SUR 340 Photogrammetry

SUR 340 Photogrammetry

Parallax

1. The following measurements were made on four different sets of adjacent left

and right photographs:

5. The distance between two ground control points A and B is XXXXXXXXXXmeters. The

elevation of A is 208.9 meters. Parallax measurements in two adjacent photographs

containing image points a and b of the ground control points A and B are pa = 72.21

mm and pb = 74.16 mm. The coordinates of a and b in the left photo are xa = 48.28

mm and ya = 50.60 mm; xb = 67.66 mm and yb = XXXXXXXXXXmm. The focal length of the

camera is XXXXXXXXXXmm. Compute the length of the ai

ase, the flying height and the

elevation of point B.

SUR 340 Photogrammetry

SUR 340 Photogrammetry

Parallax Calculations

1. Ground Point A is imaged in two overlapping photographs as image point ( a ). The x

coordinate of Point A in the left photograph is 1.040 inches and the x’ coordinate in the

ight photograph is XXXXXXXXXXCompute the stereographic parallax of image point ( a).

inchesxxP XXXXXXXXXX' =−−=−=

2. Two overlapping photographs are set up for parallax measurement. The distance

etween the principal points ( D ) is 263.4 mm. The distance between image point ( a ) in

the left and right photos is 172.5 mm. Compute the stereographic parallax of image point

( a ).

mmdDP a XXXXXXXXXX =−=−=

3. A pair of overlapping vertical photographs was taken from a flying height of 1233 m

above sea level with a 152.4 mm focal length camera. The air base was 390 meters.

Flight light coordinates are measured as xa = 53.4 mm; ya =50.8 mm; x’a = -38.3 mm; y’a

= 50.9 mm; xb = 88.9 mm; yb = -46.7; x’b = -7.1 mm; and y’b = -46.7 mm. Calculate the

elevations of point A and B and the horizontal length of line AB.

mmp

mmp

a

XXXXXXXXXX

XXXXXXXXXX

=−−=

=−−=

levelseaabovem

p

BfHh

levelseaabovem

p

BfHh

B

a

A

614

0.96

XXXXXXXXXX

585

7.91

XXXXXXXXXX

=

∗

−=−=

=

∗

−=−=

m

p

yBYm

p

xBX

m

p

yBYm

p

xBX

B

B

a

a

A

a

a

A

190

0.96

7.46390;361

0.96

9.88390

216

7.91

8.50390;227

7.91

4.53390

−=

−

∗===∗==

=∗===∗==

XXXXXXXXXXmAB XXXXXXXXXX =−−+−=

SUR 340 Photogrammetry

SUR 340 Photogrammetry

Parallax Calculations 2

4. An overlapping pair of vertical photos was exposed with a 152.4 mm focal length

camera from a flying height of 5.320 feet above datum. Control point C has an elevation

of 865 feet above datum and the parallax of its images on the stereopair is 86.27 mm.

Calculate the air base.

XXXXXXXXXXfeet

f

phHB 522,2

4.152

XXXXXXXXXX

=

−

=−=

5. Images of the end points of ground line AB of length 2,131.1 feet appear on a pair of

overlapping photographs. Photocoordinates measured on the left photo were xa=33.29

mm; ya = 13.46 mm; xb = 41.76 mm; and yb = XXXXXXXXXXmm. Photocoordinates measured

on the right photo were: x’a = XXXXXXXXXXmm and x’b = XXXXXXXXXXmm. Calculate the ai

ase for

this stereopair.

