Smoothing

smoothIt is a commonly used data processing method. In statistics and image processing, approximate functions are usually established to capture the main patterns in the data in order to remove noise, structural details or transient phenomena in order to smooth a data set.

During the smoothing process, signal data points are modified so that individual data points that are caused by noise are lowered and those that are lower than adjacent data points are raised, resulting in a smoother signal.

Smooth way

There are two main reasons for using smoothing for data analysis:

• If the assumption of smoothness is reasonable, more information can be obtained from the data;
• Provides flexible and robust analysis. There are many different algorithms for smoothing, but data smoothing is usually done using density estimation and histograms.

Smoothing Algorithm

• Moving average: Often used to capture important trends in repeated statistical surveys. In image processing and computer vision, smoothing is used for scale-space representations.
• Rectangular smoothing/unweighted smoothing: replaces points in the signal with the average of m connected points, where m is a positive integer called the "smoothing width", usually an odd number.

Specific applications of smoothing

• Additive smoothing
• Good-Turing estimate
• Jelinek-Mercer smoothing (interpolation)
• Katz smoothing ( backoff )
• Witten-Bell smoothing
• Absolute discounting
• Kneser – Ney smoothing