UNIT 14 ACCURACY ASSESSMENT

Full text

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Image Classification
UNIT 14 ACCURACY ASSESSMENT
Structure
14.1 Introduction
Objectives
14.2 Concept of Accuracy Assessment
Definition
Need for Accuracy Assessment
Sources of Errors
14.3 Consideration of Sampling Size and Scheme
14.4 Calculation of Classification Accuracy
Error Matrix
Generation of Error Matrix
Interpretation of Error Matrix
Limitations
14.5 Kappa Analysis
Calculation Steps
Advantages
14.6 Summary
14.7 Unit End Questions
14.8 References
14.9 Further/Suggested Reading
14.10 Answers
14.1 INTRODUCTION
In the previous unit, you have learnt about different image classification
methods which help us to create thematic maps. We also discussed the
advantages and limitations of some of the commonly used classification
algorithms. Both supervised and unsupervised classification needs direct or
indirect information of the surface characteristics e.g., for unsupervised
classification the user must define the classes based on prior information of
surface and in case of supervised classification, it is based on training samples
from the surface. Quality and quantity of training samples, therefore, have
considerable implication on the accuracy of the classified images.
Once you have an interpreted map, the obvious step is that you would want to
know how much accurate those outputs are because inaccuracies in outputs
will have their bearing on the map’s utility and users would have greater
confidence in utilising data if its accuracy is high. Hence, assessment of
accuracy is a very important part of the interpretation as it not only tells you
about quality of maps generated or classified images but also provides you
with a benchmark to compare different interpretation and classification
methods.
In this unit, you will learn about accuracy assessment and related concepts and
methods. We will also discuss the role of sampling size for the purpose of
accuracy assessment.

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Objectives
After studying this unit, you should be able to:
•define accuracy assessment;
•discuss need for accuracy assessment;
•generate a error matrix for interpreted outputs;
•explain the role of sampling size in accuracy assessment; and
•list measures for accuracy assessment.
14.2 CONCEPT OF ACCURACY ASSESSMENT
Accuracy assessment is the final step in the analysis of remote sensing data
which help us to verify how accurate our results are. It is carried out once the
interpretation/classification has been completed. Here, we are interested in
assessing accuracy of thematic maps or classified images which is known as
thematic or classification accuracy. The accuracy is concerned with the
correspondence between class label and ‘true’ class. A ‘true’ class is defined as
what is observed on the ground during field surveys. For example, a class
labeled as water on a classified image/map is actually water on the ground.
In order to perform accuracy assessment correctly, we need to compare two
sources of information which include:
•interpreted map/classified image derived from the remote sensing data and
•reference map, high resolution images or ground truth data.
Relationship between these two sets of information is commonly expressed in
two forms, namely -
•error matrix that describes the comparison of these two sources of
information and
•Kappa coefficient which consists a multivariate measure of agreement
between rows and columns of error matrix.
The error matrix and kappa coefficient have been discussed in detail in the
sections 14.4 and 14.5, respectively. However, let us first discuss what
accuracy assessment is along with its need and sources of errors.
14.2.1 Definition
Accuracy is referred to in many different contexts. In the context of image
interpretation, accuracy assessment determines the quality of information
derived from remotely sensed data. Assessment can be either qualitative or
quantitative. In qualitative assessment, you determine if a map ‘looks right’ by
comparing what you see in the map or image with what you see on the ground.
However, quantitative assessments attempt to identify and measure remote
sensing based map errors. In such assessments, you compare map data with
ground truth data, which is assumed to be 100% correct.
Accuracy of image classification is most often reported as a percentage correct
and is represented in terms of consumer’s accuracy and producer’s accuracy.
The consumer’s accuracy (CA) is computed using the number of correctly
classified pixels to the total number of pixels assigned to a particular category.
It takes errors of commission into account by telling the consumer that, for all
Accuracy defines
correctness and it
measures the degree of
agreement between a
standard that assumed to
be correct and a map
created from an image. A
visually interpreted map or
classified image is only
said to be highly accurate,
when it corresponds
closely with the assumed
standard.