( )

( ) mmxxp

mmxxp

aaa

XXXXXXXXXX

XXXXXXXXXX

'

'

=−−=−=

=−−=−=

2

1

22

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

a

a

a

a

p

y

p

y

p

x

p

x

ABB

feetB 1687

61.85

46.13

72.86

76.95

61.85

29.33

72.85

76.41

1.2131

2

1

22

=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛ −

−

+⎟

⎠

⎞

⎜

⎝

⎛ −

=

6. The parallax of image point ( a ) and ( c ) were measured in two overlapping vertical

photographs as 91.67 mm and 92.60 mm respectively. The elevation of Point C is known

to be 1, 938 feet above sea level. The flying height of the photographs is known to be

4,045 feet above sea level. Compute the elevation of Point C.

mmppp cb XXXXXXXXXX −=−=−=Δ

XXXXXXXXXXlevelseaabovefeet

p

hHp

hh

a

C

CA 917,167.91

XXXXXXXXXX =−−+=

−Δ

+=

SUR 340 Photogrammetry

Parallax

1. The following measurements were made on four different sets of adjacent left

and right photographs:

5. The distance between two ground control points A and B is XXXXXXXXXXmeters. The

elevation of A is 208.9 meters. Parallax measurements in two adjacent photographs

containing image points a and b of the ground control points A and B are pa = 72.21

mm and pb = 74.16 mm. The coordinates of a and b in the left photo are xa = 48.28

mm and ya = 50.60 mm; xb = 67.66 mm and yb = XXXXXXXXXXmm. The focal length of the

camera is XXXXXXXXXXmm. Compute the length of the ai

ase, the flying height and the

elevation of point B.

SUR 340 Photogrammetry

SUR 340 Photogrammetry

Parallax Calculations

1. Ground Point A is imaged in two overlapping photographs as image point ( a ). The x

coordinate of Point A in the left photograph is 1.040 inches and the x’ coordinate in the

ight photograph is XXXXXXXXXXCompute the stereographic parallax of image point ( a).

inchesxxP XXXXXXXXXX' =−−=−=

2. Two overlapping photographs are set up for parallax measurement. The distance

etween the principal points ( D ) is 263.4 mm. The distance between image point ( a ) in

the left and right photos is 172.5 mm. Compute the stereographic parallax of image point

( a ).

mmdDP a XXXXXXXXXX =−=−=

3. A pair of overlapping vertical photographs was taken from a flying height of 1233 m

above sea level with a 152.4 mm focal length camera. The air base was 390 meters.

Flight light coordinates are measured as xa = 53.4 mm; ya =50.8 mm; x’a = -38.3 mm; y’a

= 50.9 mm; xb = 88.9 mm; yb = -46.7; x’b = -7.1 mm; and y’b = -46.7 mm. Calculate the

elevations of point A and B and the horizontal length of line AB.

mmp

mmp

a

XXXXXXXXXX

XXXXXXXXXX

=−−=

=−−=

levelseaabovem

p

BfHh

levelseaabovem

p

BfHh

B

a

A

614

0.96

XXXXXXXXXX

585

7.91

XXXXXXXXXX

=

∗

−=−=

=

∗

−=−=

m

p

yBYm

p

xBX

m

p

yBYm

p

xBX

B

B

a

a

A

a

a

A

190

0.96

7.46390;361

0.96

9.88390

216

7.91

8.50390;227

7.91

4.53390

−=

−

∗===∗==

=∗===∗==

XXXXXXXXXXmAB XXXXXXXXXX =−−+−=

SUR 340 Photogrammetry

SUR 340 Photogrammetry

Parallax Calculations 2

4. An overlapping pair of vertical photos was exposed with a 152.4 mm focal length

camera from a flying height of 5.320 feet above datum. Control point C has an elevation

of 865 feet above datum and the parallax of its images on the stereopair is 86.27 mm.

Calculate the air base.

XXXXXXXXXXfeet

f

phHB 522,2

4.152

XXXXXXXXXX

=

−

=−=

5. Images of the end points of ground line AB of length 2,131.1 feet appear on a pair of

overlapping photographs. Photocoordinates measured on the left photo were xa=33.29

mm; ya = 13.46 mm; xb = 41.76 mm; and yb = XXXXXXXXXXmm. Photocoordinates measured

on the right photo were: x’a = XXXXXXXXXXmm and x’b = XXXXXXXXXXmm. Calculate the ai

ase for

this stereopair.

