# Scale of a vertical photograph

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```					Scale of a vertical photograph

Due to perspective geometry of photographs, the scale of photograph varies as a function of
focal length, flying height, and the reduced level of terrain over a certain reference datum. In
figure 2, for a vertical photograph, L is exposure station, f is its focal length, H is the flying
height above datum, h represents the height of ground point A above datum. Point A is
imaged as a in the photograph. From the construction and using similar triangles Loa and
LOAA, we can write the following relations (Wolf and Dewitt, 2000)

Figure 2: Scale for vertical photo

havg   Average terrain elevation
Savg   Best single scale to use for a photo or group of photographs
Determination of Scale of photograph Scale of photograph can be determined by various
methods such as

1. By using known full length and altimeter reading, the datum scale can be found.
2. Any scale can be determined if havg known. havg can be obtained from a topographic
map.
3. By comparing length of the line on the photo with the corresponding ground length.
To arrive at fairly representative scale for entire photo, get several lines in different
area and the average of various scales can be adopted.
4. Use the formula

Scale along plate parallels Referring to figure 1, the scale along various plate parallels are as
follows:

1. Scale through the plate parallels passing through principal point, P with q as tilt angle

2. Scale along an isometric parallel through nadir point, V

1. Scale along an isometric parallel through isocentre I

This shows that the scale along plate parallel through isocentre of a tilted photo is same as
that over the whole surface of a vertical photo if ground surface is plane. For any other plate
parallel, scale will depend on the tilt angle. Also, the scale along any plate parallel is
constant.

Ground co-ordinates for vertical photographs In figure 3, X and Y are ground co-ordinates
with respect to a set of axes whose directions are parallel with the photographic axes and
whose origin is directly below the exposure station, x and y indicate x and y photo
coordinates with respect to the photo coordinate system with origin at o axes as shown. Using
similar triangles, we can write the following relations:
Click on the image for larger view

Figure 3: Ground coordinates from vertical photographs
Flying height for vertical photographs The flying height can be calculated by two approaches

   Direct
   Indirect

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Description: Civil Engineering Geometric Design concepts of GPS, DGPS, Photgammertery, digital image processing.