How to fit Plane (z=ax+by+c) to 3D point cloud data?

Question

Swati Jain 2017-9-22

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/357947-how-to-fit-plane-z-ax-by-c-to-3d-point-cloud-data

评论： Stephen 2020-6-29

Hi, I am trying to do plane fit to 3D point data. Point cloud file is attached. Here is my code I tried using least square method

clc;
clear all;
close all;
 %%%%%%%%%%%%%%%%%%%%%%%%%%%reading %%%%%%%%%
arr = step_mask('Step_scan01_ex.xlsx','Sheet1', 'A:C');
 %subplot(1,3,1)
x=arr(:,1);
y=arr(:,2);
z=arr(:,3)
plot3(arr(:,1),arr(:,2),arr(:,3),'.'); grid on
xlabel('x(mm)'); ylabel('y(mm)'); zlabel('z(mm)');
title('Masked plot');
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%least squares method %%%%%%%%%%%
   [xnum,ynum]=size(arr);
   % 
   for i = 1: xnum 
   xz (i) = x (i) * z (i);
   yz (i) = y (i) * z (i); 
   xy (i) = x (i) * y (i); 
   end 
   Sxz = sum (sum (xz)); 
   Syz = sum (sum (yz)); 
   Sz = sum (sum (z)); 
   Sxy = sum (sum (xy)); 
   Sx =  ynum*sum (x); 
   Sy =  sum (y); 
   Sx2 = sum (x.^2); 
   Sy2 =  sum (y.^2); 
   A = [Sx2 Sxy Sx; Sxy Sy2 Sy; Sx Sy xnum * ynum]; 
   Z = [Sxz; Syz; Sz]; 
   W = A \ Z; 
   w1 = W (1); 
   w2 = W (2); 
   w3 = W (3); 
   l = - w1/(w1^2 + w2^2 + 1)^0.5; 
   m = - w2/(w1^2 + w2^2 + 1)^0.5; 
   n = 1/(w1^2 + w2^2 + 1)^0.5; 
   p = w3/(w1^2 + w2^2 + 1)^0.5;
   %%%%%%%%%%%%%%%%Generating and displaying the obtained plane %%%%%%%%%
   z_2=zeros(7340,1);
   for i = 1: xnum 
    z_2(i)=(-l/n)*x(i)+(-m/n)*y(i)+(p/n);
    i=i+1;
   end 
a=-l/n;
b=-m/n;
c=p/n;
averagev = sum(sum(z_2))/(xnum * ynum); 
   figure;
   plot3(x,y,z_2,'.'); grid on
   xlabel('x'); ylabel('y'); zlabel('z(mm)');
   title('Fitted Plane');
   sa = abs(z-z_2);
   figure;
  plot3(x,y,sa,'.'); grid on
   xlabel('x'); ylabel('y'); zlabel('z(mm)');
   title('Substracted Plane');

Result of this code is not looking fine to me. Could anyone please suggest what is the best way to fit plane with 3D pint data?

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Answer 1

Star Strider 2017-9-22

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/357947-how-to-fit-plane-z-ax-by-c-to-3d-point-cloud-data#answer_282719

在 MATLAB Online 中打开

Try this:

arr = xlsread('Step_scan01_ex.xls');
x=arr(:,1);
y=arr(:,2);
z=arr(:,3);
DM = [x, y, ones(size(z))];                             % Design Matrix
B = DM\z;                                               % Estimate Parameters
[X,Y] = meshgrid(linspace(min(x),max(x),50), linspace(min(y),max(y),50));
Z = B(1)*X + B(2)*Y + B(3)*ones(size(X));
figure(1)
plot3(arr(:,1),arr(:,2),arr(:,3),'.')
hold on
meshc(X, Y, Z)
hold off
grid on
xlabel('x(mm)'); ylabel('y(mm)'); zlabel('z(mm)');
title('Masked plot');
grid on
text(-20, 50, 450, sprintf('Z = %.3f\\cdotX %+.3f\\cdotY %+3.0f', B))