( )

( ) mmxxp

mmxxp

aaa

XXXXXXXXXX

XXXXXXXXXX

'

'

=−−=−=

=−−=−=

2

1

22

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

a

a

a

a

p

y

p

y

p

x

p

x

ABB

feetB 1687

61.85

46.13

72.86

76.95

61.85

29.33

72.85

76.41

1.2131

2

1

22

=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛ −

−

+⎟

⎠

⎞

⎜

⎝

⎛ −

=

6. The parallax of image point ( a ) and ( c ) were measured in two overlapping vertical

photographs as 91.67 mm and 92.60 mm respectively. The elevation of Point C is known

to be 1, 938 feet above sea level. The flying height of the photographs is known to be

4,045 feet above sea level. Compute the elevation of Point C.

mmppp cb XXXXXXXXXX −=−=−=Δ

XXXXXXXXXXlevelseaabovefeet

p

hHp

hh

a

C

CA 917,167.91

XXXXXXXXXX =−−+=

−Δ

+=

Answered Same DayNov 26, 2021

SOLUTIONS

1a)Calculate the parallax for each point

Parallox

P = x − x'

Point X(left photo) X’ (right photo) Parallax, P

a 2.36 inches -1.07 inches 2.360 − (−1.07) = 3.43 inches

68.05 mm -21.61 mm 68.05 − (−21.61) = 89.66 mm =

3.53 inches

c 3.92 inches 0.39 inches 3.92 − (0.39) = 3.57 inches

d 100.37 mm 8.52 mm 100.37 − (8.52) = 91.85 mm =

3.616 inches

1b) Elevaion is given by the formula

?? = ? −

??

??

Where

H is the flying height

hA is the elevation of the given point

pa is the parallax

B is Length of Air Base

f is the focal length

The values of ‘H’, ‘B’ and ‘f’ being same for all the points, lesser the value

of (Bf)/p , higher is the value of elevation.

Again higher the value of pa , lesser is the value of (Bf)/p

Hence, the value of elevation ‘h’ will be the highest for the largest value of

parallax p.

Point‘d’ with largest value of parallax will have the highest elevation.

Point ‘a’ with the least value of parallax will have the lowest elevation.

2. Given focal length, f = 6 inches

Flying height above datum, H = 8100 feet

Ai

ase, B = 4450 feet

Elevations of points A, B, C and D respectively are hA, hB, hC and hD

h

A = H −

Bf

=...

1a)Calculate the parallax for each point

Parallox

P = x − x'

Point X(left photo) X’ (right photo) Parallax, P

a 2.36 inches -1.07 inches 2.360 − (−1.07) = 3.43 inches

68.05 mm -21.61 mm 68.05 − (−21.61) = 89.66 mm =

3.53 inches

c 3.92 inches 0.39 inches 3.92 − (0.39) = 3.57 inches

d 100.37 mm 8.52 mm 100.37 − (8.52) = 91.85 mm =

3.616 inches

1b) Elevaion is given by the formula

?? = ? −

??

??

Where

H is the flying height

hA is the elevation of the given point

pa is the parallax

B is Length of Air Base

f is the focal length

The values of ‘H’, ‘B’ and ‘f’ being same for all the points, lesser the value

of (Bf)/p , higher is the value of elevation.

Again higher the value of pa , lesser is the value of (Bf)/p

Hence, the value of elevation ‘h’ will be the highest for the largest value of

parallax p.

Point‘d’ with largest value of parallax will have the highest elevation.

Point ‘a’ with the least value of parallax will have the lowest elevation.

2. Given focal length, f = 6 inches

Flying height above datum, H = 8100 feet

Ai

ase, B = 4450 feet

Elevations of points A, B, C and D respectively are hA, hB, hC and hD

h

A = H −

Bf

=...

SOLUTION.PDF## Answer To This Question Is Available To Download

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