Home > functions > common > morphology > vb_ellipsoid_check.m

vb_ellipsoid_check

PURPOSE ^

SYNOPSIS ^

function [Ncor,r,U,S] = vb_ellipsoid_check(xyz, Vol, R)

DESCRIPTION ^

INPUTS:
  xyz:  an N*3 array of N points contained in cluster
 Vol : Volume of ellipsoid

OUTPUTS:
  U: eigenvector (principal direction)
  r :radius of principal axis for Vol
 Ncor : Number of points inside the ellipsoid

 Copyright (C) 2011, ATR All Rights Reserved.
 License : New BSD License(see VBMEG_LICENSE.txt)

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [Ncor,r,U,S] = vb_ellipsoid_check(xyz, Vol, R)
0002 %
0003 %INPUTS:
0004 %  xyz:  an N*3 array of N points contained in cluster
0005 % Vol : Volume of ellipsoid
0006 %
0007 %OUTPUTS:
0008 %  U: eigenvector (principal direction)
0009 %  r :radius of principal axis for Vol
0010 % Ncor : Number of points inside the ellipsoid
0011 %
0012 % Copyright (C) 2011, ATR All Rights Reserved.
0013 % License : New BSD License(see VBMEG_LICENSE.txt)
0014 
0015 N   = size(xyz,1);
0016 X0  = sum(xyz)/N;
0017 xyz = xyz - repmat(X0, [N 1]);
0018 
0019 % covariance matrix
0020 XX  = xyz'*xyz;
0021 
0022 % eigenvector of covariance matrix
0023 [U, S] = eig(XX);
0024 
0025 % eigenvalue of covariance matrix
0026 S = sqrt(diag(S));
0027 
0028 if exist('R','var'),
0029     R = sort(R);
0030     [S, ix] = sort(S);
0031     U = U(:,ix);
0032     S = R;
0033 end;
0034 
0035 
0036 % Vol = (4*pi/3)*R^3 = (4*pi/3)*r(1)*r(2)*r(3)
0037 R3 = Vol*(3/pi*4);
0038 
0039 % radius of principal axis for Vol
0040 r = S*(R3/prod(S))^(1/3);
0041 
0042 % transform to principal coordinate
0043 y = xyz*U;
0044 
0045 % normalized radius
0046 dd = (y(:,1)/r(1)).^2 + (y(:,2)/r(2)).^2 + (y(:,3)/r(3)).^2 ;
0047 
0048 % find inside of ellipsoid
0049 ix = find( dd <= 1 );
0050 
0051 % Number of points inside the ellipsoid
0052 Ncor = length(ix);
0053 
0054

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