Mean Filter

Updated 02 Oct 2026

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What it is
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  replaces each pixel with anaverage of neighboring values
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Formula
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  for a $3\times3$ neighborhood, $g(x,y)=\frac19\sum_{i=-1}^{1}\sum_{j=-1}^{1}f(x+i,y+j)$ .
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Properties
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  a linaer smoothing filter with equal weights
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  weights sum to $1$ , preserving a constant region away from boundary effects
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  larger neighborhoods produce stronger smoothing but remove more detail
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Distinguish from
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  Median Filter selects an order statistic rather than averaging
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  Gaussian Blur gives different weights according to distance from the cetner
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Related
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  Spatial Filtering
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  Image Padding
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Linked references 3