using PyPlot
using NtToolBox
# using Autoreload
# arequire("NtToolBox")

n = 256*2;

f0 = load_image("NtToolBox/src/data/hibiscus.png", n);

figure(figsize=(5,5))
imageplot(f0)

cconv = (f, h) -> real(plan_ifft((plan_fft(f)*f).*(plan_fft(h)*h))*((plan_fft(f)*f).*(plan_fft(h)*h)));

# include("NtToolBox/src/ndgrid.jl")
t = [collect(0 : Base.div(n, 2)); collect(-Base.div(n, 2) + 1 : -1)]
(X2, X1) = meshgrid(t, t)
normalize = h -> h./sum(h)
h = sigma -> normalize(exp(-(X1.^2 + X2.^2)./(2*sigma^2)));

blur = (f, sigma) -> cconv(f, h(sigma));

include("NtSolutions/segmentation_1_edge_detection/exo1.jl");

## Insert your code here.

s = [[n]; collect(1:n-1)]
nabla = f -> cat(3, f - f[s, :], f - f[:, s]);

v = nabla(f0);

figure(figsize = (10, 10))
imageplot(v[:,:,1], L"\frac{d}{dx}", [1,2,1])
imageplot(v[:,:,2], L"\frac{d}{dy}", [1,2,2]);

sigma = 1
d = sqrt(sum(nabla(blur(f0, sigma)).^2, 3));

figure(figsize=(5,5))
imageplot(d[:, :]);

include("NtSolutions/segmentation_1_edge_detection/exo2.jl")

## Insert your code here.

include("NtSolutions/segmentation_1_edge_detection/exo3.jl")

## Insert your code here.

function diiv(v)
    v0 = v[:, :, 1]
    v1 = v[:, :, 2]
    t = [collect(2:n); [1]]
    return v0[t, :] - v0 + v1[:,t] - v1
end;

delta = f -> diiv(nabla(f));

figure(figsize=(5,5))
imageplot(delta(f0))

dotp = (a, b) -> sum(a.*b)
@sprintf("Should be 0: %.10f ", (dotp(nabla(f0), nabla(f0)) + dotp(delta(f0), f0)))

sigma = 4
    
figure(figsize = (5, 5))
NtToolBox.plot_levelset(delta(blur(f0, sigma)), 0, f0)

include("NtSolutions/segmentation_1_edge_detection/exo4.jl")

## Insert your code here.

dx = f -> (f[s, :] - f[t, :])./2
dy = f -> transpose(dx(transpose(f)));

s = [collect(2:n); [1]]
t = [[n]; collect(1:n-1)]

d2x = f -> f[s, :] + f[t, :] - 2.*f
d2y = f -> transpose(d2x(transpose(f)))
dxy = f -> dy(dx(f));

hessian = f -> cat(3, d2x(f), dxy(f), d2y(f));

sigma = 6
g = grad(blur(f0, sigma));

H = hessian(blur(f0, sigma));

a = H[:, :, 1:2].*cat(3, g[:, :, 1], g[:, :, 1]) + H[:, :, 2:3].*cat(3, g[:, :, 2], g[:, :, 2]);

figure(figsize=(5,5))
NtToolBox.plot_levelset(sum(a.*g, 3)[:, :], 0, f0);

include("NtSolutions/segmentation_1_edge_detection/exo5.jl")

## Insert your code here.
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