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Iterative Closest Point

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Iterative Closest Point

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30 May 2010 (Updated )

An implementation of various ICP (iterative closest point) features.

demo.m
%% demo.m
%
% Shows a couple of sample registrations using 
% ICP - Iterative Closest Point
%
% Jakob Wilm and Martin Kjer, Technical University of Denmark, 2012

m = 80; % width of grid
n = m^2; % number of points

[X,Y] = meshgrid(linspace(-2,2,m), linspace(-2,2,m));

X = reshape(X,1,[]);
Y = reshape(Y,1,[]);

Z = sin(X).*cos(Y);

% Create the data point-matrix
D = [X; Y; Z];

% Translation values (a.u.):
Tx = 0.5;
Ty = -0.3;
Tz = 0.2;

% Translation vector
T = [Tx; Ty; Tz];

% Rotation values (rad.):
rx = 0.3;
ry = -0.2;
rz = 0.05;

Rx = [1 0 0;
      0 cos(rx) -sin(rx);
      0 sin(rx) cos(rx)];
  
Ry = [cos(ry) 0 sin(ry);
      0 1 0;
      -sin(ry) 0 cos(ry)];
  
Rz = [cos(rz) -sin(rz) 0;
      sin(rz) cos(rz) 0;
      0 0 1];

% Rotation matrix
R = Rx*Ry*Rz;

% Transform data-matrix plus noise into model-matrix 
M = R * D + repmat(T, 1, n);

% Add noise to model and data
rng(2912673);
M = M + 0.01*randn(3,n);
D = D + 0.01*randn(3,n);

%% Run ICP (standard settings)
[Ricp Ticp ER t] = icp(M, D, 15);

% Transform data-matrix using ICP result
Dicp = Ricp * D + repmat(Ticp, 1, n);

% Plot model points blue and transformed points red
figure;
subplot(2,2,1);
plot3(M(1,:),M(2,:),M(3,:),'bo',D(1,:),D(2,:),D(3,:),'r.');
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('Red: z=sin(x)*cos(y), blue: transformed point cloud');

% Plot the results
subplot(2,2,2);
plot3(M(1,:),M(2,:),M(3,:),'bo',Dicp(1,:),Dicp(2,:),Dicp(3,:),'r.');
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('ICP result');

% Plot RMS curve
subplot(2,2,[3 4]);
plot(0:15,ER,'--x');
xlabel('iteration#');
ylabel('d_{RMS}');
legend('bruteForce matching');
title(['Total elapsed time: ' num2str(t(end),2) ' s']);

%% Run ICP (fast kDtree matching and extrapolation)
[Ricp Ticp ER t] = icp(M, D, 15, 'Matching', 'kDtree', 'Extrapolation', true);

% Transform data-matrix using ICP result
Dicp = Ricp * D + repmat(Ticp, 1, n);

% Plot model points blue and transformed points red
figure;
subplot(2,2,1);
plot3(M(1,:),M(2,:),M(3,:),'bo',D(1,:),D(2,:),D(3,:),'r.');
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('Red: z=sin(x)*cos(y), blue: transformed point cloud');

% Plot the results
subplot(2,2,2);
plot3(M(1,:),M(2,:),M(3,:),'bo',Dicp(1,:),Dicp(2,:),Dicp(3,:),'r.');
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('ICP result');

% Plot RMS curve
subplot(2,2,[3 4]);
plot(0:15,ER,'--x');
xlabel('iteration#');
ylabel('d_{RMS}');
legend('kDtree matching and extrapolation');
title(['Total elapsed time: ' num2str(t(end),2) ' s']);

%% Run ICP (partial data)

% Partial model point cloud
Mp = M(:,Y>=0);

% Boundary of partial model point cloud
b = (abs(X(Y>=0)) == 2) | (Y(Y>=0) == min(Y(Y>=0))) | (Y(Y>=0) == max(Y(Y>=0)));
bound = find(b);

% Partial data point cloud
Dp = D(:,X>=0);

[Ricp Ticp ER t] = icp(Mp, Dp, 50, 'EdgeRejection', true, 'Boundary', bound, 'Matching', 'kDtree');

% Transform data-matrix using ICP result
Dicp = Ricp * Dp + repmat(Ticp, 1, size(Dp,2));

% Plot model points blue and transformed points red
figure;
subplot(2,2,1);
plot3(Mp(1,not(b)),Mp(2,not(b)),Mp(3,not(b)),'bo',...
      Mp(1,b),Mp(2,b),Mp(3,b),'go',...
      Dp(1,:),Dp(2,:),Dp(3,:),'r.')
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('Red: z=sin(x)*cos(y), blue: transformed point cloud');

% Plot the results
subplot(2,2,2);
plot3(Mp(1,not(b)),Mp(2,not(b)),Mp(3,not(b)),'bo',...
      Mp(1,b),Mp(2,b),Mp(3,b),'go',...
      Dicp(1,:),Dicp(2,:),Dicp(3,:),'r.');
axis equal;
xlabel('x'); ylabel('y'); zlabel('z');
title('ICP result');

% Plot RMS curve
subplot(2,2,[3 4]);
plot(0:50,ER,'--x');
xlabel('iteration#');
ylabel('d_{RMS}');
legend('partial overlap');
title(['Total elapsed time: ' num2str(t(end),2) ' s']);

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