Prewitt operator

The Prewitt operator is an edge detection - filter similar to the Sobel operator named and after Judith MS Prewitt. However, the weighting of the current image line or column is dispensed with. Analogous to the Sobel operator, the edge detector calculates two gradient images and one gray value image in the horizontal and vertical directions : ${\displaystyle \mathbf {G_{x}} }$ ${\displaystyle \mathbf {G_{y}} }$ ${\displaystyle \mathbf {A} }$

${\displaystyle \mathbf {G_{x}} ={\begin{bmatrix}-1&0&+1\\-1&0&+1\\-1&0&+1\end{bmatrix}}*\mathbf {A} }$   and   ${\displaystyle \mathbf {G_{y}} ={\begin{bmatrix}-1&-1&-1\\0&0&0\\+1&+1&+1\end{bmatrix}}*\mathbf {A} }$

The edge thickness and the edge direction are calculated identically to the Sobel filter . ${\displaystyle \mathbf {G} ={\sqrt {\mathbf {G_{x}} ^{2}+\mathbf {G_{y}} ^{2}}}}$ ${\displaystyle \mathbf {\Theta } =\arctan \left({\frac {\mathbf {G_{y}} }{\mathbf {G_{x}} }}\right)}$

The computing time can be reduced by utilizing the separability .

example Pictures

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  Original image

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  Horizontal gradient  ${\displaystyle \mathbf {G_{x}} }$

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  Vertical gradient  ${\displaystyle \mathbf {G_{y}} }$

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  Gradient strength ${\displaystyle \mathbf {G} }$

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  Gradient direction ${\displaystyle \mathbf {\Theta } }$

See also

• Sobel operator
• Roberts operator
• Laplace filter

Individual evidence

1. ^ Judith MS Prewitt: Object enhancement and extraction . In: Bernice Sacks Lipkin and Azriel Rosenfeld (Eds.): Picture Processing and Psychopictorics . Academic Press, New York 1970, pp. 75-149 .