# User Contributed Dictionary

### Verb

smoothing- present participle of smooth

#### Translations

- French: lissage

# Extensive Definition

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 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

### 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"

### Other

## External links

- Chapter on data smoothing from the instruction manual for Wolfram Research's Mathematica

smoothing in German: Glättung

smoothing in Spanish: Suavizado

smoothing in Hebrew: החלקה

smoothing in Swedish:
Utjämning