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Accuracy Assessment
areas identified as category X, a certain percentage are actually correct. The
producer’s accuracy (PA) informs the image analyst of the number of pixels
correctly classified in a particular category as a percentage of the total number
of pixels actually belonging to that category in the image. Producer’s accuracy
measures errors of omission.
14.2.2 Need for Accuracy Assessment
The need for assessing accuracy of a map generated from any remotely sensed
product has become a universal requirement and an integral part of any
classification project. The user community needs to know accuracy of the
classified image data being used. Moreover, different projects have different
accuracy requirement and only those classified images which are above a
certain level of accuracy can be used. Furthermore, accuracy becomes a
critical issue while working in a Geographical Information System (GIS)
framework where you use several layers of remotely sensed data. In such
cases, it would be very important to know the overall accuracy which is
dependent upon knowing the accuracy of each of data layers.
There are a number of reasons why assessment of accuracy is so important.
Some of them are given below:
•accuracy assessment allows self-evaluation and to learn from mistakes in
the classification process
•it provides quantitative comparison of various methods, algorithms and
analysts and
•it also ensures greater reliability of the resulting maps/spatial information
to use in decision-making process.
The need for accuracy assessment is emphasised in literature as well as in
anecdotal evidence. For example, maps of wetlands from various states of
India (e.g., Jammu and Kashmir, Rajasthan, Tamil Nadu, West Bengal) have
been made by several central, state and local agencies using techniques that
included satellite images, aerial photographs and field data. Simply comparing
the various wetland maps would yield little agreement about location, size and
extent of these. In the absence of a valid accuracy assessment you may never
know which of these maps to use.
A map using remotely sensed or other spatial data cannot be regarded as the
final product without taking necessary steps towards assessing accuracy or
validity of that map.
A number of methods exist to investigate accuracy/error in spatial data
including visual inspection, non-site-specific analysis, generating difference
images, error budget analysis and quantitative accuracy assessment.
14.2.3 Sources of Errors
Classification error occurs when a pixel (or feature) belonging to one category
is assigned to another category. Errors of omission occur when a feature is left
out of the category being evaluated. Errors of commission occur when a
feature is incorrectly included in the category being evaluated. For example,
errors of omission are the allotment of errors of barren land on the ground to
the agricultural land category on the map. This has caused the removal of an
area of real barren land on the ground from the map. In the same way, errors of
commission will be the assignment an area of agricultural land on the ground
The term consumer’s
accuracy is used when a
classified image is
examined from the user’s
point of view. Producer’s
accuracy is used when
same is viewed from
analyst’s perspective.

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to the barren land on the map. Hence, an error of omission in one category will
be counted as an error of commission in another category.
As you know that accuracy assessment is performed by comparing the map
produced by remote sensing analysis to a reference map based on a different
information source. One might ask why remote sensing analysis is needed if
the reference map for comparison already exists. One of the primary purposes
of accuracy assessment and error analysis in this case is to permit quantitative
comparisons of different interpretations. Classifications done from images
acquired at different times, classified by different procedures, or produced by
different individuals can be evaluated using a pixel-by-pixel and point-by-
point comparison. The results must be considered in the context of the
application to determine which is the most correct or most useful for a
particular purpose. In order to be compared, both the map to be evaluated, the
reference map must be accurately registered geometrically to each other. They
must have been classified using same scheme and at the same level of detail.
One simple method of comparison is to calculate the total area assigned to
each category in both maps and to compare the overall figures. This type of
assessment is called non-site-specific accuracy (Fig. 14.1a). On the other
hand, site-specific accuracy is based on a comparison of the two maps at
specific locations (i.e. individual pixels in two digital images) (Fig. 14.1b). In
this type of comparison, it is obvious that the degree to which pixels in one
image spatially align with pixels in the second image contributes to the
accuracy assessment result. It is important to note that errors in classification
should be distinguished from errors in registration or positioning of
boundaries. Another useful form of site-specific accuracy assessment is to
compare field or training data at a number of locations within the image,
similar to the way spatial accuracy assessment using ground check points is
performed for digital orthophotographs and terrain models.
Fig. 14.1: (a) Non-site-specific accuracy in which two images are compared based on
their total areas. Note that the area of image 1(i.e. A+B+C) is equal to the area
of image 2 (i.e. A+B+C) and (b) site-specific accuracy in which two images are
compared on a site-by-site (i.e. cell-by-cell or pixel by pixel) (source: modified
from Campbell, 1996)
In non-site-specific
accuracy, for example,
two images or maps can
be compared only on the
basis of total area in each
category as shown in Fig.
14.1a. In site-specific
accuracy two images are
compared on the basis of
pixel-by-pixel or cell-by-
cell as shown in Fig.
14.1b.

