Centreline fitting in 3d (3D line fitting)

Hello everyone,

I've got a centreline data set of a vessel and I want to connect the points to get an estimation of the length, however there are a few anomalous points off the main vessel ( i.e. noise ).

Any thoughts about how to fit the line / remove the points?

So far I was thinking of using the datatip to manually select unwanted points, but this would obviously take ages. I've tried using "smooth3" to clean up the data, but it didn't do much for me.

Here's the image below:

Cheers, Will

Answer 1

[Image Analyst]

What I would try is to calculate the distances from every point to all other points. Then I would sort those distances in order of decreasing distance. Now it looks like some outliers might be fairly close to other outliers but in general the outliers are not close to more than 3 or 4 other outliers. So for a point to be valid, meaning close to a big group of other coordinates, the 5th closest (5th smallest) distance should be closer (smaller) than some specified tolerance distance. If that distance it larger, then it's far away and an outlier. So untested code would be something like

% Extract individual x, y, z vectors from the 3D data array.
allX = xyz(:, 1);
allY = xyz(:, 2);
allZ = xyz(:, 3);
fixed_xyz = xyz; % Initialize our good output array.
largestAllowableDistance = 10;  % Whatever works for you.
for k = 1 : size(xyz, 1)
    thisX = xyz(k, 1);
    thisY = xyz(k, 2);
    thisZ = xyz(k, 3);
    distances = sqrt((thisX-allX).^2 + (thisY-allY).^2 + (thisZ - allZ).^2);
    [sortedDistances, sortOrder] = sort(distances, 'descend');
    if sortedDistances(5) > largestAllowableDistance
        % It's an outlier so remove it.
        fixed_xyz(k, :) = []; % Setting to null removes that row.
    else
        % It's near the curve.
    end
end

[William]

Nice solution :)

Just one thing:

fixed_xyz(k, :) = [];

is included in the loop, so as it removes a row it later miss counts the loop as a matrix dimension mismatch.

Index of element to remove exceeds matrix dimensions

Fitting regardless of this error shows outlier removal.

[Image Analyst]

Instead of the line

fixed_xyz(k, :) = []

just keep track of the rows and delete them all later

rowsToDelete = [];  % Put this before the loop.

In the loop

rowsToDelete  = [rowsToDelete , k];

After the loop delete all the rows you recorded.

fixed_xyz(rowsToDelete, :) = [];

[William]

Not as I presumed... By counting down from max to min we avoid dimension errors but the reduction is just shrinking the z axis not isolating the line

Looks like this atm:

largestAllowableDistance = 110; 

fixed_xyz = zeros(size(x,1), 3);
fixed_xyz(:,1)=x;
fixed_xyz(:,2)=y;
fixed_xyz(:,3)=z;

for k = size(fixed_xyz,1):-1:1
    distances = sqrt((x(k)-x).^2 + (y(k)-y).^2 + (z(k) - z).^2);
    % List distances between every other point
    [sortedDistances, sortOrder] = sort(distances, 'descend');
    % Too sparse if closest distances are far away
    if sortedDistances(5) > largestAllowableDistance
        fixed_xyz(k, :) = [];
    end
end

[Image Analyst]

You forgot to attach your data, x, y, and z, and code to read them in, and your plotting code. Make it easy for me to help you, not hard.

[William]

Here it is:

figure(1)
clf(1)
subplot(1,2,1)
plot3(fixed_xyz(:,2),fixed_xyz(:,1),fixed_xyz(:,3),'square','Markersize',4,'MarkerFaceColor','b','Color','b');
view([44,6])
zlim([0 max(z)])
subplot(1,2,2)
plot3(y,x,z,'square','Markersize',4,'MarkerFaceColor','b','Color','b');            
view([44,6])
zlim([0 max(z)])

[Image Analyst]

Try this:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

storedStructure = load('x.mat');
x = storedStructure.x;
storedStructure = load('y.mat');
y = storedStructure.y;
storedStructure = load('z.mat');
z = storedStructure.z;

% Plot original data.
subplot(1,2, 1)
plot3(y,x,z,'square','Markersize',4,'MarkerFaceColor','b','Color','b');            
title('Original data', 'FontSize', fontSize);
view([44,6])
grid on;
zlim([0 max(z)])
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
drawnow;

% ADJUSTABLE PARAMETERS.
largestAllowableDistance = 10;  % Whatever works for you.
numAllowableNeighbors = 9;

fixed_xyz = [x, y, z]; % Initialize our good output array.
rowsToDelete = [];
for k = 1 : length(x);
    thisX = x(k);
    thisY = y(k);
    thisZ = z(k);
    distances = sqrt((thisX-x).^2 + (thisY-y).^2 + (thisZ - z).^2);
    [sortedDistances, sortOrder] = sort(distances, 'ascend');
    if sortedDistances(numAllowableNeighbors) > largestAllowableDistance
        % It's an outlier so record what row we need to remove.
    rowsToDelete  = [rowsToDelete , k];
  else
        % It's near the curve.
    end
end
% Remove the rows.
fixed_xyz(rowsToDelete, :) = [];

subplot(1,2, 2)
plot3(fixed_xyz(:,2),fixed_xyz(:,1),fixed_xyz(:,3),'square','Markersize',4,'MarkerFaceColor','b','Color','b');
view([44,6])
zlim([0 max(z)])
grid on;
title('Fixed data', 'FontSize', fontSize);

Answer 2

[William]

Super, thanks so much