Image quality assessment and statistical evaluation

Lecture 3

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).

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MODISTrue143

Cloud

Cloud in ETM+

Striping Noise and Removal

CPCACPCA

Combined Principle Combined Principle Component AnalysisComponent Analysis

Xie et al. 2004

Speckle Noise and Removal

G-MAPG-MAP

Blurred objectsBlurred objectsand boundaryand boundary

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).

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

1. Histogram

Histogram of A Single Band of Landsat TM Data of Charleston, SC

Metadata of the image

What is metadata?

a. Open water,b. Coastal wetlandc. Upland

2. Viewing individual pixel values at specific locations or within a

geographic area

There are different ways in ENVI There are different ways in ENVI to see pixel valuesto see pixel values Cursor location/valueCursor location/value Special pixel editorSpecial pixel editor 3D surface view3D 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. One-half of the area below the distribution curve is to the right of the median, and one-half is to the left

The The meanmean is the arithmetic average and is defined as the sum of all brightness value observations divided by the number of observations.

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Min Max Variance Standard deviation Coefficient of variation

(CV) Skewness Kurtosis Moment

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Measures of Distribution (Histogram) Measures of Distribution (Histogram) Asymmetry and Peak SharpnessAsymmetry and Peak Sharpness

SkewnessSkewness is a measure of the asymmetry of a histogram and is is a measure of the asymmetry of a histogram and is computed using the formula: computed using the formula:

A perfectly symmetric histogram has a A perfectly symmetric histogram has a skewnessskewness value of zero. value of zero. If a distribution has a long right tail of large values, it is 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 positively skewed, and if it has a long left tail of small values, it is negatively skewed.is negatively skewed.

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A histogram may be symmetric but have a peak that is very A histogram may be symmetric but have a peak that is very sharp or one that is subdued when compared with a perfectly sharp or one that is subdued when compared with a perfectly normal distribution. A perfectly normal distribution (histogram) normal distribution. A perfectly normal distribution (histogram) has zero has zero kurtosiskurtosis. The greater the positive kurtosis value, the . The greater the positive kurtosis value, the sharper the peak in the distribution when compared with a sharper the peak in the distribution when compared with a normal histogram. Conversely, a negative kurtosis value normal histogram. Conversely, a negative kurtosis value suggests that the peak in the histogram is less sharp than that of suggests that the peak in the histogram is less sharp than that of a normal distribution. a normal distribution. KurtosisKurtosis is computed using the formula: is computed using the formula:

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Measures of Distribution (Histogram) Measures of Distribution (Histogram) Asymmetry and Peak SharpnessAsymmetry and Peak Sharpness

In this example Kurtosis does not subtract 3. http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.ht

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We can use ENVI/IDL to calculate them

ENVI 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.

CovarianceCovariance 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.

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CorrelationTo 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:

lk

klkl ss

r cov

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”.

example

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

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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 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

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

Univariate statistics

covariance

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

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