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Accuracy Assessment
Check Your Progress I
1) List the prerequisites for accuracy assessment.
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
14.3 CONSIDERATION OF SAMPLING SIZE AND
SCHEME
Sample size is an important consideration while assessing the accuracy of
remotely sensed data. Collection of sample size needs time and money.
Therefore, it must be kept to a minimum. Yet it is critical to maintain a large
enough sample size so that analysis performed is statistically valid. In remote
sensing literature, many researchers have published equations and guidelines
for choosing the appropriate sample size. The majority of them have used an
equation based on the binomial distribution or the normal approximation to
the binomial probability distribution to compute the required sample size.
These techniques are statistically sound for computing the sample size needed
to compute the overall accuracy of a classification or the overall accuracy of a
single category. The equations are based on the proportion of correctly
classified samples (e.g., pixels, clusters or polygons), on some allowable error.
However, these techniques were not designed to choose a sample size for
creating an error matrix. In the case of an error matrix, it is not simply a matter
of correct or incorrect. Given an error matrix with n land cover categories, for
a given category there is 1 (one) correct answer and n–1 incorrect answers.
Sufficient samples must be acquired to be able to adequately represent this
confusion. Therefore, the use of these techniques for determining the sample
size for an error matrix is not inappropriate. Instead, the use of the
multinomial probability distribution is recommended.
Traditional thinking about sampling does not often apply because of the large
number of pixels in a remotely sensed image. For example, a 0.5% sample of
a single Landsat TM scene can be over 3,00,000 pixels. Most, if not all,
assessments should not be performed on a per-pixel basis because of problems
with exact single pixel location. Practical considerations more often dictate the
sample size selection. A balance between what is statistically sound and what
is practically attainable must be found. A generally accepted rule of thumb is
to use a minimum of 50 samples for each land class (LC) category in the error
matrix. This rule also tends to agree with the results of computing sample size
using the multinomial distribution. If the area is especially large or the
classification has a large number of LC categories (i.e. more than 12
categories), the minimum number of samples should be increased to 75 to 100
samples per category.
The number of samples for each category can also be weighted based on the
relative importance of that category within the objectives of the mapping or on
the inherent variability within each of the categories. Sometimes, it is better to
concentrate the sampling on the categories of interest and increase their
Spend
5 mins
Binomial distribution
treats errors for all classes
equally, and therefore, can
only estimate the accuracy
of the map as whole.
Error matrix is the
established form for
reporting site-specific
error. It is also known as
confusion matrix.
Multinomial distribution
investigates the errors
associated with individual
classes. It is based on the
confusion matrix.

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number of samples while reducing the number of samples taken in less
important categories. Also, it may be useful to take fewer samples in
categories that show little variability such as water or forest plantations and
increase sampling in the categories that are more variable such as uneven-aged
forests or riparian areas. In summary, the goal is to balance the statistical
recommendations to obtain an adequate sample from which to generate an
appropriate error matrix within the objectives, time, cost and practical
limitations of the mapping project.
Along with sample size, sampling scheme is an important part of any accuracy
assessment. Selection of the proper scheme is absolutely critical in generating
an error matrix that is representative of the entire classified image. Poor choice
in sampling scheme can result in significant biases being introduced into the
error matrix that may over or under estimate true accuracy. In addition, the use
of proper sampling scheme may be essential depending on the analysis
techniques to be applied to the error matrix. Many researchers have expressed
opinions about proper sampling scheme to use, including everything from
simple random sampling to stratified, systematic and unaligned sampling.
Despite all these opinions, very little work has actually been performed in this
area. One of the studies carried out on sampling simulations on three
geographically diverse areas such as forest, agriculture and rangeland
concluded that in all cases simple random sampling and stratified random
sampling provided satisfactory results. Despite the desirable statistical
properties of simple random sampling, this sampling scheme is not always
very practical to apply. Simple random sampling tends to under-sample small
but possibly very important areas unless the sample size is significantly
increased. For this reason, stratified random sampling is recommended where
a minimum number of samples are selected from each stratum (i.e. category).
Even stratified random sampling can be somewhat impractical because of
having to collect ground information for the accuracy assessment at random
locations on the ground.
There are two problems which arise while using random locations:
•location can be very difficult to access and
•they can only be selected after the classification has been performed.
The second condition limits accuracy assessment data of being collected late
in the project instead of in conjunction with the training data collection,
thereby increasing costs of the project. In addition, in some projects time
between project beginning and accuracy assessment may be so long as to
cause temporal problems in collecting reference data.
14.4 CALCULATION OF CLASSIFICATION
ACCURACY
You have learnt about the theoretical concept of accuracy assessment and
sample size and scheme consideration for it. Let us now discuss about the
methods to calculate accuracy. As we have discussed in the introductory
section, accuracy is often expressed in terms of consumer’s and producer’s
accuracies which is obtained from an error matrix. Now you will read about
the error matrix, its generation and interpretation.

