Description of demo_estimate_Point_2D_from

0001 %% demo_estimate_Point_2D_from_Lines
0002 %
0003 % see Sect. 10.6.2.1, Figs. 10.24-10.26
0004 %
0005 % four types of estimation of intersection point (vanishing point)
0006 %       ALGe algebraic Euclideanly
0007 %       ALGs algebraic spherically
0008 %       SSDe geometric Euclideanly
0009 %       MLEe ML Euclideanly
0010 %       MLEs ML spherically
0011 %
0012 % comparison of empirical and theoretical covariance matrices
0013 %
0014 % Wolfgang Förstner
0015 % wfoerstn@uni-bonn.de
0016 %
0017 % last changes: Susanne Wenzel 06/18
0018 % wenzel@igg.uni-bonn.de
0019 
0020 addpath(genpath('../../General-Functions'))
0021 
0022 global min_redundancy
0023 global plot_option
0024 global print_option
0025 global print_option_estimation
0026 
0027 close all
0028 % clear all
0029 clearvars
0030 clc
0031 
0032 sugr_INIT
0033 ss = plot_init;
0034 min_redundancy=100000;
0035 
0036 disp('=====================================================================')
0037 disp('   Point estimation (geometric, ALG, ML; Euclideanly, spherically)   ')
0038 disp('                    Figures 10.24 - 10.26                            ')
0039 disp('---------------------------------------------------------------------')
0040 
0041 %% Control parameters
0042 N_samples     = 100;                  % number of cases (for first trial)
0043 %N_samples     = 1000;                  % number of cases
0044 disp(strcat('Number of samples            : ' , num2str(N_samples)));
0045 
0046 % sample sizes
0047 N             = 50;                   % number of lines per case
0048 disp(strcat('Number of lines              : ' , num2str(N)));
0049 
0050 % parameters for line generation
0051 d             = 1.0;                  % size of square [-d,+d]^2 image wrt c=1
0052 resolution    = 1000;                 % number of pixels per d
0053 
0054 
0055 disp(strcat('Size of image                : ' , num2str(resolution)));
0056 
0057 %
0058 lengthq       = 200;                  % average length of line segments
0059 disp(strcat('Average length of lines      : ' , num2str(lengthq)));
0060 sigma         = 1.0;                  % std. dev. of pixels on line
0061 disp(strcat('Std. dev. of pixels on lines : ' , num2str(sigma)));
0062 
0063 % initial seed
0064 init_rand      = 11;                  % random seed
0065 
0066 % type of simulation
0067 sim_type = 0; % close unknown point  -->  Figs. 10.24-10.25
0068 %sim_type = 1; % far unknown point     -->  Fig.  10.26
0069 
0070 % factor for plotting the standard ellipses
0071 factor_p      = 1000;   
0072 
0073 % rigorous variance propagation for observed line segment
0074 %rigorous      = 0;
0075 rigorous      = 1;
0076 
0077 %% initialize random seed
0078 init_rand_seed(init_rand);
0079 
0080 %% Generate lines
0081 
0082 if N_samples >1 
0083     print_option_estimation=0;
0084 end
0085 %
0086 switch sim_type
0087     case 0
0088         x_tilde_e      =[1.3;1.7];
0089     case 1
0090         x_tilde_e     = [0,200]';
0091 end
0092 disp(strcat('True point                   : [',num2str(x_tilde_e(1)),',',num2str(x_tilde_e(2)),']'));
0093 
0094 %
0095 x_tilde       = sugr_Point_2D(x_tilde_e,10^-10*eye(2));   % true point
0096 
0097 % -------------------------------------------------------------------------
0098 % generate true lines
0099 lines = sugr_generate_true_Lines_2D_one_Point(x_tilde.h,d,N,lengthq,resolution);
0100 
0101 % show representatative result
0102 plot_option = 2;                                                           %#ok<NASGU>
0103 print_option = 2;                                                          %#ok<NASGU>
0104 
0105 if sim_type == 0    
0106     
