Edge Detection

Automatically detecting edges in images is an important task in image processing. An edge detector takes an input image and generates another image where the edges in the original image are highlighted by gray$/$white colors while other pixels are black. For each $33-$pixel subset $A,$ of an image, we can calculate the magnitude of the gradient at the center pixel of A as a weighted sum of all the values in A $.$ One common technique is called the Sobel operator specified as

$M=\sqrt[\phantom{2}]{s_x^2+s_y^2}$

where $s_x$ and $s_y$ can be defined as$,$

$s_x=\left[\begin{array}{ccc}-1& 0& 1\\ -2& 0& 2\\ -1& 0& 1\end{array}\right]$:$A,$ and $,s_y=\left[\begin{array}{ccc}1& 2& 1\\ 0& 0& 0\\ -1& -2& -1\end{array}\right]$:$A$

Note that the colon in linear algebra means double dot product which is different from its use in MATLAB. So the formula above means that each pixel $s_x$ and $s_y$ will be a weighted sum of the values of the neighboring pixels in the original image using the weights specified in the $33$ matrices above. For example, $s_x$ specifies that the current pixel and its top and bottom neighbors are not used $($weights are zero$),$ while the top right neighbor has a weight of $1$ and the top left has weight of $-1,$ etc. The final output pixel is then the root sum squared $s_x$ and $s_y.$

Create a function called edgy that takes an original image input, and produces a processed image. Both the input and the output argument are grayscale images, that is$,$ matrices of uint$8$ values.

Note that the output has two fewer rows and columns than the input since the pixels in the first and last columns and rows do not have enough neighbors for the required computation.

Here is an example input and output $($click here for the imane$).$Code to call your function $($o

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Variable output has an incorrect value.