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Accuracy Assessment
14.4.1 Error Matrix
Once a classification exercise has been carried out, there is a need to determine the
degree of error in the end product which includes identified categories on the map.
Errors are the result of incorrect labeling of the pixels for a category. The most
commonly used method of representing the degree of accuracy of a classification is
to build a k×k array, where k represents the number of categories. For example, in
Table 14.1, the left hand side of the table is marked with the categories on the
standard (i.e. reference) map/data. The top side of same table is marked with the
same k categories but these categories represent end product of a created map to
be evaluated. The values in the matrix indicate the numbers of pixels. This
arrangement establishes a standard form which helps to find site-specific error in the
end product and is known as error matrix. Error matrix is useful for the
determination of overall errors for each category and misclassifications by category,
as a result it is also known as confusion matrix. The strength of a confusion matrix
is that it not only identifies the nature of the classification errors but also their
quantities.
Table 14.1: A hypothetical error matrix
Classification result (i.e. classified image to be evaluated)
Forest Bush Crop Urban Open Water Unclassified Row Accuracy
land total (producer’s
accuracy)
Forest 440 40 0 0 30 10 10 520 0.83
Bush 20 220 0 0 40 10 20 290 0.71
Crop 10 10 210 10 50 10 60 300 0.58
Urban 20 0 20 240 100 10 40 390 0.56
Open land 0 0 10 10 230 010250 0.88
Water 0 20 0 0 0 240 10 260 0.89
Column 490 290 240 260 450 280 240 1580
total
Reliability 0.90 0.76 0.88 0.92 0.51 0.86
(user’s
accuracy)
Error matrix is a set array (rows and columns) that can be used to evaluate the
degree of correctness of classified image. According to Campbell (1987), it is
a method of reporting site-specific error. It is derived from a comparison of
two types of maps such as a standard (reference) map and a classified map. It
has two-dimensional arrangement in which rows show the reference data and
column show the classified data.
14.4.2 Generation of Error Matrix
For generation of the error matrix you require two images namely, classified image
(i.e. image under evaluation) and a standard or reference map derived from field
survey. Sometimes, high resolution images are also used in the absence of a
reference map. By comparing these two data, you can determine exactly how each
site on standard/reference data is represented in the classified image. Before making
Ground truth (i.e. reference image)
An error matrix is a
square array of rows and
columns in which each
row and column repre-
sents one category/class in
the interpreted map. Error
matrix is also known as
confusion matrix, evalua-
tion matrix, or a contin-
gency table.

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a comparison, the classifier or analyst should make a network of appropriate (i.e.
neither very small nor very large) uniform cells that form the units of comparison for
site-specific accuracy assessment. Then two images are superimposed either by
manually or digitally depending on the availability of the images. Then superimposed
images are analysed on the basis of a cell-by-cell in case of manual comparison or
pixel-by-pixel in case of digital assessment and tabulated for each cell/pixel the
dominant category shown on the standard/reference data and category of the
corresponding cell/pixel on the classified image. The classifier also keeps a count of
the numbers of cells or pixels in each reference category as they are assigned to
categories on the created image (see Table 14.1). Finally, the summation of the
tabulation forms the basis for generation of the error matrix.
14.4.3 Interpretation of Error Matrix
Table 14.1 shows an example of an error/confusion matrix based on a classification
result. Now let us try to understand how a confusion matrix is composed and how
do you calculate accuracy based on the matrix.
You can read about the various components of the confusion matrix outlined below:
•rows correspond to classes in the ground truth map (or test set)
•columns correspond to classes in the classification result
•diagonal elements in the matrix represent the number of correctly classified
pixels of each class, i.e. the number of ground truth pixels with a certain class
name that actually obtained the same class name during classification. In the
example above, 440 pixels of forest in the test set were correctly classified as
forest in the classified image
•off-diagonal elements represent misclassified pixels or the classification errors,
i.e. the number of ground truth pixels that ended up in another class during
classification. In the example above, 40 pixels of forest in the test set were
classified as bush in the classified image
a) off-diagonal row elements represent ground truth pixels of a certain class
which were excluded from that class during classification. Such errors are
also known as errors of omission or exclusion. For example, 50 ground
truth pixels of crop were excluded from the crop class in the classification
and ended up in the open land class
b) off-diagonal column elements represent ground truth pixels of other
classes that were included in a certain classification class. Such errors
are also known as errors of commission or inclusion. For example,
100 ground truth pixels of urban were included in the open land class
by the classification and
•numbers in the column unclassified represent the ground truth pixels that
were found not classified in the classified image.
Accuracy or Producer’s Accuracy
Producer’s accuracy is defined as the probability that any pixel in that
category has been correctly classified. It is the values in column accuracy
(producer’s accuracy) present the accuracies of the categories in the classified
image as shown in Table 14.1. It is calculated as given below:

