**Photogrammetry Project 01**

**Andrew Davidhazy**

**Imaging and Photographic Technology**

**School of Photographic Arts and Sciences /
RIT**

This is a project suggested to test whether
one can make a
good estimate of the size of an object following the principles
associated with
"radial displacement" as generally associated with aerial photography.
The
objective here is to replicate the procedure on a terrestrial basis.

What is needed for this project:

- A camera (film or digital)
- A length of black tape about 1 –
4 feet long
- A tripod that will hold the
camera steady
- A level

You will need to identify a location where
there is an
"inside" corner on a building or room. The
diagram below should give you a visual illustration of
what the
location might look like. Click on the image to see a larger graphic in
a new window.

To
set up for this
project proceed as follows:

- Attach a piece of tape 1-4 feet
long to the corner of a room and about 4-5 feet off the floor. Make
sure the tape is level and parallel to the floor
- 2. Placing the camera on the tripod
adjust its position so that it is at a distance such that with the back
of the camera parallel to the wall in front of it and perpendicular the one
to your side, the camera's field of view includes the full length of the black
tape attached to this "side" wall. Probably something like 20 feet will work.
Also, using the level, make sure the camera is not tilted up or down.
- While looking through the
viewfinder have a buddy place a small mark or piece of tape on the wall
in front of the camera so that it appears to be exactly in the middle
of the viewfinder.
- Measure the distance from the
corner of the walls to the small mark you just placed on the wall. This
should be the same as the distance from the wall to your side to your
camera’s lens. Also, the distance from the floor to the mark and the
floor to the center of the camera lens should also match.

At this point
notice that the
optical axis of the lens will be at right angles to the wall in front
and the
piece of black tape will appear somewhere to the right of the
viewfinder and
you should be able to see the corner of the room as well as the part of
the
black tape nearest the camera.

Make a
photograph with the camera
lens set to infinity focus and use the smallest aperture you have
available.
You will be depending on the Depth of Field of the lens to ensure that
all
objects of interest are reproduced sharply.

Before or after
making the
photograph make a measurement of the distance between the center of the
camera's lens and the wall in front of it in any units you wish. Feet
or
meters. Record this as distance **A**.

While you are
at it you should
also make a measurement of the length of the tape you attached to the
wall.
Keep a record of this as this will allow you to check later how close
you came
to determining the length of the tape photogrammetrically.

Make a
photograph of the scene. If
the tape you placed on the wall was somewhat higher on the wall than
your
camera then the view in the viewfinder and on a print made from the
negative or
a digital file would look somewhat like the illustration below (without
the
diagonal lines). Click on the image to see a larger graphic in a new
window.

Now draw the
diagonal lines
extending from one corner to the other on the print. The print now will
start
to look like the sample drawing shown above.

If you had
everything aligned
properly before you made the photograph you will notice that the
diagonal lines
will cross over or very close to where the mark was placed on the wall
by your
buddy. In aerial photography terms the "nadir", or point on the ground
below
the airplane and leading to the center of the earth, is located where
the
optical center or principal point of the photograph is determined to be
by the
crossing diagonal lines.

Now, on the
print using any
convenient measurement tool, measure the distance in mm, inches or
other units,
from the black mark on the wall or the intersection of the diagonal
lines (they
should be close to the same location), to
the farthest point of the black tape that you attached
to the
wall. Make a record of this
distance and call it **R**.

Then, using the
same units as
above, measure the length of the image of the black tape on the print.
Make a
record of it and call it **B**.

To determine
the length of the
tape from the measurements you have just made you simply multiply **B** times **A**
and divide by **R. **

Note that this
process is
completely independent of how big or small the print that you make is.
It is
also independent of lens focal length. All that matters is the "radial
displacement"!

In this
example, we will assume
the camera was 20 feet from the wall in front or 20 feet from the base
of the
length of tape attached to the side wall. If you print out the larger
version of the illustration above (click on it to get larger version)
you will note that on the print, the distance from the
center of the photograph to the farthest point of the tape measured
away from
the center of the photograph is 43 mm. The length of the image of the
piece of
tape measures about 13 mm.

Therefore the
length of tape in
reality (as measured from this image) is 13 mm x 20
feet / 43 mm
or .302 x 20 feet or 6.05 feet which
is about 72.6 inches.

How long was
the piece of tape
actually on the wall? Let's say 5 feet 8 inches or 68 inches. The
discrepancy
therefore is 72.6 - 68 or 4.6 inches out of 68 inches or about 6.7%. If
you asked
passersby to estimate the length of the tape just by looking at the
scene how
close can they do this on the average?

**Points to
ponder:**

1. How much of
an error in tape length would be introduced by a 1 mm error

in measurement?

2. Why is this
method independent
of lens focal length?

3. Why is this
method independent
of print magnification?

4. Can the
subject be tilted and one still end up with
a good measurement?

Why or why not?

5. Under what
conditions will this
method yield the most and least accuracy?

6. How far off the "nadir" point can the camera point
and still make reasonably

accurate measurements (difficult question!