I have 3d points and I should determine a method to produce and visualize a "center line" down the central axis

Load and visualize the file data (attached). This is data cloud of 3d points . You will want to examine the first "field" coordinates associated with each "node"(x,y,z). The units are in mm. Load the second field "error". Determine a method to produce and visualise a "center line" down the central axis of figure. Determine a method to calculate the radius/diameter of the figure at a number of points down this center line. Provide an estimate of the overall figure "length" and "volume".

[jonas]

This reads like homework

[jonas]

Okay, fair enough. The question reads like an assignment, hence my comment.

[jonas]

What is going on in this thread. Are you trying to delete the question? It's not very polite when Image Analyst gave you so much help.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Image Analyst]

I'd use plot3() to plot the points. Then I'd use pca() to find the central principal component axes, then use plot3() again to plot those axes through the points.

http://www.mathworks.com/matlabcentral/answers/8626-how-do-i-get-help-on-homework-questions-on-matlab-answers

[lalik lavender]

I have a bachelor degree in biomedical science and want to study biomedical engineering thus I am in a first step of using MATLAB.It is not a home work and these data is a stomach 3d data.

Excuse me, but I don't know how to calculate pca of 3D data.

[Image Analyst]

See attached demo that works with 3-D data (an image). See if you can adapt it. Let me know if you still need help.

[Image Analyst]

lalik, haven't heard back from you so I don't know if you were able to figure it out or not. OK, try this:

% Read data.
data = xlsread('dataex.xlsx')
% Plot data.
subplot(1, 2, 1);
x = data(:, 1);
y = data(:, 2);
z = data(:, 3);
plot3(x, y, z, 'b.', 'MarkerSize', 8);
grid on;
title('Original Data', 'FontSize', 20);
xlabel('x', 'FontSize', 20);
ylabel('y', 'FontSize', 20);
zlabel('z', 'FontSize', 20);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

% Get the PC coefficients.
coeffs = pca(data(:, 1:3))
pcs = data(:, 1:3) * coeffs
% Get the data transformed into PC space.
pc1 = pcs(:, 1);
pc2 = pcs(:, 2);
pc3 = pcs(:, 3);
subplot(1, 2, 2);
plot3(pc1, pc2, pc3, 'r.', 'MarkerSize', 8);
grid on;
title('Transformed Data', 'FontSize', 20);
xlabel('PC #1', 'FontSize', 20);
ylabel('PC #2', 'FontSize', 20);
zlabel('PC #3', 'FontSize', 20);

[Image Analyst]

lalik's "Answer" moved here since it's a comment to me rather than an answer to the original question:

Thank you for your answers. I need to determine the central axis of original data, but I don't know how to use transformed data for determining center line of original data! Is it necessary to use pca approach for defining central axis of 3-D data??

[Image Analyst]

See adjusted code to plot the PC axes on the original XYZ data:

clc;    % Clear the command window.
clearvars;
close all;  % Close all figures (except those of imtool.)
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 22;

% Read data.
data = xlsread('dataex.xlsx')
% Plot data.
subplot(1, 2, 1);
x = data(:, 1);
y = data(:, 2);
z = data(:, 3);
plot3(x, y, z, 'b.', 'MarkerSize', 8);
grid on;
title('Original Data', 'FontSize', 20);
xlabel('x', 'FontSize', 20);
ylabel('y', 'FontSize', 20);
zlabel('z', 'FontSize', 20);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0, 0.04, 1, 0.96]);

% Get the PC coefficients.
coeffs = pca(data(:, 1:3))
pcs = data(:, 1:3) * coeffs
% Get the data transformed into PC space.
pc1 = pcs(:, 1);
pc2 = pcs(:, 2);
pc3 = pcs(:, 3);
subplot(1, 2, 2);
plot3(pc1, pc2, pc3, 'r.', 'MarkerSize', 8);
grid on;
title('Transformed Data', 'FontSize', 20);
xlabel('PC #1', 'FontSize', 20);
ylabel('PC #2', 'FontSize', 20);
zlabel('PC #3', 'FontSize', 20);

% Get the max and min of each PC
pc1Min = min(pc1)
pc2Min = min(pc2)
pc3Min = min(pc3)
pc1Max = max(pc1)
pc2Max = max(pc2)
pc3Max = max(pc3)
pc1Mean = mean(pc1)
pc2Mean = mean(pc2)
pc3Mean = mean(pc3)
xMean = mean(x)
yMean = mean(y)
zMean = mean(z)

% Since pcs = xyz * coeffs, to go the other way
% xyz = pcs / coeffs
pc1Limits = [pc1Min - pc1Mean, 0, 0; pc1Max - pc1Mean, 0, 0]
pc2Limits = [0, pc2Min - pc2Mean, 0; 0, pc2Max - pc2Mean, 0]
pc3Limits = [0, 0, pc3Min - pc3Mean; 0, 0, pc3Max - pc3Mean]
xyz1Limit = pc1Limits / coeffs
xyz2Limit = pc2Limits / coeffs
xyz3Limit = pc3Limits / coeffs
% Switch back to subplot 1.
subplot(1, 2, 1);
% Plot the lines along the principal axes.
% Need to add the mean of x, y, and z back in to center the axes.
hold on;
plot3(xyz1Limit(:, 1) + xMean, xyz1Limit(:, 2) + yMean, xyz1Limit(:, 3) + zMean, 'k-', 'LineWidth', 4);
plot3(xyz2Limit(:, 1) + xMean, xyz2Limit(:, 2) + yMean, xyz2Limit(:, 3) + zMean, 'k-', 'LineWidth', 4);
plot3(xyz3Limit(:, 1) + xMean, xyz3Limit(:, 2) + yMean, xyz3Limit(:, 3) + zMean, 'k-', 'LineWidth', 4);

[jordan Ashton]

This was very helpful. I have xyz points from a point cloud that is similar to the above data. I need to fit a cylinder to the data. Ideally it would be something similar to this where I am able to use the x or y data to define the diameter and z for length, and it would have to have the correct axis. Do you have an idea of how I could fit a cylinder to the data so that it is all enclosed? Thank you

[Image Analyst]

You could look at just the x and y points and call convhull. Then find the containing circle with

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects?s_tid=srchtitle

Then take the height of the cylinder from the max and min in the z direction.

[jordan Ashton]

Thank you for your help. I tried this out and it is very close to the final solution I need. However, I believe because my point cloud is at an angle (line of axis is tilted) it is giving me a radius that is larger than expected. Do you know of any way to fix this? Thank you

[jordan Ashton]

Is it also possible to calculate the length of the central axis lines in the orginal example?

[Image Analyst]

@jordan Ashton, start a new question with your code, data, and a screenshot.

[jordan Ashton]

@Image Analyst Okay. Link to question: https://www.mathworks.com/matlabcentral/answers/1682859-find-radius-of-xyz-data