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Accuracy Assessment
Total number of correct pixels in a category
Accuracy (Producer’s Accuracy) = ———————————————————————
Total number of pixels of that category derived
from the reference data (i.e., row total)
The water category of Table 14.1, for example, has accuracy 0.89 meaning that
approximately 89% of the water ground truth pixels also appear as water
pixels in the classified image. This statistics is also known as errors of
commission.
The average accuracy is calculated as given below:
Sum of all accuracy figures in accuracy column
Average Accuracy = ——————————————————————
Total number of categories in the test set
The average accuracy of data given in Table 14.1
= (0.83+0.71+0.58+0.56+0.88+0.89) / 6
= 4.428 / 6 = 0.74
= 74.25%
This means average accuracy of the classification shown in Table 14.1 is
74.25% (or 0.74).
Reliability or User’s Accuracy
User’s accuracy is defined as the probability that a pixel classified on the
image actually represents that category on the ground. The figures in row
reliability (user’s accuracy) present the reliability of classes in the classified
image (Table 14.1). It is calculated as given below:
Total number of correct pixels in a category
Reliability (User’s Accuracy) = ————————————————————————
Total number of pixels of that category derived
from the reference data (i.e., column total)
The water category of Table 14.1, for example, has reliability 0.86 meaning
that approximately 86% of the water pixels in the classified image actually
represent water on the ground. This statistics is also called errors of omission.
The average reliability is calculated as given below:
Sum of all reliability figures in reliability row
Average reliability = —————————————————————
Total number of categories in the test set
Average reliability of data given in Table 14.1
= (0.90+0.76+0.88+0.92+0.51+0.86) / 6
= 4.81 / 6 = 0.80
= 80.27%
It indicates average reliability of the classification shown in Table 14.1 as
80.27% (or 0.80).
From the accuracy and reliability values for different classes given in Table 14.1, it
can be concluded that the test set classes crop and urban were difficult to classify
Accuracy for water
category of Table 14.1 can
be calculated as given
below:
Total number of correct
pixels for water = 240.
Total number of pixel in
water row
= 0+20+0+0+0+240+10
= 270.
Hence, accuracy for water
= 240/270 = 0.89
Reliability for water
category of Table 14.1 can
be calculated as shown
below:
Total number of correct
pixels for water = 240.
Total number of pixel in
water column
= 10+10+10+10+0+240
= 280.
Hence, reliability for water
= 240/280 = 0.86.

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as many of such test set pixels were excluded from the crop and urban categories,
thus the areas of these classes in the classified image are probably underestimated.
On the other hand, class open land in the image is not very reliable as many test set
pixels of other categories were included in the open land category in the classified
image. Thus, the area of open land category in the classified image is probably
overestimated.
Overall Accuracy
We have discussed about the individual classes and their accuracies. It is also
desirable to calculate a measure of accuracy for the entire image across all
classes present in the classified image. The collective accuracy of map for all
the classes can be described using overall accuracy, which calculates the
proportion of pixels correctly classified.
The overall accuracy is calculated as given below:
Sum of the diagonal elements
(as shown in bold letters in Table 14.1)
Overall accuracy = —————————————————————
Total number of accuracy sites (pixels)
For the sample data presented in Table 14.1, the overall accuracy
= (440+220+210+240+230+240) / (490+290+240+260+450+280)
= 1580 / 2010 = 0.78
= 78%.
It indicates that overall accuracy of the classification shown in Table 14.1 is 78%.
14.4.4 Limitations
Use of confusion matrix for accuracy assessment has become a standard
practice in quality assessment of remote sensing products. However, it is not
free from limitations due to three crucial assumptions involved in the
classification accuracy assessment:
•that the reference data are truly representative of the entire classification,
which is quite unlikely
•the reference data and classified image are perfectly co-registered, which
is impossible and
•there is no error in the reference data, which again is highly unlikely.
The actual accuracy of our classification is unknown because it is impossible
to perfectly assess the true class of every pixel. It is possible to produce a
misleading assessment of classification accuracy. Depending on how the
reference data are collected, our estimate of accuracy may be either
conservative or optimistic. If our estimate is less than the actual classification
accuracy, then we have made a conservative estimate. Some of the sources of
conservative estimates are:
•errors in reference data
•positional errors and
•minimum mapping unit of reference grid.

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Accuracy Assessment
•positional errors and
•minimum mapping unit of reference grid.
Similarly, if estimate of accuracy is more than the actual classification
accuracy, then we have made an optimistic estimate. Some of the sources of
optimistic data estimate are:
•using training data for accuracy assessment
•sampling of reference data not independent of training data sampling and
•sampling from homogeneous groups of pixels.
Therefore, if error matrix is generated by using improper reference data
collection methods, then the assessment can be misleading. Sampling methods
used for reference data should be reported in detail so that potential users can
judge whether there may be significant biases in the classification accuracy
assessment.
Check Your Progress II
Study the error matrix shown in Table 14.2. Calculate accuracy and reliability
of the forest category.
Table 14.2: Error matrix
Classification result (i.e. image to be evaluated)
Forest Water Urban
Forest 77 8 0
Water 6 84 0
Urban 0 0 74
Accuracy of the forest class is ............................................................................
..............................................................................................................................
Reliability of the forest class is ...........................................................................
..............................................................................................................................
14.5 KAPPA ANALYSIS
You have been introduced above that a commonly cited measure of mapping
accuracy is the overall accuracy which is the number of correctly classified
pixels (sum of major diagonal cells in the error matrix) divided by total
number of pixels checked. Though, overall accuracy is a measure of accuracy
for the entire image across all classes, it ignores off-diagonal elements (i.e.
errors of omission and commission). Further, it is difficult to compare
different overall accuracy values if different number of accuracy sites were
used.
Two other accuracies such as producer’s and consumer’s accuracies are
traditionally calculated from error matrix. The producer’s accuracy is a
measure of how well a certain area is classified. The consumer’s or user’s
accuracy is a measurement of reliability of the classification or probability
Ground
truth
(i.e. reference
image)
Spend
5 mins

