Image%20quality%20assessment%20and%20statistical%20evaluation

1
Image quality assessment and statistical
evaluation

• Lecture 3
• February 4, 2005

2
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).

3
154
155
Cloud
155
160
162
MODIS True 143
163
164
4
Cloud in ETM
5
Striping Noise and Removal
CPCA
Combined Principle Component Analysis
Xie et al. 2004
6
Speckle Noise and Removal
Blurred objects and boundary
G-MAP
Gamma Maximum A Posteriori Filter
7
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.

8
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).

9
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

10

• Histogram of A Single Band of Landsat TM Data of
  Charleston, SC
• Metadata of the image
• What is metadata?

1. Open water,
2. Coastal wetland
3. Upland

11
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

12
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. One-half 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.

13
Cont

• Min
• Max
• Variance
• Standard deviation
• Coefficient of variation (CV)
• Skewness
• Kurtosis
• Moment

14
(No Transcript)
15
Measures of Distribution (Histogram) Asymmetry
and Peak Sharpness
Skewness is a measure of the asymmetry of a
histogram and is computed using the formula
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.
16
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
17

• In this example Kurtosis does not subtract 3.
• http//www.itl.nist.gov/div898/handbook/eda/sectio
  n3/eda35b.htm

18
We can use ENVI/IDL to calculate them

• ENVI
• Entire image,
• Using ROI
• Using mask
• examples
• IDL
• examples

19
(No Transcript)
20
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 variancecovariance and correlation
  matrices are used in remote sensing principal
  components analysis (PCA), feature selection,
  classification and accuracy assessment.

21
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 bands brightness
  value is not accompanied by a predictable change
  in another bands 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.

22
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
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.
23
example
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
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
24
Band 1 Band 2 Band 3 Band 4
Mean (mk) 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 1 562.25 - - -
Band 2 135 264.80 - -
Band 3 718.75 275.25 1007.50 -
Band 4 537.50 64 663.75 570
Band 1 Band 2 Band 3 Band 4
Band 1 - - - -
Band 2 0.35 - - -
Band 3 0.95 0.53 - -
Band 4 0.94 0.16 0.87 -
covariance
Correlation coefficient
Covariance
25
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 11 lines