0107     figure('name','estimate intersection points','Color','w','Position',[10,50,0.5*ss(1),0.85*ss(2)])
0108     subplot(3,2,1)
0109     hold on
0110     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);    
0111     title('Original line segments')
0112     
0113     subplot(3,2,2)
0114     hold on
0115     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0116     
0117     subplot(3,2,3)
0118     hold on
0119     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0120         
0121     subplot(3,2,4)
0122     hold on
0123     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0124         
0125     subplot(3,2,5)
0126     hold on
0127     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0128     
0129     subplot(3,2,6)
0130     hold on
0131     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0132     
0133 end
0134 
0135 % do not plot samples in the following
0136 plot_option  = 0;
0137 print_option = 0;
0138 % -------------------------------------------------------
0139 est_x_samples_aE = zeros(N_samples,2);
0140 sigma_2_aE_D     = zeros(N_samples,1);
0141 sigma_2_aE_O     = zeros(N_samples,1);
0142 
0143 est_x_samples_a = zeros(N_samples,2);
0144 sigma_2_a_D     = zeros(N_samples,1);
0145 sigma_2_a_O     = zeros(N_samples,1);
0146 
0147 est_x_samples_g = zeros(N_samples,2);
0148 sigma_2_g_D     = zeros(N_samples,1);
0149 sigma_2_g_O     = zeros(N_samples,1);
0150 
0151 est_x_samples_g_x = zeros(N_samples,2);
0152 sigma_2_g         = zeros(N_samples,1);
0153 
0154 est_x_samples_ml = zeros(N_samples,2);
0155 sigma_2_ml        = zeros(N_samples,1);
0156 sigma_2_ml_D     = zeros(N_samples,1);
0157 sigma_2_ml_O     = zeros(N_samples,1);
0158 
0159 est_x_samples_mH = zeros(N_samples,2);
0160 sigma_2_mH        = zeros(N_samples,1);
0161 sigma_2_mH_D     = zeros(N_samples,1);
0162 sigma_2_mH_O     = zeros(N_samples,1);
0163 
0164 start = cputime;
0165 for n = 1:N_samples
0166      if N_samples < 100
0167         fprintf(num2str(n)),fprintf(',')
0168         if mod(n,10) == 0
0169             disp(' ')
0170         end
0171     else
0172         if mod(n,10) == 0
0173             fprintf(num2str(n)),fprintf(',')
0174         end
0175         if mod(n,100) == 0
0176             disp(' ')
0177         end
0178     end
0179     % perturb lines
0180     lstruct = sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0181     
0182     
0183     %% Estimate point algebraically - Euclideanly
0184     [est_p_aE,sigma_0_est_DE,sigma_0_est_OE] = ...
0185         sugr_estimation_algebraic_Point_2D_from_Lines(lstruct,0);
0186     est_x_aE_e = est_p_aE.h(1:2)'/est_p_aE.h(3);
0187     est_x_samples_aE(n,:) = est_x_aE_e;
0188     sigma_2_aE_D(n) = sigma_0_est_DE^2;
0189     sigma_2_aE_O(n) = sigma_0_est_OE^2;    
0190     
0191     if sim_type == 0
0192         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')
0193         
0194         subplot(3,2,2)
0195         hold on
0196         plot(x_tilde_e(1)+factor_p*(est_x_aE_e(1)-x_tilde_e(1))/3,...
0197             x_tilde_e(2)+factor_p*(est_x_aE_e(2)-x_tilde_e(2))/3,'.g');
0198     end
0199     
0200     %% Estimate point algebraically - spherically
0201     [est_p_a,sigma_0_est_D,sigma_0_est_O] = ...
0202         sugr_estimation_algebraic_Point_2D_from_Lines(lstruct,1);
0203     est_x_a_e = est_p_a.h(1:2)'/est_p_a.h(3);
0204     est_x_samples_a(n,:) = est_x_a_e;
0205     sigma_2_a_D(n) = sigma_0_est_D^2;
0206     sigma_2_a_O(n) = sigma_0_est_O^2;    
0207     
0208     if sim_type == 0
0209         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')        
0210         
0211         subplot(3,2,3)
0212         hold on
0213         plot(x_tilde_e(1)+factor_p*(est_x_a_e(1)-x_tilde_e(1))/3,...