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that a pixel on a map actually represents the category on the ground. The class
producer’s and consumer’s errors are illustrated in our example in the above
section. All these “naïve” accuracy measures can produce results due to
classification of pixels by chance, therefore; do not provide avenues to
compare accuracy statistically. This paves way for use of other accuracy
assessment methods. In this section, we will discuss another commonly used
method known as Kappa analysis, in which off-diagonal elements are
incorporated as a product of the row and column marginal totals. It is a
discrete multivariate technique used to assess classification accuracy from an
error matrix. Kappa analysis generates a kappa coefficient or Khat statistics, the
values of which range between 0 and 1.
Kappa coefficient (Khat) is a measure of the agreement between two maps
taking into account all elements of error matrix. It is defined in terms of error
matrix as given below:
Khat = (Obs – exp)/(1 – Exp)
Where,
Obs = Observed correct, it represents accuracy reported in error matrix
(overall accuracy)
Exp = Expected correct, it represents correct classification
14.5.1 Calculation Steps
Kappa coefficient is calculated in the following steps:
Step 1: Construction of error (confusion) matrix (e.g., Table 14.3)
Table 14.3: Error matrix
Classification result (i.e. image to be evaluated)
Forest Water Urban Row Commission
Marginals error
Forest 28 14 15 57 51%
Water 115 5 21 29%
Urban 1120 22 9%
Column Marginals 30 30 40 100
Omission error 7% 50% 50%
Step 2: Calculation of observed correct
Grand total = Sum of rows and columns
= 28+1+1+14+15+1+15+5+20 = 100
Total correct = Sum of the diagonal = 28+15+20 = 63
Observed correct = Total correct / Grand total = 63 / 100 = 0.63
Overall accuracy = 63%.
Step 3: Calculation of expected correct
Ground truth (i.e.
reference image)
Omission error =
100 – producer’s accuracy
Commission error =
100 – user’s accuracy

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Accuracy Assessment
Table 14.4: Error matrix showing the products of row and column
marginals based on Table 14.3
Classification result (i.e. image to be evaluated)
Forest Water Urban
Forest 30x57=1710 30x57=1710 40x57=2280
Water 30x21=630 30x21=630 40x21=840
Urban 30x22=660 30x22=660 40x22=880
Grand total = Sum of products of row and column marginals
= 1710+1710+2280+630+630+840+660+660+880
= 10000
Total correct = Sum of products of diagonal
= 1710+630+880
= 3220
Expected correct = Total correct / Grand total
= 3220/10000
= 0.32
Note: For the calculation of expected correct you need to prepare an error matrix
showing products of row and column marginals as shown in Table 14.4.
Step 4: Calculation of Khat
Now you have values of observed correct and expected correct.
Observed correct = 0.63
Expected correct = 0.32
As you know that
Khat = (Observed – Expected) / (1 – Expected)
This implies,
Khat = (0.63 – 0.32) / (1 – 0.32)
= 0.31/0.68
= 0.45.
Kappa coefficient of 0.45 implies that the classification process was avoiding
45% of the error that a completely random classification would generate
(Congalton, 1991).
14.5.2 Advantages
One of the advantages of using this method is that you can statistically
compare two classification products. For example, two classification maps can
be made using different algorithms and you can use the same reference data to
verify them. Two Khats can be derived like Khat1, Khat2. For each Khat, the
variance can also be calculated. Kappa coefficient, unlike the overall accuracy,
includes errors of omission and commission. Computation of the Kappa
Ground truth
(i.e. reference
image)

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kappa and average mutual information (AMI). AMI is based on use of
posteriori entropies for one map given that the class identity from the second map
allows evaluation of individual class performance. Unlike the percentage correct or
Kappa, that measures correctness, the AMI measures consistency between two
maps. It provides an alternate viewpoint because it is used to access similarity of
maps. For example, it can be used to compare the consistency between maps of
the same region that have entirely different themes.
Accuracy assessment is still relatively new and is an evolving area in remote sensing.
The effectiveness of different methods and measurement are still being explored and
debated.
14.6 SUMMARY
We have studied in this unit about the concepts of accuracy assessments. This can
be summarised in the following points:
•Assessing accuracy for each category as well as for the whole image is
essential to compare the results of various classification techniques and
quality and reliability of the results obtained.
•Accuracy in image classification is affected because of errors of inclusion
and errors of exclusion.
•Sampling size is an important consideration for accuracy assessment and
sufficient number of samples should be taken for the same.
•Error/confusion matrix can be used for accuracy and reliability
assessments.
•Overall accuracy is a measure of accuracy for the whole image across all
categories.
•Kappa coefficient is another method for accuracy assessment having a
number of advantages over other methods.
14.7 UNIT END QUESTIONS
1) How is accuracy defined?
2) What is a confusion matrix?
3.) Describe errors of omission and errors of commission.
14.8 REFERENCES
•Campbell, J. B., (1987), Introduction to Remote Sensing. The Guilford
Press, New York.
•Campbell, J. B., (1996), Introduction to Remote Sensing. Taylor and
Francis, London.
•Congalton, R. G., (1991), A review of assessing the accuracy of classifications
of remotely sensed data, Remote Sensing of Environment, Vol 37, pp 35-
46.
14.9 FURTHER/SUGGESTED READING
Spend
30 mins

