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| | Authors Anton from Saint-Louis de Kent, loves to spend time ceramics, property developers [http://victorybaptistchurchchildersburg.com/qtoa/index.php?qa=223&qa_1=launch-condo-apartment-launch-properties-new-launch-landed real estate in singapore] singapore and tea tasting. Last month just arrived at Historic Monuments Zone of Querétaro. |
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| A '''separable filter''' in [[image processing]] can be written as product of two more simple filters.
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| Typically a 2-dimensional [[convolution]] operation is separated into 2 onedimensional filters. This reduces the cost of computing the operator.
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| == Examples ==
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| 1. A twodimensional [[smoothing]] filter is separated in this sample:
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| :<math>
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| \frac{1}{3}
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| \begin{bmatrix}
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| 1 \\ 1 \\ 1
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| \end{bmatrix}
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| *
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| \frac{1}{3}
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| \begin{bmatrix}
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| 1 & 1 & 1
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| \end{bmatrix}
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| =
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| \frac{1}{9}
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| \begin{bmatrix}
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| 1 & 1 & 1 \\
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| 1 & 1 & 1 \\
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| 1 & 1 & 1
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| \end{bmatrix}
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| </math>
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| 2. [[Gaussian blur]] (smoothing)
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| :<math>
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| \frac{1}{4}
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| \begin{bmatrix}
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| 1 \\ 2 \\ 1
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| \end{bmatrix}
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| *
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| \frac{1}{4}
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| \begin{bmatrix}
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| 1 & 2 & 1
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| \end{bmatrix}
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| =
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| \frac{1}{16}
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| \begin{bmatrix}
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| 1 & 2 & 1 \\
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| 2 & 4 & 2 \\
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| 1 & 2 & 1
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| \end{bmatrix}</math>
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| 3. [[Sobel operator]] (edge detection)
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| :<math>
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| \mathbf{G_x} = \begin{bmatrix}
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| \quad~ & \quad~ & \quad~ \\[-2.5ex]
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| 1 & 0 & -1 \\
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| 2 & 0 & -2 \\
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| 1 & 0 & -1
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| \end{bmatrix} * A =
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| \begin{bmatrix}
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| 1 \\ 2 \\ 1
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| \end{bmatrix} *
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| \begin{bmatrix}
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| +1 & 0 & -1
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| \end{bmatrix} * A
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| </math>
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| This works also for [[Prewitt operator]].
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| [[Category:Image processing]]
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Revision as of 16:31, 4 March 2014
Authors Anton from Saint-Louis de Kent, loves to spend time ceramics, property developers real estate in singapore singapore and tea tasting. Last month just arrived at Historic Monuments Zone of Querétaro.