/
test_mex.m
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test_mex.m
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clearvars; clc; close all;
% This script will just plot the scalar fields and check the derivatives
% using FEM (central differences).
ydim = 512;
xdim = 511;
% 2D Grid
[v, u] = ndgrid(1:ydim, 1:xdim);
xstep = 1 / (0.5 * (xdim - 1));
ystep = 1 / (0.5 * (ydim - 1));
X = (u - 1) .* xstep - 1; % [-1, 1]
Y = (v - 1) .* ystep - 1; % [-1, 1]
% [ X, Y, xstep, ystep ] = ndgrid_normalized( xdim, ydim );
%HERMITE NOISE
figure;
noise = Hermite2D(X, Y);
imshow(noise, [min(noise(:)) max(noise(:))]);
title('Hermite2D');
% 2D Gradient
[noise_deriv, gradNoise] = Hermite2DDeriv(X, Y);
figure;
plot_2D_scalar_and_grad(noise_deriv, gradNoise);
title('Hermite2DDeriv');
err = abs(noise_deriv - noise);
assert(max(err(:)) < 1e-6, ...
'scalar field from Hermite2DDeriv does not match Hermite2D!');
% Check the gradient using finite differences (central)
epsilon = 1e-6;
[pos, ~] = Hermite2DDeriv(X + epsilon, Y);
[neg, ~] = Hermite2DDeriv(X - epsilon, Y);
dx = (pos - neg) / (2 * epsilon);
[pos, ~] = Hermite2DDeriv(X, Y + epsilon);
[neg, ~] = Hermite2DDeriv(X, Y - epsilon);
dy = (pos - neg) / (2 * epsilon);
gradNoiseFEM = permute(cat(3, dx, dy), [3 1 2]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-8, 'FEM derivative does not match!');
% Also check the gradient using Matla's approximation
[dx, dy] = gradient(noise_deriv, xstep, ystep);
gradNoiseFEM = permute(cat(3, dx, dy), [3 1 2]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-3, 'FEM derivative does not match!');
%PERLIN NOISE TESTS
figure;
noise = Perlin2D(X, Y);
imshow(noise, [min(noise(:)) max(noise(:))]);
title('Perlin2D');
% 2D Gradient
[noise_deriv, gradNoise] = Perlin2DDeriv(X, Y);
figure;
plot_2D_scalar_and_grad(noise_deriv, gradNoise);
title('Perlin2DDeriv');
err = abs(noise_deriv - noise);
assert(max(err(:)) < 1e-6, ...
'scalar field from Perlin2DDeriv does not match Perlin2D!');
% addpath('C:\Users\IggyMenou\Documents\NYU\detection_nets\matlab\export_fig');
% export_fig('grad_field.jpg', gcf, '-jpg', '-a4');
% Check the gradient using finite differences (central)
epsilon = 1e-6;
[pos, ~] = Perlin2DDeriv(X + epsilon, Y);
[neg, ~] = Perlin2DDeriv(X - epsilon, Y);
dx = (pos - neg) / (2 * epsilon);
[pos, ~] = Perlin2DDeriv(X, Y + epsilon);
[neg, ~] = Perlin2DDeriv(X, Y - epsilon);
dy = (pos - neg) / (2 * epsilon);
gradNoiseFEM = permute(cat(3, dx, dy), [3 1 2]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-8, 'FEM derivative does not match!');
% Also check the gradient using Matla's approximation
[dx, dy] = gradient(noise_deriv, xstep, ystep);
gradNoiseFEM = permute(cat(3, dx, dy), [3 1 2]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-3, 'FEM derivative does not match!');
% 3D Grid
xdim = 63;
ydim = 64;
zdim = 65;
[D, V, U] = ndgrid(1:zdim, 1:ydim, 1:xdim);
X = 2 * (U - 1) ./ (xdim - 1) - 1; % [-1, 1]
Y = 2 * (V - 1) ./ (ydim - 1) - 1; % [-1, 1]
Z = 2 * (D - 1) ./ (zdim - 1) - 1; % [-1, 1]
%HERMITE 3D NOISE
figure;
noise = Hermite3D(X, Y, Z);
plot_3D_scalar(noise);
title('Hermite3D');
% 3D Gradient
[noise_deriv, gradNoise] = Hermite3DDeriv(X, Y, Z);
err = abs(noise_deriv - noise);
assert(max(err(:)) < 1e-6, ...
'scalar field from Hermite3DDeriv does not match Hermite3D!');
figure;
plot_3D_scalar_and_grad(noise_deriv, gradNoise);
title('Hermite3DDeriv');
set(gcf,'Renderer','OpenGL')
title('Hermite3DDeriv');
% Check the gradient using finite differences (central)
epsilon = 1e-6;
[pos, ~] = Hermite3DDeriv(X + epsilon, Y, Z);
[neg, ~] = Hermite3DDeriv(X - epsilon, Y, Z);
dx = (pos - neg) / (2 * epsilon);
[pos, ~] = Hermite3DDeriv(X, Y + epsilon, Z);
[neg, ~] = Hermite3DDeriv(X, Y - epsilon, Z);
dy = (pos - neg) / (2 * epsilon);
[pos, ~] = Hermite3DDeriv(X, Y, Z + epsilon);
[neg, ~] = Hermite3DDeriv(X, Y, Z - epsilon);
dz = (pos - neg) / (2 * epsilon);
gradNoiseFEM = permute(cat(4, dx, dy, dz), [4 1 2 3]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-8, 'FEM derivative does not match!');
%PERLIN 3D NOISE
figure;
noise = Perlin3D(X, Y, Z);
plot_3D_scalar(noise);
title('Perlin3D');
% 3D Gradient
[noise_deriv, gradNoise] = Perlin3DDeriv(X, Y, Z);
err = abs(noise_deriv - noise);
assert(max(err(:)) < 1e-6, ...
'scalar field from Perlin3DDeriv does not match Perlin3D!');
figure;
plot_3D_scalar_and_grad(noise_deriv, gradNoise);
title('Perlin3DDeriv');
set(gcf,'Renderer','OpenGL')
title('Perlin3DDeriv');
% Check the gradient using finite differences (central)
epsilon = 1e-6;
[pos, ~] = Perlin3DDeriv(X + epsilon, Y, Z);
[neg, ~] = Perlin3DDeriv(X - epsilon, Y, Z);
dx = (pos - neg) / (2 * epsilon);
[pos, ~] = Perlin3DDeriv(X, Y + epsilon, Z);
[neg, ~] = Perlin3DDeriv(X, Y - epsilon, Z);
dy = (pos - neg) / (2 * epsilon);
[pos, ~] = Perlin3DDeriv(X, Y, Z + epsilon);
[neg, ~] = Perlin3DDeriv(X, Y, Z - epsilon);
dz = (pos - neg) / (2 * epsilon);
gradNoiseFEM = permute(cat(4, dx, dy, dz), [4 1 2 3]);
err = abs(gradNoiseFEM - gradNoise);
assert(max(err(:)) < 1e-8, 'FEM derivative does not match!');
% Now just do a time series of a 3D grid (because I can't visualize 4D
% noise :-) )
figure;
for i = 1:4
subplot(2,2,i);
W = ones(size(X,1), size(X,2), size(X,3)) * i;
noise = Perlin4D(X, Y, Z, W);
plot_3D_scalar(noise);
title(['Perlin4D w=', num2str(i)]);
end
disp('Tests pass!');