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•Campbell, J. B., (2006), Introduction to Remote Sensing. Taylor and
Francis, London
•Jensen, J. R., (2004), Introduction to Digital Image Processing: A Remote
Sensing Perspective, Prentice Hall, New Jersey.
•Janssen, L. L. F. and van der Wel, F. J. M., (1994), Accuracy assessment
of satellite derived land-cover data: a review, Photogrammetric
Engineering and Remote Sensing, Vol 60, pp 419-426.
14.10 ANSWERS
Check Your Progress I
Standard (reference) image and classified image data are the basic
prerequisites for accuracy assessment.
Check Your Progress II
Accuracy of forest class is 0.9059, which is equal to 90.59%.
Reliability of forest class is 0.9277, which is equal to 92.77%.
Unit End Questions
1) Refer to subsection 14.2.1
2) Refer to subsection 14.4.1
3) Refer to subsections 14.2.3 and 14.4.3

74
Processing and
Classification of Remotely
Sensed Images GLOSSARY
Average accuracy: It is the sum of accuracy values in accuracy column which
is divided by the number of classes in the test set.
Average reliability: It is the sum of reliability values in reliability column di-
vided by the number of classes in the test set.
Atmospheric correction: It is the correction for the influence of atmosphere on
the image by relative or absolute means.
Band radio: It is a narrow section of wavelengths or frequencies in radio
broadcasting.
BRDF (Bi-directional Reflectance Distribution Function): A function
which describes the magnitude of upwelling radiance of the target in terms of
illumination angle and the angle of view of the sensor.
Bi-linear interpolation: Involves the estimation of value at a pixel position,
the nearest four neighbours around the pixel forming a rectangular plane are
selected. An inverse weighted average of the known values based on their
distances to the location of the pixel whose value is to be estimated is bi-linear
interpolation.
Confusion matrix: It contains information about actual and predicted classifi-
cations done by a classification system. Performance of such systems is
commonly evaluated using data in the matrix.
Contrast: Ratio between the energy emitted or reflected by an object and its
immediate surroundings.
Contrast enhancement: It is an image processing procedure that improves
the contrast ratio of images. The original narrow range of digital values is
expanded to utilise full range of available digital values.
Contrast ratio: The ratio of reflectances between the brightest and darkest
parts of an image.
Contrast stretching: It involves the expanding of a measured range of digital
numbers in an image to a larger range to improve contrast of the image and its
component parts.
Co-variance: An average product of the differences between the pixels values
in each band and the mean of each band. It measures the tendencies of pixel
values for the same pixel but in different bands, to vary with each other in
relation to the means of their respective bands.
Cubic convolution: A high-order resampling technique in which brightness
value of a pixel in a corrected image is interpolated from the brightness values
of 16 nearest pixels around the location of the corrected pixel.
Digital image processing: The computer manipulation of digital number
values of an image.

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Digital number: It is the value assigned to a pixel in a digital image.
Distortions: Are the errors in the remotely sensed image in terms of the pixel
shape, position or the recorded value.
Enhancement: A process of enhancing certain features in the image making it
more interpretable to the human eye for a particular application.
Geocoding: It is a special case of rectification that includes geographical
registration or coding of pixels in an image. Geocoded data are images that
have been rectified to a particular map projection and pixel size. The use of
standard pixel sizes and coordinates permits convenient overlaying of images
from different sensors and maps in a GIS.
Geometric correction : It involves image processing procedure that corrects
spatial distortions in an image.
Gray scale: It is a sequence of gray tones ranging from black to white.
Histogram: It is a way of expressing frequency of occurrence of values in a
data set within a series of equal ranges or bins, height of each bin representing
frequency at which values in data set fall within the chosen range. A cumula-
tive histogram expresses frequency of all values falling within a bin and lower
in the range. A smooth curve derived mathematically from a histogram is
termed the probability density function.
Histogram equalisation: A process of re-distributing pixel values so that
there are approximately the same number of pixels with each value within a
range thereby creating a nearly flat histogram for output image.
Hue: It represents the dominant wavelength of a colour.
Image classification: The process of dividing all channels within a multichan-
nel digital remote sensing dataset into discrete surface cover categories or
information themes.
Image enhancement: The process of altering the appearance of an image so
that the interpreter can extract more information.
Image interpretation: It is a process in which a person extracts information
from an image.
Image interpretation key: The characteristic or combination of characteris-
tics that enable an interpreter to identify an object on an image.
Input-to-output mapping: Represents locations of the points in the slave are
transferred to the reference by calculating them based on the coefficients of
the polynomial transformation.
Intensity: The brightness ranging from black to white.
Mean: Statistical average which is calculated as the sum of a set of values
divided by the number of values in the set.

