Problem $1(10$ Points$)$

Given the following image with pixel values appear inside each pixel.

As K$-$means method can be used for image segmentation

$\backslash$table$[[127,92,201,31],[2,23,101,77],[123,255,123,112]]$

The following array represents pixels' color values.

$\backslash$table$[[$Xi Yj Pixel Color,,$],[1,1,127],[1,2,92],[1,3,201],[1,4,31],[2,1,2],[2,2,23],[2,3,101],[2,4,77],[3,1,123],[3,2,255],[3,3,123],[3,4,112]]$

a$)$ You are asked to create two clusters $)=(2$ starting with the following centroids $)=((3,1,123)$ and $)=((2,4,77).$ Construct clusters with their final centroids?

b$)$ After finishing Part a$.$ draw the resulted image based on the final clusters space you achieved?