23 lines
1.0 KiB
TeX
23 lines
1.0 KiB
TeX
\section{Moving Average Filter}
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% Basic box filter formula
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% Recursive form
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% Gauss Blur Filter
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% Repetitive Box filter to approx Gauss
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% Simple multipass, n/m approach, extended box filter
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The moving average filter is a simplistic filter which takes an input function $x$ and produces a second function $y$.
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A single output value is computed by taking the average of a number of values symmetrical around a single point in the input.
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The number of values in the average can also be seen as the width $w=2r+1$, where $r$ is the \qq{radius} of the filter.
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The computation of an output value using a moving average filter of radius $r$ is defined as
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\begin{equation}
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\label{eq:symMovAvg}
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y[i]=\frac{1}{2r+1} \sum_{j=-r}^{r}x[i+j] \text{.}
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\end{equation}
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It is well-known that a moving average filter can approximate a Gaussian filter by repetitive recursive computations.
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As is known the Gaussian filter is parametrized by its standard deviation $\sigma$.
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To approximate a Gaussian filter one needs to express a given $\sigma$ in terms of moving average filters.
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