
=y-
h·y
H
where:
* x
c
, y
c
: Corrected photo co ordinates (mm)
* x , y : Measured photo co ordinates (mm)
4. Ov erlap and Co v erage
– Longitudinal o v erlap:
O
l
=
(
1-
B
S·L
p
)
×100
where:
* O
l
: Longitudinal o v erlap (%)
* L
p
: Length of photo in fligh t direction (m)
– Lateral o v erlap:
O
s
=
(
1-
W
S·W
p
)
×100
where:
* O
s
: Lateral o v erlap (%)
* W : Distance b et w een adjacen t fligh t lines (m)
* W
p
: Width of photo p erp endicular to fligh t direction (m)
– Ground co v erage of a single photo:
A
g
=
L
p
·W
p
S
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5. Tilt and Crab Correction
– Tilt correction for displacemen t:
d
t
=
t·r
2
f
where:
* d
t
: Displacemen t due to tilt (mm)
* t : Tilt angle (radians)
* r : Radial dis tance from iso cen ter (mm)
– Crab angle effect:
?x =r·sinc
where:
* ?x : Lateral displacemen t due to crab (mm)
* c : Crab angle (degrees)
2