--- /dev/null
+## 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
+
+
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff