|Scale & Area Measurement
Scale is the ratio of a
distance on an aerial photograph to that same distance on the ground in
the real world. It can be expressed in unit equivalents like 1 inch =
1,000 feet (or 12,000 inches) or as a dimensionless representative
fraction (1/12,000) or as a dimensionless ratio (1:12,000).
This is an extremely important
concept to internalize; scale determines what you can see, the accuracy
of your estimates and how certain features will appear. With experience
you will understand the differences between 1:5,000 aerial photography
and 1:10,000 scale photography. When conducting an analysis that is
based on air photos it will sometimes be necessary to make estimates
regarding the numbers of objects, the area covered by a certain amount
of material or it may be possible to identify certain features based on
their length. To use this dimension of air photo interpretation it will
be necessary for you to be able to make estimates of lengths and areas
which requires knowing the photo's scale. Sometimes this is printed on
the photo, but you should never trust it, and sometimes it is unknown.
This module is designed to give you the basics necessary to determine
photo scale and make estimates of length and area.
The diagram below illustrates
some important concepts about the geometry of the flat surface that
apply to the calculation of scale and area from air photos. The first
thing to notice is that the distance from D to E and A to B are
proportional to the ratio of the focal length (f) to the height above
the ground (H). This allows for the calculation of proportional lengths
because the angles formed on either side of the lens, labeled point C
on the diagram, are identical. Also note that the center point of the
image (the Principal Point, PP) and the actual center point on the
ground (Nadir) fall along the optical axis of the camera in this
Knowledge of the camera
focal length and the aircraft altitude makes it possible to determine
photo scale (PS) and the representative fraction (RF) of a photo.
The photo scale and
representative fraction may be calculated as follows:
PS = f / H
Variables: PS - Photo
Scale, f - camera focal length, H - altitude above the ground
Photo Scale is equal to camera
focal length divided by the Height (altitude) of the plane.
RF = 1/(H / f)
Variables: RF -
Representative Fraction, f - camera focal length, H - altitude above
the ground Representative Fraction (RF) is equal to one divided by
the ratio of altitude (H) and camera focal length.
While the foregoing method of
deriving photo scale is theoretically sound, it often happens that
either camera focal length or altitude above the ground are unknown. In
such cases, scales may be determined by the ratio of photo distance
between two points to map distance (MD) using the map scale (MS) or
ground distance (GD) between the two points.
PS = PD / GD
Variables: PS - Photo
Scale, PD - Photo Distance, GD - Ground Distance
PD and GD are different due to
the source the measurement is referring to. Ground Distance (GD) and
Map Distance (MD) are used to differentiate a measurement you make from
the map source and a real world distance that you calculate from map
scale, measure using the map's scale bar or measure yourself with a
measuring tape in the field. When calculating scale, PD (Photo
Distance) and GD (the real world Ground Distance) must be in the
same units in order to yield a unitless Representative Fraction
(RF); the Map Scale Reciprocal (MSR) and the Photo Scale Reciprocal
(PSR) are both unitless.
RF = 1 / [(MD*MSR)/PD)]
or RF = 1 / [(PD*PSR)/MD)]
Variables: MD = Map
Distance, MSR = Map Scale Reciprocal, PSR - Photo Scale Reciprocal, PD
- Photo Distance
In applying this technique,
the two points selected should be diametrically opposed in such a way
that a line connecting them passes near the principal point (PP). If
the points are approximately equidistant from the PP, the effect of
photographic tilt upon the scale measurement will be minimized.
Features selected must also be chosen for easy recognition and
measurement. Flat terrain is preferred; hilly terrain should be avoided
to minimize the effects of relief
displacement. The significance of the principle point and the
nadir, as well as relief displacement, will be discussed later with
regard to the geometry of air photos. For the concepts introduced in
this module it is necessary to focus on the basics.
Ground distance can be
measured with surveying equipment, it may be known in advance, it can
be calculated by multiplying the measured distance on a map by the map
scale, or it can be approximated using the map's scale bar. If the path
or road you wish to measure curves you can use a piece of string or a
ruler to measure the length; lay the piece of string on the road
segment, and then straighten it out and measure how long it is.
