M. Mustoe
Photo Interp Quantifiers

 

Scale Determination Vertical Photomaps ONLY
A. In a map
RF = MD/GD
MD= Map Distance
GD= Ground Distance

B. On a Photograph
RF= PD/GD
PD= Photo Distance
GD= Ground Distance

TWO METHODS for determining scale:
A. Comparison Method
B. Flight Altitude Method.

Students should be aware of marginal information on the magazine.

A. Comparison Method:
Scale RF = Photo Distance/Ground Distance

Ground Distance is derived by existing ground truth
or
Ground Distance is derived by comparison of two points on a map

Use the mid point of the photo as much as possible

Units stay the same on each equation:

Example:
Photo Distance: 4 cm
Ground Distance: 2 Km

4cm / 2km X 100,000 (cm in 1 km) = 4/200,000 = 1/50,000 or 1:50000

B. Focal Length Flight Altitude Method

Step 1 Read marginal information on the photo
RF = f/H
RF = f= Focal Length of the Camera/H flight altitude (height of camera lens above mean or average sea level

Example:
f=6 inches or 15.24 cm
H= 10,000 Feet or 3,048 meters

15.2/3048 X 100 (cm in a meter) = 15.2/304,800 = 1/20,000 1:20,000

NOTE If the aircraft is flying over uneven terrain:
RF SCALE = f Focal length / H flight altitude - h average ground elevation

Example:
f = 6'' or 15.2 cm H = 10,000' or 3048 m h= 850' or 259.08 m

15.2 cm / (3,048-259.08) X 100 (cm in a meter) = 15.2/278,900 =
1/18,300 or 1:18,300

And In Addition...the
Proportional Method
AB = the MD

In this method you are taking the line from the map and setting it up in a proportion.
AB= a linear distance on the map with the known RF.
A'B" is the same distance measured on the photo map.



Example

3.59 X = 1.12 (25,000)

3.59X = 28,000

X= 7799,4 or 7800

RESOLUTION

The resolution of an aerial photograph is the ability for the eye to resolve two adjacent objects on the ground. The formula is:

Rg = (Rs) (f)
     _________
            H

Rg = ground resolution , line pairs/m

Rs = system resolution line pairs /mm

f = Camera Focal Length mm

H = height of camera above ground m

If you were working with a camera at 3000 m with an f of 152mm and an Rs of 30 line pairs/mm what would ground resolution be?

152mm X Rs of 30 line pairs/mm / 3000 m =

Rg= 1.52 In other words objects no more than 1.52 ms apart could be distinguished by the eye.


Finding the Nadir or Principle Point of an Image
The nadir or Principle Point (PP) of the picture is the exact middle of the photograph and is found by intersecting two lines which have been aligned with the fiducial marks on the sides of the image.

Direct Determination of Object Heights from Air Photos

Image Displacement Method

Height of Object (HO) = d   [H]
                                     r 

Where d = the length of the displaced image on the photo

r = the radial distance form the principal point to the tope of the displaced image (same units as d)

H is the aircraft flying height above the base of the displaced object (this must be expressed in the UNITS desired for the object).

Note:
Photo must be truly vertical.
You must find the nadir or principle point of the image,,,the direct and specific middle of the image where the camera was centred on.
You must know the precise altitude of the aircraft.
Both BASE and TOP Of displaced object must be visible.
Degree of image displacement must be large enough to be precisely measured with a scale (engineers scale)

Example:

ho = 5mm (the measured size of a tree on the ground, measured from the photo) / 50 mm ( radial distance from the principle point in the photo to the top of the tree in the image) X 300 m the altitude of the aircraft.

Height of tree is 30 m.

NOTE this is an odd formula that allows you to mix units....that is the d and r in this formula .... if the d and r are in inches H and h will be in feet...and if d and r are in mm then H and d will be in meters.


Using the Shadow Method of Height Determination
Note:
Object must be perpendicular to the surface
Object's shadow must be cast from it true tip and not the side
The shadow must be clear on open ground and level with the base of the object
so it can be measured easily
The ANGLE of the sun above the horizon at the time the photo was taken must be known.

Angular Elevation of the sun is the SUN Angle ø
The tan of the ø is the object's height

Object Height (Ho) = Shadow length X tan ø

To determine sun angle take a tower or structure of a known height and measure its shadow. For example, given A tower known to be 100 m high that casts a shadow 75 m long...... Through transposition then:

tanø = 100/75 = 1.333 This number BECOMES (and is) Tanø for any applicable measurement of any vertical structure within the picture....in other words,

You may now, find the shadow of any structure on the photo..(within the parameters of the model) and multiply this by 1.333 and get the height of that object.


The angle can also be found using an emphemeris when there are no known structures structure heights.

Stereo Parallax Method
Needed, two photos (a pair) taken on the same flight line
Align the photos on the flight line

You must first Determine the average photo base length by locating the pp in each photo. One PP of the two is called (considered to be) the CPP (Corresponding Priciple point).

The numbers given are in mm

Use the following formula

Height of Object (ho) = (H)   dP
                                       P+dP

H= Height of Aircraft above the base expressed in the desired units for the onjects found height

dP =Differential Paralax

P = absolute Parallax

 

Use the diagram to see how this is done