Roberts operator

The Roberts Cross is a simple edge detection - algorithm of image processing and one of the oldest operators. The operator was introduced by Lawrence Roberts in 1963 . Here the difference between crossed pixels is calculated. This is why this operator is also known as the Roberts cross operator . The edge image can be calculated quickly and easily, but the operator is poorly suited for noisy images. It also produces narrower edges than comparable edge detectors.

The operator uses a 2 × 2 matrix as the convolution matrix . If you multiply both by −1, you also get a pair of Roberts filter matrices.

${\displaystyle \mathbf {b'_{x}} =\mathbf {h_{1}} *\mathbf {b} ={\begin{bmatrix}+1&0\\0&-1\end{bmatrix}}*\mathbf {b} }$

${\displaystyle \mathbf {b'_{y}} =\mathbf {h_{2}} *\mathbf {b} ={\begin{bmatrix}0&+1\\-1&0\end{bmatrix}}*\mathbf {b} }$

With as the entrance picture. ${\displaystyle b}$

The edge thickness can then be calculated using. ${\displaystyle b'=|b_{x}'|+|b_{y}'|\!\,}$

In simpler terms, the gradient for each pixel can be calculated as follows: ${\displaystyle b'\!\,}$

${\displaystyle b'(x,y)=|b(x,y)-b(x+1,y+1)|+|b(x+1,y)-b(x,y+1)|\!\,}$

example Pictures

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  Original image

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  Image filtered with h_1

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  Image filtered with h_2

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  Gradient strength image

Individual evidence

1. ^ Machine Perception Of Three-Dimensional Solids