Apply Sobel, Prewitt, Laplacian of Gaussian, and Canny edge detector on lena image provided with this document. Quantitively analyze the performance $($using RMSE metric$)$ of above$-$mentioned algorithms at five different variance levels $($var$=0\mathrm{.}01,0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}5,1)$ of Gaussian noise $($added to the image manually$).$ Square root of following relation can be used to compute RMSE

MSE $=\frac{1}{R*C}{\displaystyle \underset{i=1}{\overset{R}{}}}{\displaystyle \underset{j=1}{\overset{c}{}}}|f(i,j)-f(i,j){|}^2$

where $R$ indicates the number of image rows and $C$ refers to the number of columns, $f(i,j)$ represents the reference image whereas $f(i,j)$ refers to the image with detected edges using different methods $($with different variance levels of Gaussian noise$).$ Reference image can be the image with edges using a Canny Edge detector $($threshold $=0\mathrm{.}1,$ sigma $=1)$ when there is no Gaussian noise.

Analyze the performance of Canny Edge detector $($in terms of detected edges$)$ with varying threshold value and explain the obtained results.

Briefly discuss the strength of Canny Edge detector over rest of detection schemes mentioned above.

Why directional edge detectors perform better in the images of unconstrained natural environment?