PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
May 2014
395
Dr. Abdullah:
In order to understand the subject of accuracy
analysis one needs to be familiar with few basic statistical
terms. Without understanding these basic and simple terms,
individuals who are involved in maps accuracy analysis will
remain confused and sometime helpless. On a high level, the
subject of statistics which is a branch of mathematics that
can be defined as the science that deals with the collection,
tabulation, analysis, and interpretation of measured
quantities. Isn’t this exactly the process that we, the mapping
community deal with everyday before we deliver ortho photo
or Lidar data to our clients? Since the answer is yes, then
we need to understand a few fundamental terms in statistics
that would make our live much easier. The terms I am
referring to are:
• Sample
• Population
• Accuracy
• Precision
•Mean or average
• Standard deviation
• Root mean squares error
In the following sections, I will provide
a high level and simple explanation
for each of these terms, followed
by numerical example on how to
compute each of the last three of
these terms. Throughout the following
discussions, the term “observation” or
I am ever confused with the subject of
calculating statistics for accuracy evalua-
tion. I am a project director who needs to
understand the process. Is there a simple
way for me to understand how to compute
and evaluate products accuracy accord-
ing to the ASPRS map accuracy standard?
Anonymous
“measurement” means a reading of X, Y, or Z taken by an
operator during the process of accuracy verification for
ortho photo or Lidar dataset.
Population and Sample:
Practically, we cannot afford
to test the accuracy of all the items in our deliverables
whether it is ortho photo tiles or Lidar LAS files.
Therefore, we select a representative set of tiles or
“
sample”
to represent all of the tiles or the “
population”
.
We then test the accuracy of the sample for the purpose
of estimating the accuracy of all tiles (population). I hope
this clarifies the terms “sample” and “population”.
Accuracy
: Accuracy is the closeness or nearness of the
measurement (in X, Y, and Z) to the true values of the
quantity (X, Y, or Z) being measured. In our mapping
business, the surveyed ground controls come as close as
it can be to the true values for the coordinates. However,
we can say, the true value of the coordinates is not
measurable and cannot be reached due to the inherited
errors in any measurement technique. Therefore, although
we consider the surveyed coordinates as the “truth”, one
needs to understand that such surveyed coordinates have
errors inherent in them during surveying and therefore
they are not the true values of the coordinates.
Precision
: The term precision (or repeatability) refers to
the closeness with which the measurements agree with one
another. When we evaluate the relative accuracy of Lidar
data points, from one point to another, within a tile or a
swath, we in essence are evaluating the precision of the
Lidar system. Precise set of data does not necessarily mean
accurate, on the other hand, an accurate dataset is not
necessarily precise as it is illustrated in Figure 1.
Figure 1 Accuracy and Precision
