- present participle of smooth
- French: lissage
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.
Linear smoothersIn 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.
Specific smoothing and filter types
- Additive smoothing
- Butterfly filter
- Butterworth filter
- Digital filter
- Kalman filter
- Kernel smoother
- Laplacian smoothing
- Low-pass filter
- Recursive filter
- Savitzky–Golay smoothing filter
- Local regression also known as "loess" or "lowess"
smoothing in German: Glättung
smoothing in Spanish: Suavizado
smoothing in Hebrew: החלקה
smoothing in Swedish: Utjämning