Data smoothing

Abstract

A method of transforming an array X of input values x(i) into an array Y of output values y(i), the method comprising calculating each value y(i) of the array Y as a function of at least an exponentially weighted moving average a(i) of the array X, calculated in ascending order of the array X value indices, and an exponentially weighted moving average b(i) of the array X, calculated in descending order of the array X value indices, or an exponentially weighted moving average b′(j) of an array X′ containing the values of the array X in reverse order, calculated in ascending order of the array X′ value indices, where i, j are the array value indices, wherein 0≤i<N, j=N−1−i, N is the array size. A computer system that implements said method, and a non-transitory computer readable medium comprising program instructions allowing for implementing said method.

Description

FIELD OF THE INVENTION[0001]The invention relates to data smoothing.BACKGROUND OF THE INVENTION[0002]There are many applications supposing collection of large arrays of input data requiring further smoothing, i.e. obtaining output values by means of separation of trends from noise and inconsistent values. Data smoothing is an integral part of various image editing techniques focused on eliminating specific defects (such as, for example, excessive detailing, scanning defects, scratches, dust).[0003]There are a lot of smoothing techniques, and most of them use several input values to calculate the output one. The higher the smoothing degree, the more input values are to be used and the more calculations are to be performed.[0004]Among the existing techniques, special mention should be made of exponentially weighted moving average characterized by recursive calculation of output values, whereby the amount of calculations does not depend on the degree of smoothing. Thus, this technique ...

AI Technical Summary

Benefits of technology

The present invention solves the problem of the prior art by using an array of input values to create an array of output values. The output values are calculated using a moving average of the input values, which is weighted based on its own value and the value of the next input value in ascending or descending order. This results in a more accurate and reliable output. The technical effect of this invention is to provide a more efficient and reliable method for transforming input values to output values.

Problems solved by technology

However, at the same time, the exponentially weighted moving average is characterized by two main drawbacks: partial transfer of input data in the smoothing direction (on the graph it looks like absence of smoothing of the extreme left input value and a shift in the smoothing direction, on the image it looks like blurring of the original image with a shift to the right) and the exponential shape of the blur that does not look like a conventional Gaussian blur.

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