Look at the portion of the
USGS Quadrangle below. The scale bar at the bottom can be used to
measure a map distance (MD). The corresponding distance on the photo
you measure with a ruler. Your MD and PD measurements need to be in the
same units (m, ft, in or cm) for the calculations.
The part of the scanned map
that shows our area of interest has been rescaled slightly from the
original source map. Use the scale bar and the edge of a piece of paper
to measure off the lengths of road segments you can locate on the map
and the photo. Using the scale bar segments labeled with feet, measure
the distance of a road, this will be MD. Now find that same road
segment on the photo and measure it with a ruler in inches, this will
be PD. Remember that MD and PD have to be in the same units, so you
have to convert one of the measurements before doing the calculation so
the units cancel or the resulting fraction is unitless.
1. Scale ratio is
also referred to as the proportional scale. 1:20,000 is read as "one to
twenty thousand". The scale ratio is always written as one unit on the
photo or map to the corresponding number of units on the ground.
2. Representative fraction
scale (RF): Two other terms refer to the representative fraction scale
- the fractional scale and the RF scale which is the scale ratio
written in fractional form, 1/20,000.
3. Equivalent scale:
Equivalent scale is also known as the descriptive scale. For
example: one inch equals 5,280 feet (1 inch = 5,280 feet); two inches
equals one mile (2 inches = 1 mile); and 100 feet per inch.
4. Graphic scale: Also
called a bar scale, used on maps and drawings to represent length scale
on paper with length units.
Fractions and Equivalent Scales
This chart lists some
common representative fractions and the equivalent scales in words. The
unit conversions involved are important to be able to calculate
yourself, this chart provides some examples.
Distance Unit conversions are
important to understand, it is not necessary to memorize all of them
but you should be aware of the more common ones. Also, it is important
to get a grasp of the magnitude of some units relative to other units;
if you're converting from feet to meters, should the resulting
number be bigger or smaller? If you are not familiar with unit
conversions, or you are calculator dependent, you may need some
practice setting up the calculations so that the units cancel.
units and transformations
1 meter =
100 centimeters = 1,000 millimeters
1 foot = 12 inches, 1 yard
= 3 feet, 1 meter = 3.28 feet
meter = 10.76 square feet , 1 acre = 43,560 square feet, 1 square
kilometer = 230.4 acres
If one inch on
the photo is equivalent to 1,000 feet on the ground (or 12,000 inches)
: RF = 1/12,000; MS = 1/12,000; MSR = 12,000 and the map scale
denominator is also equal to 12,000, different words for the same
thing! The 12,000 part is what is important, that is the real
world distance per unit distance on the photo or map, it doesn't have
to be inches, it can be millimeters or centimeters or whatever. The
important part to remember is that both terms are inches, or whatever
unit you choose, so the resulting fraction is unitless.
The important thing to
keep in mind, once you have mastered measuring distances, is that areas
have squared units. For a rectangular area its length x width, so if
you measure both and convert these distances remember that if you are
multiplying them together the resulting units are squared.
For example, if an area is 100
meters by 500 meters, it is 50,000 square meters. Now if you wanted to
change that number to square feet its not x 3.28, its x 10.76
(3.28x3.28), there are 3.28 feet per meter. Also, it helps to think it
though; if you're converting from square meters to square feet should
the resulting number be bigger or smaller? Knowing units and distances
will help you learn how to arrange the calculations and to recognize
The precision of a measurement
is dependent upon; your ability to determine photo scale, the precision
of the conversion factors, the precision of the measuring device (e.g.
using a standard 12 inch ruler or a millimeter scaled ruler) and the
accuracy with which you can determine the edges of a feature or area.
Athletic fields have
standard dimensions, you can use these lengths to calculate photo scale.
