X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fvrml-1.0.13%2Fbest_dir.m;fp=octave_packages%2Fvrml-1.0.13%2Fbest_dir.m;h=7e999a5d5b79de69b8937583a58c1e24960a4d95;hp=0000000000000000000000000000000000000000;hb=c880e8788dfc484bf23ce13fa2787f2c6bca4863;hpb=1705066eceaaea976f010f669ce8e972f3734b05

diff --git a/octave_packages/vrml-1.0.13/best_dir.m b/octave_packages/vrml-1.0.13/best_dir.m
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+## Copyright (C) 2002 Etienne Grossmann <etienne@egdn.net>
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+##       [d,w,rx,cv,wx] = best_dir( x, [a , sx ] )
+##
+## Some points  x,  are observed and one assumes that they belong to
+## parallel planes. There is an unknown direction  d  s.t. for each
+## point  x(i,:), one has :
+##
+##         x(i,:)*d == w(j(i)) + noise
+##
+## where j is known(given by the matrix  a ), but  w  is unknown.
+##
+## Under the assumption that the error on  x  are i.i.d. gaussian,
+## best_dir() returns the maximum likelihood estimate of  d  and  w.
+##
+## This function is slower when cv is returned.
+##
+## INPUT :
+## -------
+## x  : D x P    P points. Each one is the sum of a point that belongs
+##               to a plane and a noise term.
+##
+## a  : P x W    0-1 matrix describing association of points (rows of 
+##               x) to planes :
+##
+##           a(p,i) == 1 iff point x(p,:) belongs to the i'th plane.
+##
+##                                                Default is ones(P,1)
+## 
+## sx : P x 1    Covariance of x(i,:) is sx(i)*eye(D). 
+##                                                Default is ones(P,1)
+## OUTPUT :
+## --------
+## d  : D x 1    All the planes have the same normal, d. d has unit
+##               norm.
+##
+## w  : W x 1    The i'th plane is { y | y*d = w(i) }.
+##
+## rx : P x 1    Residuals of projection of points to corresponding plane.
+##
+##
+##               Assuming that the covariance of  x  (i.e. sx) was known
+##               only up to a scale factor, an estimate of the
+##               covariance of  x  and  [w;d]  are
+##
+##                 sx * mean(rx.^2)/mean(sx)       and
+##                 cv * mean(rx.^2)/mean(sx),  respectively.
+##
+## cv : (D+W)x(D+W) 
+##               Covariance of the estimator at [d,w] ( assuming that
+##               diag(covariance(vec(x))) == sx ). 
+##
+## wx : (D+W)x(D*P)
+##               Derivatives of [w;d] wrt to x.
+##
+## Author  : Etienne Grossmann <etienne@egdn.net>
+## Created : March 2000
+##
+function [d,w,rx,cv,wx] = best_dir( x, a, sx )
+
+[D,P] = size(x) ;
+## Check dimension of args
+if nargin<2, 
+  a = ones(P,1) ; 
+elseif size(a,1) != P,
+  error ("best_dir : size(a,1)==%d != size(x,2)==%d\n",size(a,1),P);
+  ## keyboard
+end
+if isempty (a)
+  error ("best_dir : a is empty. This will not do!\n");
+  ## keyboard
+end
+
+W = size(a,2) ;
+if nargin<3, 
+  sx = ones(P,1) ;
+else
+  if prod(size(sx)) != P,
+    error ("best_dir : sx has %d elements, rather than P=%d\n",
+	   prod(size(sx)),P);
+    ## keyboard
+  end
+  if !all(sx)>0,
+    error ("best_dir : sx has non positive element\n");
+    ## keyboard
+  end
+end
+sx = sx(:);
+
+
+## If not all points belong to a plane, clean  a.
+
+keep = 0 ;
+if ! all(sum([a';a'])),		# trick for single-column  a
+
+  ## if verbose, printf ("best_dir : Cleaning up useless rows of 'a'\n"); end
+  keep = find(sum([a';a'])) ;
+  ## [d,w,cv] = best_dir(x(keep,:),a(keep,:),sx(keep)) ;
+  ## return ;
+  x = x(:,keep);
+  a = a(keep,:);
+  sx = sx(keep);
+  P_orig = P ;
+  P = prod(size(keep));
+end
+
+## If not all planes are used, remove some rows of a.
+if !all(sum(a)),
+  keep = find(sum(a)) ;
+  if nargout >= 4, 
+    [d,ww,rx,cv2] = best_dir(x,a(:,keep),sx) ;
+    cv = zeros(W+D,W+D) ;
+    cv([1:3,3+keep],[1:3,3+keep]) = cv2 ;
+  else             
+    [d,ww,rx]    = best_dir(x,a(:,keep),sx) ;
+  end
+  w = zeros(W,1);
+  w(keep) = ww ;
+  return
+end
+## Now,  a  has rank  W  for sure.
+
+## tmp = diag(1./sx) ;
+tmp = (1./sx)*ones(1,W) ;
+tmp2 = inv(a'*(tmp.*a))*(a.*tmp)' ; ;
+tmp = x*(eye(P) - tmp2'*a') ; 
+## tmp = tmp*diag(1./sx)*tmp' ;
+tmp = (tmp.*(ones(D,1)*(1./sx)'))*tmp' ;
+
+[u,S,v] = svd(tmp) ;
+d = v(:,D) ;
+w = tmp2*x'*d ;
+
+rx = (x'*d - a*w) ;
+
+if nargout >= 4,
+  wd = [w;d];
+  ## shuffle = ( ones(D,1)*[0:P-1]+[1:P:P*D]'*ones(1,P) )(:) ;
+  ## [cv,wx] = best_dir_cov(x',a,sx,wd) ;
+  ## ## wx = wx(:,shuffle) ;
+
+  [cv,wx] = best_dir_cov(x,a,sx,wd) ;
+
+  ##  [cv2,wx2] = best_dir_cov2(x,a,sx,wd) ;
+  ##    if any(abs(cv2(:)-cv(:))>eps),
+  ##      printf("test cov : bug 1\n") ;
+  ##      keyboard
+  ##    end
+  ##    if any(abs(wx2(:)-wx(:))>eps),
+  ##      printf("test cov : bug 2\n") ;
+  ##      keyboard
+  ##    end
+
+end
+
+
+if keep,
+  tmp = zeros(P_orig,1) ;
+  tmp(keep) = rx ; 
+  rx = tmp ;
+  if nargout >= 5,
+    k1 = zeros(1,P_orig) ; k1(keep) = 1 ; k1 = kron(ones(1,D),k1) ;
+    tmp = zeros(D+W,P_orig*D) ;
+    tmp(:,k1) = wx ;
+    wx = tmp ;
+  end
+end
+
+endfunction
+
+