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Smoothing - Wikipedia, the free encyclopedia
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Smoothing
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In
statistics and
image processing, to smooth a
data set is to create an approximating
function that attempts to capture important
patterns in the data, while leaving out
noise or other fine-scale structures/rapid phenomena. Many different
algorithms are used in smoothing. One of the most common algorithms is the "
moving average", often used to try to capture important trends in repeated
statistical surveys. In
image processing and
computer vision, smoothing ideas are used in
scale-space representations.
Smoothing may be distinguished from the related and partially overlapping concept of
curve fitting in the following ways:
curve fitting often involves the use of an explicit function form for the result, whereas the immediate results from smoothing are the "smoothed" values with no later use made of a functional form if there is one;
the aim of smoothing is to give a general idea of relatively slow changes of value with little attention paid to the close matching of data values, while curve fitting concentrates on achieving as close a match as possible.
smoothing methods often have an associated tuning parameter which is used to control the extent of smoothing.
However, the terminology used across applications is mixed. For example, use of an
interpolating spline fits a smooth curve exactly through the given data points and is sometimes called "smoothing".
Contents
Linear smoothers
In the case that the smoothed values can be written as a
linear transformation of the observed values, the smoothing operation is known as a linear smoother; the matrix representing the transformation is known as a smoother matrix or
hat matrix.
See also