0214             x_tilde_e(2)+factor_p*(est_x_a_e(2)-x_tilde_e(2))/3,'.g');
0215     end
0216     
0217     %% Estimate point geometrically
0218     [est_p_g,sigma_0_g,xe] = sugr_estimation_geometric_Point_2D_from_Lines(lstruct);
0219     est_x_g_e              = est_p_g.h(1:2)'/est_p_g.h(3);
0220     est_x_samples_g(n,:)   = est_x_g_e;
0221     est_x_samples_g_x(n,:) = xe;
0222     sigma_2_g(n)           = sigma_0_g^2;
0223     
0224     if sim_type == 0
0225         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')        
0226         
0227         subplot(3,2,4)
0228         hold on
0229         plot(x_tilde_e(1)+factor_p*(est_x_g_e(1)-x_tilde_e(1))/3,...
0230             x_tilde_e(2)+factor_p*(est_x_g_e(2)-x_tilde_e(2))/3,'.g');
0231     end
0232     
0233     %% estimate ML
0234     T = 0.01;
0235     maxiter = 3;
0236     [est_p_ml,sigma_0_ml,~] = sugr_estimation_ml_Point_2D_from_Lines(lstruct,est_p_a.h,T,maxiter);
0237     [est_x_ml_e,Cxx_ml]     = sugr_get_Euclidean_Point_2D(est_p_ml);
0238     est_x_samples_ml(n,:)   = est_x_ml_e;
0239     sigma_2_ml(n)           = sigma_0_ml^2;
0240     
0241     if sim_type == 0
0242         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')
0243         
0244         subplot(3,2,5)
0245         hold on
0246         plot(x_tilde_e(1)+factor_p*(est_x_ml_e(1)-x_tilde_e(1))/3,...
0247             x_tilde_e(2)+factor_p*(est_x_ml_e(2)-x_tilde_e(2))/3,'.g');
0248     end
0249     %% estimate ML-Hessian
0250     T = 0.01;
0251     maxiter = 3;
0252     [est_p_mH,sigma_0_mH,R] = sugr_estimation_ml_Point_2D_from_Lines_Hessian(lstruct,est_p_a.h,T,maxiter);
0253     [est_x_mH_e,Cxx_mH]  = sugr_get_Euclidean_Point_2D(est_p_mH);
0254     est_x_samples_mH(n,:) = est_x_mH_e;
0255     sigma_2_mH(n) = sigma_0_mH^2;    
0256     
0257     if sim_type == 0
0258         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')        
0259         
0260         subplot(3,2,6)
0261         hold on
0262         plot(x_tilde_e(1)+factor_p*(est_x_mH_e(1)-x_tilde_e(1))/3,...
0263              x_tilde_e(2)+factor_p*(est_x_mH_e(2)-x_tilde_e(2))/3,'.g');        
0264         
0265         plot([-2,-2,2,2,-2],[-2,2,2,-2,-2],'-b')
0266     end
0267 end
0268 disp(['CPU time for ', num2str(N_samples),' samples              : ',num2str(cputime-start)]);
0269 
0270 %% Analyse samples
0271 [x_aE_e,Cxx_aE_e] = sugr_get_Euclidean_Point_2D(est_p_aE);
0272 [x_a_e, Cxx_a_e]  = sugr_get_Euclidean_Point_2D(est_p_a);
0273 [x_g_e, Cxx_g_e]  = sugr_get_Euclidean_Point_2D(est_p_g);
0274 [x_ml_e,Cxx_ml_e] = sugr_get_Euclidean_Point_2D(est_p_ml);
0275 [x_mH_e,Cxx_mH_e] = sugr_get_Euclidean_Point_2D(est_p_mH);
0276 
0277 if N_samples > 2
0278     %% determine empirtical means and covariance matrices
0279     est_x_mean_aE  = mean(est_x_samples_aE);
0280     est_x_cov_aE   = cov(est_x_samples_aE);
0281     est_x_mean_a   = mean(est_x_samples_a);
0282     est_x_cov_a    = cov(est_x_samples_a);
0283     est_x_mean_g   = mean(est_x_samples_g);
0284     est_x_cov_g    = cov(est_x_samples_g);
0285     est_x_mean_ml  = mean(est_x_samples_ml);
0286     est_x_cov_ml   = cov(est_x_samples_ml);
0287     est_x_mean_mH  = mean(est_x_samples_mH);
