MATLAB: Detect the centerline of 3D data points

Question

Hello, everyone. I am trying to detect the centerline of a set of 3D points. These 3D points are plotted and the figure is attached.

Does anybody know how to detect the centerline of these 3D data points. The equation of this centerline may be z = k1*x+k2*y+b; The coordinates of the 3D points are stored in X, Y, Z.

Answer 1

If the parametric equations for the line is L(t)=m+t*d, the following should give a good estimate of m and d, as long as the sampling of the surface is uniformly distributed,

A=[X(:),Y(:),Z(:)];
 m=mean(A,1).';
 A=A-m.';
   [~,~,V]=svd(A,0);
    d=V(:,1);