Image Quality Assessment and Statistical Evaluation

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Image Quality Assessment and Statistical
Evaluation

• Chapter 4

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Image Processing Mathematical Notation

• i a row (or line) in the imagery
• j a column (or sample) in the imagery
• k a band of imagery
• l another band of imagery
• n total number of picture elements (pixels) in
  an array
• Bvijk brightness value at row i, column j, and
  bank k
• Bvik i th brightness value in band k
• Bvil i th brightness value in band l
• mink minimum brightness value of band k
• maxk maximum brightness value of band k

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Univariate Description Image Statistics

• Measure of Central Tendency in Remote Sensing
  data
• Mode the value that occurs most frequently in a
  distribution and is usually the highest point on
  the curve (histogram)
• Median the value midway in the frequency
  distribution
• Mean (?) the arithmetic average and is defined
  as the sum of all brightness value observations
  divided by the number of observations
• The mean of a single band of imagery ?k, composed
  of n brightness values (Bvik) is computed using
  the formula

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Univariate Description Image Statistics

• Measures of Dispersion
• Range is computed as the difference between the
  maximum (maxk) and minimum (mink) values
• Variance of a sample is the average squared
  deviation of all possible observations from the
  sample mean
• Standard deviation the positive square root of
  the variance

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Multivariate Image Statistics

• Covariance the joint variation of two variables
  about their common mean
• SP Corrected sum of products

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Multivariate Image Statistics

• Pearsons product-moment correlation coefficient
  The estimation of the degree of interrelation
  between variables
• Coefficient of determinationexpresses 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 r2

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Spatial Autocorrelation

• Is the statistical relationship among measured
  points, where the correlation depends on the
  distance and direction that separates the
  locations (things that are closer to one another
  are more alike than those farther away).