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Median: The central value in a set of data such that an equal number of values are
greater than and less than the median.
Mode: Represents most commonly occurring value in a set of data. For an image
histogram, peak of the curve represents mode.
NDVI (Normalised Difference Vegetation Index): It is a remote sensing way
of measuring whether vegetation is alive or dead based on information from
visible especially red and near-infrared bands.
Orthorectification: Process of pixel-by-pixel correction of an image for
topographic distortion. Every pixel in an orthorectified image appears to view
the Earth from directly above, i.e., the image is in an orthographic projection.
Output-to-input mapping: Represents positions in the reference map which
are related to its corresponding positions in the slave by calculating them
based on the coefficients of the polynomial transformation.
Overall accuracy: Total number of correctly classified pixels (diagonal
elements) divided by the total number of test pixels.
Pan-sharpening: It is a computer-enhancement algorithm for improving the
resolution of an image. It involves combining the high spatial resolution of a
panchromatic image with the colour information from (lower resolution)
multispectral data. The result is a colour image that has high resolution of the
panchromatic image.
Pixel: A picture element; smallest element of an image that has been electroni-
cally coded in an array.
Polynomial: It is a mathematical expression consisting of variables and
coefficients.
Producer’s accuracy: Fraction of correctly classified pixels with regard to all
pixels of that ground truth class.
Rectification: Process of alignment of an image to a map (map projection
system). In many cases, the image must also be oriented so that north direction
corresponds to the top of the image. It is also known as georeferencing.
Registration: Process of alignment of one image to another image of the same
area not necessarily involving a map coordinate system.
Resampling: It is an estimation of pixel values of a rectified image.
Standard deviation: A square root of the variance of a set of values which is
used as a measurement of the spread of the values.
Supervised classification: A classification procedure guided by the analyst.
Thematic mapper: An advanced multispectral scanning Earth resources
sensor designed to achieve higher image resolution, sharper spectral separa-
tion, improved geometric fidelity and greater radiometric accuracy and resolu-
tion more than the multispectral sensor. Thematic mapper data are sensed in
seven spectral bands simultaneously.

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Trade-off: A result of changing one factor in a remote sensing system, there
are compensating changes elsewhere in the system; such a compensating
change is known as a trade-off.
Training area: A sample of the Earth’s surface with known properties; the
statistics of the imaged data within the area are used to determine decision
boundaries in classification.
Training site: An area of terrain with known properties or characteristics that
is used in supervised classification.
Unsupervised classification: The digital information extraction technique in
which the computer assigns pixels to categories with no instructions from the
operator.
Variance: The measure of central tendency.

78
Processing and
Classification of Remotely
Sensed Images ABBREVIATIONS
AMI : Average Mutual Information
ARVI : Atmospherically Resistant Vegetation Index
AVHRR : Advanced Very High Resolution Radiometer
BRDF : Bi-directional Reflectance Distribution Function
CA : Consumer’s Accuracy
DN : Digital Number
EM : Electromagnetic
EMR : Electromagnetic Radiation
ETM+:Enhanced Thematic Mapper Plus
EVI : Enhanced Vegetation Index
FWHM : Full Width at Half-Maximum
GCP : Ground Control Point
GIS : Geographical Information System
IHS : Intensity Hue Saturation
IRS : Indian Remote Sensing Satellite Series
ISODATA : Iterative Self-Organising Data Analysis Technique
ISRO : Indian Space Research Organisation
LC : Land Class
LISS : Linear Imaging Self-Scanning System
MODIS : Moderate Resolution Imaging Spectroradiometer
MSS : Multispectral Scanner
MXL : Maximum Likelihood
NASA : National Aeronautical and Space Administration
NDVI : Normalised Difference Vegetation Index
NIR : Near Infrared
PA : Producer’s Accuracy
PCA : Principal Component Analysis
RGB : Red Green Blue
RMSE : Root Mean Square Error
RMS : Root Mean Square
SDSS : Spatial Decision Support Systems
SPOT : Système Pour l’Observation de la Terre
TM : Thematic Mapper
UTM : Universal Transverse Mercator
VI : Vegetation Index