Vertical aerial photographs

Vertical Aerial Photographs


Focal LengthDistance from the focal plane to approximately the center of the camera lens.

FOR 220 Aerial Photo Interpretation and Forest Measurements


Focal LengthAngle of coverage increases as the focal length decreases

Focallength

Focalplane

Lens

Angle of coverage

Ground

Focallength

Focalplane

Lens

Angle of coverage

Ground



Fiducial marks• Optically projected geometric figures located at either the four corners of a photograph, or on the four sides of a photograph.

• They define the coordinate axes and geometric center of a single aerial photograph.

• The x-axis most nearly defines the direction of flight.

• The y-axis most nearly defines the flight line.

• The intersection of the fiducial marks represents the “principal point” of the photograph.



The three photo centersFiducial marks find the geometric center of a given photo. Useful information for both photogrammetry and photointerpretation. However, the geometric center of a photograph is only one of 3 important center points

Different types of distortion and displacement radiate from each.Different types of exploitation or compensation are possible for each.

You will need to know all 3 photo centers and their respective properties, such as associated distortion/displacement, relative location, primary influence on photogrammetry and/or photointerpretation.



The three photo centersDifferent types of distortion and displacement radiate from each.

1

Principal point: geometric center of the photograph, and the intersection of the X and Y axes.

Lens distortion is radial from the Principal Point


Ground

PPoi

nt


The three photo centers

Nadir: The point vertically beneath the camera at the time the photograph was taken.

Topographic displacementis radial from the nadir

Usually difficult to locate on a singleaerial photograph


Ground

Nad

ir

PPoi

nt

2



Isocenter: The point that falls on a line halfway between the Principal Point and the Nadir.

Tilt displacement radiatesfrom the isocenter


Ground

Nad

irIs

ocen

ter

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nt

3



On a truly vertical aerial photograph, all three photo centers will be located in the same place. This place can be located by drawing lines between opposite fiducial marks (as when defining the Principal Point).

In lab, we are going to assume that all of our photos are truly vertical.




Distortion and Displacement


Distortion and DisplacementDistortion: The shift in position of a landscape feature on a photograph that alters the perspective characteristics of the image.

• Film and print shrinkage (negligible)• Atmospheric refraction of light rays (negligible)• Motion of the landscape feature• Lens distortion

Displacement: Any shift in the position of a landscape feature on a photograph that does not alter the perspective characteristics of the image.

• Curvature of the earth (negligible)• Tilt• Topographic relief



Distortion and Displacement: Lens Distortion

• Radiates from the Principal Point.

• Causes landscape features to appear either further away, or closer to, the Principal Point than they really are.

• Most serious near the edges of a photograph.

• Can be calculated by calibrating the lens, and developing a “distortion curve” for the lens.



Distortion and Displacement: Tilt Displacement

• Radiates from the isocenter of a photograph.

• Caused by the aircraft not being perfectly horizontal at the time of exposure of the film.

• If the amount of tilt is known, photographs can be rectified (expensive).

• If we can determine the direction of the tilt, in terms of “upper side” of the tilt and the “lower side" of the tilt, we can determine how landscape features are being displaced.




Ground

Nad

irIs

ocen

ter

PPoi

ntX-axis tilt:wings up or down

Ground

Nad

irIs

ocen

ter

PPoi

nt

Y-axis tilt:Nose up or down




Ground

Nad

irIs

ocen

ter

PPoi

ntPhoto


Conceptual model



Ground

Nad

irIs

ocen

ter

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ntPhoto


Let’s look closer at conceptual displacement

Next slide…..



Some landscape feature(a’) is being displayedon a photograph (pointa) that is displacedradially inward fromthe appropriate placeon the photograph (c)by the amount d.


Photo

Grounda’

a

b

c

d

Displacement


Distortion and Displacement: Topographic Displacement• Radiates from the nadir of a photograph.

• Varies directly with the height of the landscape feature.• Varies directly with the radial distance from nadir to the top of a landscape feature.• There is no displacement at nadir.• Varies inversely with the flying height above the base of the landscape features.

• We can view in 3-dimensional images because of it.

• We can use the “similar triangles” theory to arrive at an equation to allow us to calculate topographic displacement.

In the example that follows, we will assume that the nadir and the PrincipalPoint are the same (since topographic displacement is radial from the nadir,yet the nadir is often difficult to determine, and the Principal Point is not).



Distortion and Displacement: Topographic Displacement

Units in inches or mm, same scale as photo:

r = distance on the photo from the nadir to the displaced landscape feature.r’ = actual place on the photo where the landscape feature should be located.d = relief (topographic) displacement.f = focal length.

rd r’

fnegative

lens

A

H

E

H-h

hR




Units in feet or meters:

h = height of the landscape feature.A = altitude of the aircraft above sea level.E = elevation of the landscape feature.H = Flying height above the base of the landscape feature at nadir.R = distance from the nadir to the landscape feature.

rd r’

fnegative

lens

A

H

E

H-h

hR




Similar triangles:

R

rhH

f)(

hHRfr

Thus

rd r’

fnegative

lens

A

H

E

H-h

hR




Similar triangles:

Rr

Hf '

HRfr '

Thus

rd r’

fnegative

lens

A

H

E

H-h

hRR




We are usually interestedin two things:

d (object topographicdisplacementon a photograph)

h (object height)


dnegative

lens

h


Distortion and Displacement: Topographic DisplacementCalculate “d”:

'rrd

HRf

hHRfd

hHhH

HRf

HH

hHRfd

HhHhRf

HhHHRf

HhHHRfd

)()()(

HhHhRf

HhHHRf

HhHHRfd

)()()(

HhHhRfd)(

Calculate “d” (cont.):

hHRfr

Remember,

So, substituting r for the above term

Hhrd

or,

EAhrd

rdHh

rdEAh )(

Where d = displacement of landscapefeature on photo, and h = height of landscape feature



Distortion and Displacement: Topographic DisplacementExample #1: A Ridgeline

Flying height above the base of the landscape feature at nadir = H= 10,000 feet

Height of the landscape feature relative to nadir = h = 1,000 feet

Radial distance from the nadir to thelandscape feature’s location on the photo = 3.0 inches

What is the displacement on the photorelative to nadir?

Hhrd

feetfeetinchesd

000,10)1000(0.3

inchesd 3.0

If the photo scale was 1 : 12000, whatis the error on the ground?

)12000(3.0 incheserrorground incheserrorground 3600feeterrorground 300



Distortion and Displacement: Topographic DisplacementExample #2: Tree Height

Suppose we have the measured displacement of a tree, on flatground, or d = 2.1 mm.

The distance from the top of the treeto the nadir of the photograph is79.4 mm, or r = 79.4 mm.

The flying height of the aircraft, A, above sea level is 10,000 feet.

The elevation of the area, E, from a topographic map is 2,000 feet.

Nadir

A = 10,000 feetE = 2,000 feet

79.4 mm

2.1 mm




Nadir

A = 10,000 feetE = 2,000 feet

79.4 mm

2.1 mm

Example #2:

What is the height of the tree?

rdEAh )(

mmmmfeetfeeth

4.791.2)200010000(

mmmmfeeth

4.791.2)8000(

feeth 6.211


Vertical aerial photographs

Engineering

Transcript of Vertical aerial photographs