CStats:ContraMean
The ContraMean method computes the mean
value of a data sample using contra-harmonic mean estimation to
reduce the influence of deviant pixels. The sample may be a Lua
table or a class object of type CImage, CArray, or CMatrix. For CImage and CMatrix
objects, an optional CRect object can be used to define the points used in
the calculation.
Syntax
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nMean, nStdDev = CStats:ContraMean(
table, nExp )
nMean, nStdDev = CStats:ContraMean(
CImage,
nExp )
nMean, nStdDev = CStats:ContraMean(
CImage, nExp,
CRect )
nMean, nStdDev = CStats:ContraMean(
CArray, nExp )
nMean, nStdDev = CStats:ContraMean(
CArray, nExp,
CRect )
nMean, nStdDev = CStats:ContraMean(
CMatrix,
nExp )
where
 table is a lua table containing the data.
CImage,
CArray, and CMatrix
are class objects containing the data to measure,
CRect is
a CRect rectangle
object that defines the region to measure.
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nExp is the exponent parameter of the contra
mean.
nMean and nStdDev are the mean and standard deviation,
respectively. On failure, 0,0
is returned.
This method uses the contra-harmonic mean statistic
which assigns weights to values based upon their distance from the
mean value. No rejection ("clipping") is performed. In contrast to
the geometric mean, this method can be tuned to assign less weight
to values lying above the sample or to values lying below the
sample mean. The positive or negative tail bias depends upon the
value of the exponent parameter and the severity of the weighting
depends upon the absolute value of the exponent parameter.
For an exponent parameter of value e, the statistic is
computed using a ratio of powers for each sample member x, as shown
below. (Note: The symbol ^ denotes raising a number to a power, as
in 2^3 =
8):
Statistic = Sum(
x^(e+1)/x^e ).
Thus
e=0 gives the
arithmetic mean.
e<0 gives more
weight to negative outliers.
e>0 gives more
weight to positive outliers.
Examples
Suppose a CImage I and a CRect R exist. The
following script returns the contra-mean value inside a rectangle
on the image:
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S = CStats:new()
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power = 0.5
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nVal = S:ContraMean( I,
power, R )
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Printf("mean=%lg\n", nVal)
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The following script returns the contra-mean value for a table of
data using power=0.5:
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S = CStats:new()
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t = { 4, 4, 2, 5, 6.4, -1.42, -12,
3.4 }
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Printf("mean=%lg\n",
S:ContraMean(t,0.5) )
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Related Topics