Techniques for area measurements:
Line intercept or
transect method of canopy estimation is analogous to the dot grid
method and is similarly accurate. In this method lines are superimposed
on the aerial image and the length of each line that overlays tree
canopy is compared to the total line length. Canopy cover is then
calculated as: % canopy cover = 100 x (length of lines covered by
trees/total length of lines in sample)
3) Dot Grids
Lines may be printed on a
transparent sheet or can be designated by randomly dropping a clear
scale on the photo. If streets or other features are arranged in
parallel lines, sampling bias is best avoided by using a random
arrangement of lines rather than parallel lines on the sampling
overlay. Accuracy is improved by using more short lines rather than a
few long lines.
Dot grid area
estimations involve laying a transparent grid over an area of interest
and counting the grid cells or dots that fall within that area. This is
a quick and easy way to estimate areas, or to estimate the density of
objects, and is relatively easy to understand. Each dot or grid cell is
proportional to an area according to the scale of the source image,
summing the number of dots or grid cells and multiplying by the scale
conversion allows you to estimate areas quickly.
Dot grid method of canopy
This is an easy, accurate, and
relatively rapid method for determining canopy cover, and is equally
applicable to natural woodlands and planted urban forests. A dot grid
is a sheet of transparent material imprinted with dots arranged in a
regular grid. Dot grids can be purchased from forestry suppliers or
developed with graphics software and printed onto transparency
material. The canopy cover estimate is made by laying the dot grid over
the area of the aerial photo to be sampled and counting the number of
dots that fall on tree crowns. Percent crown cover can then be
calculated as: % canopy cover =
100 x (dots falling on trees/total number of dots within sampled area).
Sampling bias may be a problem
if a regular dot grid is superimposed on a photo with features that
repeat in a regular pattern, such as rectangular city blocks in which
case make sure that the dot grid is always skewed relative to the
street grid to minimize sampling bias.
Sample size. How many dots do
you need to count? Unfortunately, there is no single answer to this
question, but you can calculate the minimum sample size of dots
required for a given application if you have some basic information
about the population of interest. Several basic principals apply when
determining the necessary sample size. The reliability of the canopy cover estimate will increase
as the dot density increases, but the increase in statistical power
begins to plateau at high sample sizes.
The graphic on the left below
is an example of the dot grid overlay method. All of the necessary
information is given. Remember that these are area units so they are
squared, and that the scale given is a linear scale (not are area
scale). On the right is a standard dot grid. Note that if this dot grid
is printed that the darker lines are intended to be one inch apart, you
will need to resize this graphic if you are going to print it on
1:20,000, each square
contains 25 dots and is 1 cm on a side. How big is this lake?
Dot Grid. Scale a grid
cell relative to the photo being measured (real world area) and divide
by 4 (how much area each dot represents)
The four diagrams below
illustrate different methods for estimating area. The scale is fixed
for each diagram (1 km). Each of these methods has tradeoffs between
precision and accuracy, but all are valid methods of estimating areas.
The two diagrams below
illustrate the transect method of estimating area. This method is
comparable to the line intercept or transect method described above
with regard to tree canopies.
Step 1 - With a piece of
lined paper, mark equal spaced lines on the edge of the photo
Step 2 - Count the number of
spaces on the notebook paper that falls within the area being measured.
Stereoplotters and GIS
With the techniques
described above it will be possible to make estimates of areas and
lengths. This can be useful when interpreting air photos because
sometimes relative sizes, and differences in areas, can lend support to
an interpretation. When exacting measurements are required however dot
grids and scaled measurements need an additional level of correction.
The devices for performing this correction are called "stereoplotters".
There are two types, analog
and digital. Analog stereo plotters require specialized knowledge and
calibration but yield extremely accurate measurements when used
correctly in conjunction with enough geometric control. The second type
of device is called an "analytical stereoplotter" and is digital. The
main benefit of these devices is that they are usable by trained
individuals and are very reliable when maintained properly.
Systems (GIS) as well as most image processing software packages, have
image registration capabilities that have replaced manual area
estimation techniques. But not in all cases is GIS feasible or
practical, and if you lack sufficient ground control points in order to
georectify the imagery the additional cost of doing so may not afford
enough accuracy so as to be cost effective.
Image registration will be
covered in another module, but suffice it to say that the manual
techniques discussed so far will provide reasonably accurate
inexpensive estimates of area and length.