Image quality assessment and
statistical evaluation
Lecture 3
February 4, 2005
Image Quality

Many remote sensing datasets contain high-quality,
accurate data. Unfortunately, sometimes error (or noise) is
introduced into the remote sensor data by:
 the environment (e.g., atmospheric scattering, cloud),
 random or systematic malfunction of the remote
sensing system (e.g., an uncalibrated detector creates
striping), or
 improper airborne or ground processing of the remote
sensor data prior to actual data analysis (e.g., inaccurate
analog-to-digital conversion).
154
155
Cloud
155
160
162
MODIS
True
143
163
164
Cloud in ETM+
Striping Noise and Removal
CPCA
Combined Principle
Component Analysis
Xie et al. 2004
Speckle Noise and
Removal
Blurred objects
and boundary
G-MAP
Gamma Maximum
A Posteriori Filter
Remote sensing sampling theory



Large samples drawn randomly from natural populations
usually produce a symmetrical frequency distribution: most
values are clustered around some central values, and the
frequency of occurrence declines away from this central
point- bell shaped, and is also called a normal distribution.
Many statistical tests used in the analysis of remotely sensed
data assume that the brightness values (DN) recorded in a
scene are normally distributed.
Unfortunately, remotely sensed data may not be normally
distributed and the analyst must be careful to identify such
conditions. In such instances, nonparametric statistical theory
may be preferred.
Remote sensing pixel values and
statistics

Many different ways to check the pixel values and statistics:
 looking at the frequency of occurrence of individual
brightness values (or digital number-DN) in the image
displayed in a histogram
 viewing on a computer monitor individual pixel
brightness values or DN at specific locations or within a
geographic area,
 computing univariate descriptive statistics to determine if
there are unusual anomalies in the image data, and
 computing multivariate statistics to determine the amount
of between-band correlation (e.g., to identify redundancy).
1. Histogram
A graphic
representation of
the frequency
distribution of a
continuous
variable.
Rectangles are
drawn in such a
way that their
bases lie on a
linear scale
representing
different intervals,
and their heights
are proportional to
the frequencies of
the values within
each of the
intervals



Histogram of A
Single Band of
Landsat TM Data
of Charleston, SC
Metadata of the
image
What is metadata?
a. Open water,
b. Coastal wetland
c. Upland
2. Viewing individual pixel values
at specific locations or within a
geographic area

There are different ways in ENVI
to see pixel values



Cursor location/value
Special pixel editor
3D surface view
3. Univariate descriptive image
statistics



The mode is the value that occurs
most frequently in a distribution
and is usually the highest point on
the curve (histogram). It is
common, however, to encounter
more than one mode in a remote
sensing dataset.
The median is the value midway in
the frequency distribution. Onehalf of the area below the
distribution curve is to the right of
the median, and one-half is to the
left
The mean is the arithmetic average
and is defined as the sum of all
brightness value observations
divided by the number of
observations.
n
k 
 BV
i 1
n
ik
Cont’
n








Min
Max
Variance
Standard deviation
Coefficient of variation
(CV)
Skewness
Kurtosis
Moment
vark 
 BV
i 1
 k 
2
ik
n 1
sk   k  vark
k
CV 
k
Measures of Distribution (Histogram)
Asymmetry and Peak Sharpness
Skewness is a measure of the asymmetry of a histogram and is
computed using the formula:
 BVik   k


sk
i 1 
skewnessk 
n
n



3
A perfectly symmetric histogram has a skewness value of zero.
If a distribution has a long right tail of large values, it is
positively skewed, and if it has a long left tail of small values, it
is negatively skewed.
Measures of Distribution (Histogram)
Asymmetry and Peak Sharpness
A histogram may be symmetric but have a peak that is very
sharp or one that is subdued when compared with a perfectly
normal distribution. A perfectly normal distribution (histogram)
has zero kurtosis. The greater the positive kurtosis value, the
sharper the peak in the distribution when compared with a
normal histogram. Conversely, a negative kurtosis value
suggests that the peak in the histogram is less sharp than that of
a normal distribution. Kurtosis is computed using the formula:
 1 n  BV    4 
k
   3
kurtosisk     ik
sk
 n i 1 
 


