Smoothing

Smoothing may be distinguished from the related and partially overlapping concept of curve fitting in the following ways: 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.

[citation needed] The operation of applying such a matrix transformation is called convolution.

In the case of simple series of data points (rather than a multi-dimensional image), the convolution kernel is a one-dimensional vector.

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.