0288     est_x_cov_mH   = cov(est_x_samples_mH);
0289     
0290     mean_sigma_2_a_OE = mean(sigma_2_aE_O);
0291     mean_sigma_2_a_DE = mean(sigma_2_aE_D);
0292     mean_sigma_2_a_O  = mean(sigma_2_a_O);
0293     mean_sigma_2_a_D  = mean(sigma_2_a_D);
0294     mean_sigma_2_g    = mean(sigma_2_g);
0295     mean_sigma_2_ml_Euclidean   = mean(sigma_2_ml);
0296     mean_sigma_2_ml_spherical   = mean(sigma_2_mH);
0297     
0298     %%
0299     est_p_aE_emp    = sugr_Point_2D(est_x_mean_aE', est_x_cov_aE);
0300     est_p_a_emp     = sugr_Point_2D(est_x_mean_a', est_x_cov_a);
0301     est_p_g_emp     = sugr_Point_2D(est_x_mean_g', est_x_cov_g);
0302     est_p_ml_emp    = sugr_Point_2D(est_x_mean_ml',est_x_cov_ml);
0303     est_p_mH_emp    = sugr_Point_2D(est_x_mean_mH',est_x_cov_mH);    
0304     
0305     if sim_type == 0
0306         subplot(3,2,1)
0307         if sim_type == 0
0308             xlim([-2.2,+2.5])
0309             ylim([-2.2,2.9])
0310         end
0311         
0312         subplot(3,2,2)
0313         
0314         title('ALGe emp (green) - ALGe theor (blue)')
0315         hold on
0316         sugr_plot_Point_2D(est_p_aE_emp,'ok','-g',2,factor_p);
0317         hold on
0318         sugr_plot_Point_2D(est_p_aE,'ok','-b',1,factor_p);
0319         axis equal
0320         if sim_type == 0
0321             xlim([-2.2,+2.5])
0322             ylim([-2.2,2.9])
0323         end
0324         
0325         subplot(3,2,3)
0326         
0327         title('ALGs')
0328         hold on
0329         %sugr_plot_Point_2D(est_p_a_emp,'ok','-g',2,factor_p);
0330         hold on
0331         sugr_plot_Point_2D(est_p_a,'ok','-k',1,factor_p);
0332         axis equal
0333         if sim_type == 0
0334             xlim([-2.2,+2.5])
0335             ylim([-2.2,2.9])
0336         end
0337         
0338         subplot(3,2,4)
0339         title('SSDe')
0340         hold on
0341         %sugr_plot_Point_2D(est_p_g_emp,'ok','-g',2,factor_p);
0342         hold on
0343         %sugr_plot_Point_2D(est_p_g,'ok','-b',1,factor_p);
0344         axis equal
0345         if sim_type == 0
0346             xlim([-2.2,+2.5])
0347             ylim([-2.2,2.9])
0348         end
0349         
0350         subplot(3,2,5)
0351         title('MLEe')
0352         % sugr_plot_Point_2D(est_p_mH_emp,'ok','-g',2,factor_p);
0353         hold on
0354         sugr_plot_Point_2D(est_p_mH,'ok','-k',1,factor_p);
0355         axis equal
0356         if sim_type == 0
0357             xlim([-2.2,+2.5])
0358             ylim([-2.2,2.9])
0359         end        
0360         
0361         subplot(3,2,6)
0362         title('MLEs (green) - ALGs (dashed)')
0363         sugr_plot_Point_2D(est_p_a,'ok','--k',1,factor_p);
0364         hold on
0365         sugr_plot_Point_2D(est_p_ml,'ok','-k',1,factor_p);
0366         axis equal
0367         if sim_type == 0
0368             xlim([-2.2,+2.5])
0369             ylim([-2.2,2.9])
0370         end
0371     end
0372     
0373 % % distance between the covariance matrices
0374 % distance_a_emp= exp(sqrt(sum(log(eigs(inv(Cxx_a_e)*est_x_cov_a)).^2)/2)/2)
0375 % distance_g_emp= exp(sqrt(sum(log(eigs(inv(Cxx_g_e)*est_x_cov_g)).^2)/2)/2)
0376 %
