%function [F, D, Fx, Fy] = filtered_gradient(I, sigma)
%Computes the filtered gradient of the grayscale double image I
%
%Inputs:
%   I: grayscale double image
%   sigma:  scalar sigma value for gaussian smoothing
%Outputs:
%   F:  Magnitude of gradient at each pixel
%   D:  Orientation of gradient at each pixel
%   Fx: Component of gradient in x direction
%   Fy: Component of gradient in x direction
function [F, D, Fx, Fy] = filtered_gradient(I, sigma)

[g, dg] = gaussian(sigma);
Fx = conv2(I, g'*dg, 'same');
Fy = conv2(I, dg'*g, 'same');

F = sqrt(Fx.^2 + Fy.^2);
D = atan(Fy ./ Fx);