Please implement Canny Edge Detector in MatLab.

$1.$ Using a Gaussian filter to smooth a given gray scale image. Your prototype could be S $=$ GaussSmoothing$($I$,$ N$,$ Sigma$).$

$2.$ Once you get the smoothed version of the input image, you need to get the image gradient of it$.$ You can use the Roberts cross or Sobel or whatever to produce the magnitude and direction of your edge map. The prototype could be $[$Mag$,$ Theta$]=$ ImageGradient$($S$).$

$3.$ Determine two thresholds for later edge processing. Use the histogram of the image gradient to find the threshold, although you need some magic numbers, e$.$g$.$ percentageOfNonEdge is the specified percentage of Non$-$edge area in Mag. Prototype could be $[$T low, T high$]=$ FindThreshold$($Mag$,$ percentageOfNonEdge$),$ where You can use T low $=0\mathrm{.}5*$T high.

$4.$ One important idea in Canny edge detector is finding local maxima of image gradient based on nonmaxima supressing techniques. The quantization method and the interpolation method, you can use either of them $($or both of them$).$ You can use a LUT to simplify your implementation. The prototype could be Mag $=$ NonmaximaSupress$($Mag$,$ Theta, method$)$;

$5.$ The nonmaxima supressing techniques will give you quite good $($thin$)$ edges. The next step is to link the edges based on the two thresholds determined before. The high threshold produces strong edges, and the low threshold produces weak edges. The idea of Canny detector is to first recursively link the strong edges. When a strong edge ends, keep growing the weak edges to fill the gaps between strong edges. We$$ve discussed that in class. The prototype could be E $=$ EdgeLinking$($Mag low, Mag high$).$

$6.$ Play with different parameters, mainly, the Gaussian smoothing parameters $($N$,$ Sigma$),$ and percentageOfNonEdge, to see different outputs.

$7.$ See if Canny detector works better than other edge detectors, you$$d better just compare different detectors on different testing images. Here, you can use the functions provided by Matlab, e$.$g$.,$

E $=$ edge$($imginput$,$sobel$)$

E $=$ edge$($imginput$,$roberts$)$

E $=$ edge$($imginput$,$zerocross$)$

$8.$ You can use set$(0,$RecursionLimit$,$N$)$ to specify a larger stack, say N $=1000.$