0377 % distance_a_ml = exp(sqrt(sum(log(eigs(inv(Cxx_ml_e)* Cxx_a_e )).^2)/2)/2)
0378 % distance_g_ml = exp(sqrt(sum(log(eigs(inv(Cxx_ml_e)* Cxx_g_e )).^2)/2)/2)
0379 end
0380 
0381 %% final distribution of points
0382 
0383 % algebraic solution
0384 if N_samples > 2
0385 %% show histograms
0386     figure('name','Histogramms','Color','w','Position',[ss(1)/2,0.3*ss(2),0.5*ss(1),0.6*ss(2)])   
0387     N_bin = ceil(sqrt(N_samples));
0388     
0389     subplot(3,2,2)
0390     hist(sigma_2_a_D,N_bin);
0391     title('Variance ALGe')
0392     
0393     subplot(3,2,3)
0394     hist(sigma_2_aE_D,N_bin);
0395     title('Variance ALGs')
0396     
0397     subplot(3,2,4)
0398     hist(sigma_2_g,N_bin);
0399     title('Variance SSDe')
0400     
0401     subplot(3,2,5)
0402     hold on
0403     hist(sigma_2_mH,N_bin);
0404     [~,r] = hist(sigma_2_mH,N_bin);
0405     %r=2*(1:ceil(sqrt(N_samples))-1/2)/N_bin;
0406     range = abs(r(N_bin)-r(1));
0407     plot(r,N_bin*range*fpdf(r,R,10000),'-r','LineWidth',2);
0408     
0409     title('Variance factor MLEe')
0410     
0411     subplot(3,2,6)
0412     hold on
0413     hist(sigma_2_ml,N_bin);
0414     [NN,r] = hist(sigma_2_ml,N_bin);
0415     %r=2*(1:ceil(sqrt(N_samples))-1/2)/N_bin;
0416     range = abs(r(N_bin)-r(1));
0417     plot(r,N_bin*range*fpdf(r,R,10000),'-r','LineWidth',2);
0418     
0419     title('Variance factor MLEs')
0420 
0421     %%  show
0422     figure('name','Distribution of points','Color','w','Position',[100,20,0.6*ss(1),0.82*ss(2)])
0423     plot_option=1;
0424     subplot(3,2,1)
0425     hold on
0426     title('Straight line segments')
0427     sugr_perturb_Lines_2D(x_tilde.h,d,lines,resolution,sigma,rigorous);
0428 
0429     subplot(3,2,2)
0430     hold on
0431     title('ALGe')
0432     for n=1:N_samples
0433         plot(est_x_mean_aE(1)+(est_x_samples_aE(n,1)-est_x_mean_aE(1)),...
0434             est_x_mean_aE(2)+(est_x_samples_aE(n,2)-est_x_mean_aE(2)),'.k');
0435     end
0436     sugr_plot_Point_2D(est_p_aE_emp,'ok','--k',1,3);
0437 
0438     plot(est_x_mean_aE(1),est_x_mean_aE(2),'ow','MarkerSize',12,'LineWidth',7);
0439     plot(est_x_mean_aE(1),est_x_mean_aE(2),'ok','MarkerSize',12,'LineWidth',3);
0440 
0441     plot(x_tilde.h(1)/x_tilde.h(3),x_tilde.h(2)/x_tilde.h(3),'+k','MarkerSize',10,'LineWidth',1);
0442 
0443     xlim_aE=xlim;
0444     ylim_aE=ylim;
0445 
0446     subplot(3,2,3)
0447     hold on
0448     title('ALGs')
0449     for n = 1:N_samples
0450         plot(est_x_mean_a(1)+(est_x_samples_a(n,1)-est_x_mean_a(1)),...
0451             est_x_mean_a(2)+(est_x_samples_a(n,2)-est_x_mean_a(2)),'.k');
0452     end
0453     sugr_plot_Point_2D(est_p_a_emp,'ok','--k',1,3);
0454 
0455     plot(est_x_mean_a(1),est_x_mean_a(2),'ow','MarkerSize',12,'LineWidth',7);
0456     plot(est_x_mean_a(1),est_x_mean_a(2),'ok','MarkerSize',12,'LineWidth',3);
0457 
0458     plot(x_tilde.h(1)/x_tilde.h(3),x_tilde.h(2)/x_tilde.h(3),'+k','MarkerSize',10,'LineWidth',1);
0459 
0460     xlim_a = xlim;
0461     ylim_a = ylim;
0462 
0463     % geometric solution
0464     subplot(3,2,4)
0465     hold on
0466     title('SSDe')
0467     for n = 1:N_samples
0468         plot(est_x_mean_g(1)+(est_x_samples_g(n,1)-est_x_mean_g(1)),...
