Describe what the following MATLAB code does. the original function name has bee

Question

Describe what the following MATLAB code does. the original function name has been replaced by f name. Specify where relevant which expressions in the textbook have been implemented. 20 points function [g x, g y] f name (IM, sigma) % (comment taken out) % [gx.gyl f name(IM, sigma) (comment taken out) epsilon =1e-2; half size=ceil(sigma sqrt(2 pi) sigma epsilon))); size =2 halfsize+1; %(comment taken out) for I =1:size for j=1:size u=[i-halfsize-1j-halfsize -1];h x(I, j)= gauss(u(1)sigma d gauss(u(2),sigma); end h x = h x/sqrt(sum(abs(h x)abs(h x)))); %(comment taken out) g x=Im filter(IM, h x, replicate, con'); g y=I m filter ; function y= gauss(x, sigma) %(comment taken out) y =exp(-x^2(2 sigma sqrt (2 pi)); function y= d gauss(x, sigma) %(comment taken out) y= x gauss (x, sigma/sigma^ 2;

Explanation / Answer

Guassian law modiefied

function [gx,gy]=gaussgradient(IM,sigma)

%GAUSSGRADIENT Gradient using first order derivative of Gaussian.

% [gx,gy]=gaussgradient(IM,sigma) outputs the gradient image gx and gy of

%size.

epsilon=1e-2;

halfsize=ceil(sigma*sqrt(-2*log(sqrt(2*pi)*sigma*epsilon)));

size=2*halfsize+1;

%generate a 2-D Gaussian kernel along x direction

for i=1:size

    for j=1:size

        u=[i-halfsize-1 j-halfsize-1];

        hx(i,j)=gauss(u(1),sigma)*dgauss(u(2),sigma);

    end

end

hx=hx/sqrt(sum(sum(abs(hx).*abs(hx))));

%generate a 2-D Gaussian kernel along y direction

hy=hx';

%2-D filtering

gx=imfilter(IM,hx,'replicate','conv');

gy=imfilter(IM,hy,'replicate','conv');

function y = gauss(x,sigma)

%Gaussian

y = exp(-x^2/(2*sigma^2)) / (sigma*sqrt(2*pi));

function y = dgauss(x,sigma)

%first order derivative of Gaussian

y = -x * gauss(x,sigma) / sigma^2;

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