WordNet

in a smooth and diplomatic manner; "`And now, he said smoothly, `we will continue the conversation"
with no problems or difficulties; "put the plans into effect quickly and smoothly"; "despite of some mishaps, everything went swimmingly" (同)swimmingly
of the margin of a leaf shape; not broken up into teeth
the act of smoothing; "he gave his hair a quick smooth"
free from obstructions; "smooth the way towards peace negotiations" (同)smooth out
make smooth or smoother, as if by rubbing; "smooth the surface of the wood" (同)smoothen
having a surface free from roughness or bumps or ridges or irregularities; "smooth skin"; "a smooth tabletop"; "smooth fabric"; "a smooth road"; "water as smooth as a mirror"
lacking obstructions or difficulties; "the bills path through the legislature was smooth and orderly"
of motion that runs or flows or proceeds without jolts or turbulence; "a smooth ride"

PrepTutorEJDIC

(またsmooth)滑らかに,円滑に;平隠に
(表面が)『滑らかな』,すべすべした;『平らな』平坦(へいたん)な / (動きが)円滑な,揺れのない / (物事が)すらすら運ぶ,順調な,平隠な / (味など)滑らかな;(練り粉など)つぶつぶ(むら)のない / 愛想のよい,取り入るような / …‘を'『滑らかにする』,平らにする,〈髪など〉‘を'なでつける《+『out(down)』+『名,』+『名』+『out(down)』》 / 〈物事〉‘を'容易にする,円滑にする《+『away(out)』+『名,』+『away(out)』》 / 〈人・気持ちなど〉‘を'静める,和らげる《+『down』+『名,』+『名』+『down』》 / 滑らか(平ら)になる;隠やかになる《+『down』》 / =smoothly

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/10/12 11:10:56」(JST)

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[Wiki en表示]

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. In smoothing, the data points of a signal are modified so individual points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis (1) by being able to extract more information from the data as long as the assumption of smoothing is reasonable and (2) by being able to provide analyses that are both flexible and robust.^[1] Many different algorithms are used in smoothing.

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. Curve fitting will adjust any number of parameters of the function to obtain the 'best' fit.

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".^{[citation needed]}

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.^{[citation needed]}

The operation of applying such a matrix transformation is called convolution. Thus the matrix is also called convolution matrix or a convolution kernel. In the case of simple series of data points (rather than a multi-dimensional image), the convolution kernel is a one-dimensional vector.

Smoothing algorithms

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. The simplest smoothing algorithm is the "rectangular" or "unweighted sliding-average smooth". This method replaces each point in the signal with the average of "m" adjacent points, where "m" is a positive integer called the "smooth width". Usually m is an odd number. The triangular smooth is like the rectangular smooth except that it implements a weighted smoothing function.^[2]

Some specific smoothing and filter types are:

Additive smoothing
Butterworth filter
Digital filter
Exponential smoothing used to reduce irregularities (random fluctuations) in time series data, thus providing a clearer view of the true underlying behaviour of the series. It also provides an effective means of predicting future values of the time series (forecasting).^[3]
Kalman filter
Kernel smoother
Kolmogorov–Zurbenko filter
Laplacian smoothing
Local regression also known as "loess" or "lowess"
Low-pass filter
Moving average a form of average which has been adjusted to allow for seasonal or cyclical components of a time series. Moving average smoothing is a smoothing technique used to make the long term trends of a time series clearer.^[3]
Ramer–Douglas–Peucker algorithm
Savitzky–Golay smoothing filter based on the least-squares fitting of polynomials to segments of the data
Smoothing spline
Stretched grid method

References

^ Simonoff, Jeffrey S. (1998) Smoothing Methods in Statistics, 2nd edition. Springer ISBN 978-0387947167^{[page needed]}
^ O'Haver, T. (January 2012). "Smoothing". terpconnect.umd.edu.
^ ^a ^b Easton, V. J.; & McColl, J. H. (1997)"Time series", STEPS Statistics Glossary

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Optimization of the treatment cycle of pressed-off leachate produced in a facility processing the organic fraction of municipal solid waste.

d'Antonio L1, Fabbricino M, Pontoni L.
Environmental technology.Environ Technol.2015 Jun;36(11):1367-72. doi: 10.1080/09593330.2014.990521. Epub 2014 Dec 16.
The paper investigates, at a laboratory scale, the applicability of anaerobic digestion for the treatment of pressed-off leachate produced in a biomechanical treatment plant for municipal solid waste. Batch tests show that the anaerobic process proceeds smoothly and produces about 10,000 mL of met
PMID 25422035

Fast gaze reorientations by combined movements of the eye, head, trunk and lower extremities.

Anastasopoulos D1, Naushahi J, Sklavos S, Bronstein AM.
Experimental brain research.Exp Brain Res.2015 May;233(5):1639-50. doi: 10.1007/s00221-015-4238-4. Epub 2015 Mar 12.
Large reorientations of the line of sight, involving combined rotations of the eyes, head, trunk and lower extremities, are executed either as fast single-step or as slow multiple-step gaze transfers. In order to obtain more insight into the mechanisms of gaze and multisegmental movement control, we
PMID 25761968

Present status of clinical care for postpartum patients with hypertensive disorders of pregnancy in Japan: findings from a nationwide questionnaire survey.

Mito A1, Arata N, Sakamoto N, Miyakoshi K, Waguri M, Osamura A, Kugishima Y, Metoki H, Yasuhi I.
Hypertension in pregnancy.Hypertens Pregnancy.2015 May;34(2):209-20. doi: 10.3109/10641955.2014.1001902. Epub 2015 Mar 16.
OBJECTIVE: To assess the present status of clinical care for postpartum patients with hypertensive disorders of pregnancy (HDP) in Japan.METHODS: We conducted a nationwide questionnaire survey of obstetricians, internists and hypertension specialists and analyzed 686 valid responses.RESULTS: Though
PMID 25774557

Quantile rank maps: A new tool for understanding individual brain development.

Chen H1, Kelly C2, Castellanos FX3, He Y4, Zuo XN5, Reiss PT6.
NeuroImage.Neuroimage.2015 May 1;111:454-63. doi: 10.1016/j.neuroimage.2014.12.082. Epub 2015 Jan 10.
We propose a novel method for neurodevelopmental brain mapping that displays how an individual's values for a quantity of interest compare with age-specific norms. By estimating smoothly age-varying distributions at a set of brain regions of interest, we derive age-dependent region-wise quantile ran
PMID 25585020