0469             est_x_mean_g(2)+(est_x_samples_g(n,2)-est_x_mean_g(2)),'.k');
0470     end
0471 
0472     sugr_plot_Point_2D(est_p_g_emp,'ok','--k',1,3);
0473 
0474     plot(est_x_mean_g(1),est_x_mean_g(2),'ow','MarkerSize',12,'LineWidth',7);
0475     plot(est_x_mean_g(1),est_x_mean_g(2),'ok','MarkerSize',12,'LineWidth',3);
0476 
0477     plot(x_tilde.h(1)/x_tilde.h(3),x_tilde.h(2)/x_tilde.h(3),'+k','MarkerSize',10,'LineWidth',1);
0478 
0479     xlim_g = xlim;
0480     ylim_g = ylim;
0481 
0482     % ml-estimation Hessian
0483 
0484     subplot(3,2,5)
0485     hold on
0486     title('MLEe')
0487     for n = 1:N_samples
0488         plot(est_x_mean_mH(1)+(est_x_samples_mH(n,1)-est_x_mean_mH(1)),...
0489             est_x_mean_mH(2)+(est_x_samples_mH(n,2)-est_x_mean_mH(2)),'.k');
0490     end
0491     sugr_plot_Point_2D(est_p_mH_emp,'ok','--k',1,3);
0492     plot(est_x_mean_mH(1),est_x_mean_mH(2),'ow','MarkerSize',12,'LineWidth',7);
0493     plot(est_x_mean_mH(1),est_x_mean_mH(2),'ok','MarkerSize',12,'LineWidth',3);
0494 
0495     plot(x_tilde.h(1)/x_tilde.h(3),x_tilde.h(2)/x_tilde.h(3),'+k','MarkerSize',10,'LineWidth',1);
0496 
0497     xlim_mH = xlim;
0498     ylim_mH = ylim;
0499 
0500     % ml-estimation
0501     subplot(3,2,6)
0502     hold on
0503     title('MLEs')
0504     for n = 1:N_samples
0505         plot(est_x_mean_ml(1)+(est_x_samples_ml(n,1)-est_x_mean_ml(1)),...
0506             est_x_mean_ml(2)+(est_x_samples_ml(n,2)-est_x_mean_ml(2)),'.k');
0507     end
0508     sugr_plot_Point_2D(est_p_ml_emp,'ok','--k',1,3);
0509 
0510     plot(est_x_mean_ml(1),est_x_mean_ml(2),'ow','MarkerSize',12,'LineWidth',7);
0511     plot(est_x_mean_ml(1),est_x_mean_ml(2),'ok','MarkerSize',12,'LineWidth',3);
0512 
0513     plot(x_tilde.h(1)/x_tilde.h(3),x_tilde.h(2)/x_tilde.h(3),'+k','MarkerSize',10,'LineWidth',1);
0514 
0515     % determine common plot bounding box
0516     xlim_ml = xlim;
0517     ylim_ml = ylim;
0518 
0519     mxlimg = [min([xlim_a(1),xlim_g(1)]),...
0520         max([xlim_a(2),xlim_g(2)])];
0521     mylimg = [min([ylim_a(1),ylim_g(1)]),...
0522         max([ylim_a(2),ylim_g(2)])];
0523 
0524     subplot(3,2,2);xlim(mxlimg);ylim(mylimg);
0525     subplot(3,2,4);xlim(mxlimg);ylim(mylimg);
0526 
0527     mxliml = [min([xlim_mH(1),xlim_ml(1)]),...
0528         max([xlim_mH(2),xlim_ml(2)])];
0529     myliml = [min([ylim_mH(1),ylim_ml(1)]),...
0530         max([ylim_mH(2),ylim_ml(2)])];
0531 
0532     subplot(3,2,2);xlim(mxlimg);ylim(mylimg);
0533     subplot(3,2,4);xlim(mxlimg);ylim(mylimg);
0534     subplot(3,2,5);xlim(mxliml);ylim(myliml);
0535     subplot(3,2,6);xlim(mxliml);ylim(myliml);
0536 
0537     % same bb for all
0538     mx = [min([xlim_a(1),xlim_g(1),xlim_mH(1),xlim_ml(1)]),...