In this example Kurtosis does not subtract 3.
http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
We can use ENVI/IDL to
calculate them

ENVI
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Entire image,
Using ROI
Using mask
examples
IDL

examples
4. Multivariate Image Statistics

Remote sensing research is often concerned with the
measurement of how much radiant flux is reflected
or emitted from an object in more than one band. It
is useful to compute multivariate statistical measures
such as covariance and correlation among the
several bands to determine how the measurements
covary. Later it will be shown that variance–
covariance and correlation matrices are used in
remote sensing principal components analysis
(PCA), feature selection, classification and
accuracy assessment.
Covariance

The different remote-sensing-derived spectral measurements for
each pixel often change together in some predictable fashion. If
there is no relationship between the brightness value in one band
and that of another for a given pixel, the values are mutually
independent; that is, an increase or decrease in one band’s
brightness value is not accompanied by a predictable change in
another band’s brightness value. Because spectral measurements of
individual pixels may not be independent, some measure of their
mutual interaction is needed. This measure, called the covariance,
is the joint variation of two variables about their common mean.
n
n
SPkl   BVik BVil  
i 1
n
 BV  BV
i 1
ik
i 1
n
il
SPkl
cov kl 
n 1
Correlation
To estimate the degree of interrelation between variables in a manner not
influenced by measurement units, the correlation coefficient, is
commonly used. The correlation between two bands of remotely sensed
data, rkl, is the ratio of their covariance (covkl) to the product of their
standard deviations (sksl); thus:
cov kl
rkl 
s k sl
If we square the correlation coefficient (rkl), we obtain the sample coefficient of
determination (r2), which expresses the proportion of the total variation in the values of
“band l” that can be accounted for or explained by a linear relationship with the values
of the random variable “band k.” Thus a correlation coefficient (rkl) of 0.70 results in an
r2 value of 0.49, meaning that 49% of the total variation of the values of “band l” in the
sample is accounted for by a linear relationship with values of “band k”.
Pixel
Band 1
(green)
Band 2
(red)
Band 3
(ni)
Band 4
(ni)
(1,1)
130
57
180
205
(1,2)
165
35
215
255
(1,3)
100
25
135
195
(1,4)
135
50
200
220
(1,5)
145
65
205
235
example
SP12

675232 
 (31,860) 
540
cov12 
 135
4
Band 1
(Band 1 x Band 2)
Band 2
130
7,410
57
165
5,775
35
100
2,500
25
135
6,750
50
145
9,425
65
675
31,860
232
5
Band 1
Band 2
Band 3
Band 4
Mean (k)
135
46.40
187
222
Variance (vark)
562.50
264.80
1007
570
(sk)
23.71
16.27
31.4
23.87
(mink)
100
25
135
195
(maxk)
165
65
215
255
Range (BVr)
65
40
80
60
Univariate statistics
Band 1 Band 2 Band 3 Band 4
Band 1
Band 2
Band 3
Band 4
Band 1
562.25
-
-
-
Band 1
Band 2
135
264.80
-
-
Band 3
718.75
275.25
1007.50
Band 4
537.50
64
663.75
Covariance
-
-
-
-
Band 2 0.35
-
-
-
-
Band 3 0.95
0.53
570
Band 4 0.94
covariance
0.16
0.87
-
Correlation coefficient
Feature space plot, or
2D scatter plot in ENVI


Individual bands of remotely sensed data are often
referred to as features in the pattern recognition
literature. To truly appreciate how two bands
(features) in a remote sensing dataset covary and if
they are correlated or not, it is often useful to
produce a two-band feature space plot
Demo of 2D scatter plot in ENVI


Bright areas in the plot represents pixel pairs that have a
high frequency of occurrence in the images
If correlation is close to 1, then all points will be almost in
1:1 lines