0539         max([xlim_a(2),xlim_g(2),xlim_mH(2),xlim_ml(2)])];
0540     my = [min([ylim_a(1),ylim_g(1),ylim_mH(1),ylim_ml(1)]),...
0541         max([ylim_a(2),ylim_g(2),ylim_mH(2),ylim_ml(2)]) ];
0542 
0543     subplot(3,2,2);xlim(mx);ylim(my);
0544     subplot(3,2,3);xlim(mx);ylim(my);
0545     subplot(3,2,4);xlim(mx);ylim(my);
0546     subplot(3,2,5);xlim(mx);ylim(my);
0547     subplot(3,2,6);xlim(mx);ylim(my);
0548     
0549     %% evaluate correctness
0550     S = 0.99;
0551     check_estimation_result(R,x_tilde_e,Cxx_a_e,ones(N_samples,1),est_x_samples_a,S,' ALGs');
0552     check_estimation_result(R,x_tilde_e,Cxx_mH_e,sigma_2_mH,est_x_samples_mH,S,' MLEe');
0553     set(gcf,'Position',[0.25*ss(1),70,0.35*ss(1),0.25*ss(2)])
0554     check_estimation_result(R,x_tilde_e,Cxx_ml_e,sigma_2_ml,est_x_samples_ml,S,' MLEs');
0555     set(gcf,'Position',[0.63*ss(1),70,0.35*ss(1),0.25*ss(2)])
0556     
0557     % Bias and  accuracy
0558     disp('----------------------------')
0559     disp('Precision, bias and accuracy')
0560     lb = max([trace(est_x_cov_aE),...
0561               trace(est_x_cov_a),...
0562               trace(est_x_cov_g),...
0563               trace(est_x_cov_ml),...
0564               trace(est_x_cov_mH)]);
0565     
0566     f = 10^-(ceil(log(lb)/log(10)/2));
0567     factor_for_bias=1/f;
0568     
0569     % provide bias, accuracy and test statistic
0570     disp('sigma = sqrt(tr(CovM)/2)')
0571     disp('bias  = true_x - est_x')
0572     disp('A     = |bias|^2 + sigma^2)')
0573     disp(['Values * ',num2str(f),':'])
0574     ALGe_bias_x________y_____sigma_________A = ...
0575         f*[-x_tilde_e'+est_x_mean_aE,sqrt(trace(est_x_cov_aE)/2),...
0576         sqrt(norm(x_tilde_e'-est_x_mean_aE)^2+trace(est_x_cov_aE)/2)]      %#ok<*NOPTS>
0577     
0578     ALGs_bias_x________y_____sigma_________A = ...
0579         f*[-x_tilde_e'+est_x_mean_a,sqrt(trace(est_x_cov_a)/2),...
0580         sqrt(norm(x_tilde_e'-est_x_mean_a)^2+trace(est_x_cov_a)/2)]
0581     
0582     SSDe_bias_x________y_____sigma_________A = ...
0583         f*[-x_tilde_e'+est_x_mean_g,sqrt(trace(est_x_cov_g)/2),...
0584         sqrt(norm(x_tilde_e'-est_x_mean_g)^2+trace(est_x_cov_g)/2)]
0585     
0586     MLEs_bias_x________y_____sigma_________A = ...
0587         f*[-x_tilde_e'+est_x_mean_mH,sqrt(trace(est_x_cov_mH)/2),...
0588         sqrt(norm(x_tilde_e'-est_x_mean_mH)^2+trace(est_x_cov_mH)/2)]
0589     
0590     MLEe_bias_x________y_____sigma_________A = ...
0591         f*[-x_tilde_e'+est_x_mean_ml,sqrt(trace(est_x_cov_ml)/2),...
0592         sqrt(norm(x_tilde_e'-est_x_mean_ml)^2+trace(est_x_cov_ml)/2)]
0593 %%
0594 end
0595 % save('vp_0_200')
demo_estimate_Point_2D_from_Lines

PURPOSE

SYNOPSIS

DESCRIPTION

CROSS-REFERENCE INFORMATION

SOURCE CODE
