forked from hjhdog1/probabilisticAXYB
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmain_fig9_R1_R2.m
222 lines (171 loc) · 7.31 KB
/
main_fig9_R1_R2.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
%% Generate Figure 9
% This code runs for 5-10 minutes (or about 8-15 mins when SGO is activated for distance minimization)
clc;
clear all;
close all;
%% Experiment Parameters and Results
nExp = 10;
% variables to store estimation errors
distX_geometric_SO3 = zeros(1, nExp);
distY_geometric_SO3 = zeros(1, nExp);
distX_geometric_trans = zeros(1, nExp);
distY_geometric_trans = zeros(1, nExp);
distX_prob_SO3 = zeros(1, nExp);
distY_prob_SO3 = zeros(1, nExp);
distX_prob_trans = zeros(1, nExp);
distY_prob_trans = zeros(1, nExp);
diffX_SO3 = zeros(1, nExp);
diffY_SO3 = zeros(1, nExp);
diffX_trans = zeros(1, nExp);
diffY_trans = zeros(1, nExp);
%% Distance Minimization Parameters
% Parameter Setting
alpha = 2.0; % translation weight
param = defaultParam; % get default solver parameters for distance min.
% param.globalOptMethod = 2; % activate stochastic global optimization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Remark:
% The translation weight is 2.0 because the distance function in the distance
% minimization algorithm is norm(R1-R2, 'frob'), which is bounded equivalent
% to twice of geodesic distance between R1 and R2. Rotation and translation
% are equally weighted when alpha=2.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Run Calibrations
tic;
for i = 1:nExp
%% Generate Synthetic Data
% parameters
n = 20; % num of date pairs (A,B)
noiseLevel_SO3 = 0.05; % rotation noise level in radian (std of the magnitude of angular displacement noise)
noiseLevel_trans = 0.05; % translation noise level in user's length unit (std of translation noise)
% true values of X,Y
X_true = randSE3(); % ground truth of X
Y_true = randSE3(); % ground truth of Y
% generate data
noiseBPosition = 'right';
noiseAPosition = 'none';
% generate data
[A,B] = generateABData_SE3(X_true, Y_true, n, noiseLevel_SO3, 1, noiseLevel_trans, 0.0, 'G', noiseAPosition, noiseBPosition); % last M pairs of (A,B) are outliers.
[A,B] = randomSorting(A,B); % random-sorting data to mix outliers
%% Solve with distance-minimization algorithm
% Solve AX = YB with geometric stochastic global optimization
[X_geometric1,Y_geometric1] = solveAXYB_SE3(A,B,alpha,param);
X_geometric = X_geometric1;
Y_geometric = Y_geometric1;
%% Solve with probabilistic algorithm
invSig_wM = eye(3);
invSig_wM = repmat(invSig_wM, [1,1,n]);
invSig_pM = eye(3);
invSig_pM = repmat(invSig_pM, [1,1,n]);
X_prob = addNoiseSE3(X_geometric, 0.02, 0.02, 'right', 'G');
Y_prob = addNoiseSE3(Y_geometric, 0.02, 0.02, 'right', 'G');
step_R = 0.01;
step_p = 0.01;
[X_prob, Y_prob, ~] = solveAXYB_prob_noiselessA(A, B, X_prob, Y_prob, invSig_wM, invSig_pM, step_R, step_p);
step_R = 0.0001;
step_p = 0.0001;
[X_prob, Y_prob, J] = solveAXYB_prob_noiselessA(A, B, X_prob, Y_prob, invSig_wM, invSig_pM, step_R, step_p);
%% Store Results
distX_geometric_SO3(i) = norm(so3(X_geometric(1:3,1:3) * X_true(1:3,1:3)'));
distY_geometric_SO3(i) = norm(so3(Y_geometric(1:3,1:3) * Y_true(1:3,1:3)'));
distX_geometric_trans(i) = norm(X_geometric(1:3,4) - X_true(1:3,4));
distY_geometric_trans(i) = norm(Y_geometric(1:3,4) - Y_true(1:3,4));
distX_prob_SO3(i) = norm(so3(X_prob(1:3,1:3) * X_true(1:3,1:3)'));
distY_prob_SO3(i) = norm(so3(Y_prob(1:3,1:3) * Y_true(1:3,1:3)'));
distX_prob_trans(i) = norm(X_prob(1:3,4) - X_true(1:3,4));
distY_prob_trans(i) = norm(Y_prob(1:3,4) - Y_true(1:3,4));
diffX_SO3(i) = norm(so3(X_geometric(1:3,1:3) * X_prob(1:3,1:3)'));
diffY_SO3(i) = norm(so3(Y_geometric(1:3,1:3) * Y_prob(1:3,1:3)'));
diffX_trans(i) = norm(X_geometric(1:3,4) - X_prob(1:3,4));
diffY_trans(i) = norm(Y_geometric(1:3,4) - Y_prob(1:3,4));
%% Display Time
t = toc;
t_left = (t/i) * (nExp-i);
disp(['exp. num. = ', num2str(i), '/', num2str(nExp), ', time taken. = ', num2str(t), 'sec, time left = ', num2str(t_left), 'sec'])
end
errMean = [mean(distX_geometric_SO3) * 180/pi, mean(distX_prob_SO3) * 180/pi;
mean(distY_geometric_SO3) * 180/pi, mean(distY_prob_SO3) * 180/pi;
mean(distX_geometric_trans), mean(distX_prob_trans);
mean(distY_geometric_trans), mean(distY_prob_trans)]
errStd = [std(distX_geometric_SO3) * 180/pi, std(distX_prob_SO3) * 180/pi;
std(distY_geometric_SO3) * 180/pi, std(distY_prob_SO3) * 180/pi;
std(distX_geometric_trans), std(distX_prob_trans);
std(distY_geometric_trans), std(distY_prob_trans)]
%% Plot Results
close all
titles = {'Errors in rotation of X', 'Errors in rotation of Y';...
'Errors in translation of X', 'Errors in translation of Y'};
figure
% tiledlayout(2,2, 'Padding', 'none', 'TileSpacing', 'compact');
for j = 1:2 % over X and Y
for i = 1:2 % over rotation and translation
x = 1:2;
data = errMean(i+2*(j-1),:);
errhigh = errStd(i+2*(j-1),:);
errlow = errStd(i+2*(j-1),:);
subplot(2,2,2*(j-1)+i)
% nexttile
bar(x,data)
hold on
er = errorbar(x,data,errlow,errhigh);
grid on
er.Color = [0 0 0];
er.LineStyle = 'none';
title(titles{j,i})
% xlabel('Methods')
ax = gca();
if j < 2
ylabel('Rotational error (^o)')
ax.YLim = [0, 2.0];
else
ylabel('Translational error')
ax.YLim = [0, 0.1];
end
% xticklabels({'distance minimization', 'proposed method'})
xticklabels({' Distance\newlineminimization', 'Proposed\newline method'})
% ax = gca();
% ax.XTickLabel = tickLabels;
pos = get(gca, 'Position');
pos(1) = 0.08 + 0.51*(i-1);
pos(2) = 0.08 + 0.51*(2-j);
pos(3) = 0.405;
pos(4) = 0.37;
set(gca, 'Position', pos)
end
end
mean([diffX_SO3', diffY_SO3', diffX_trans', diffY_trans'])
max([diffX_SO3', diffY_SO3', diffX_trans', diffY_trans']) ./ errMean(:,1)' * 100
min([diffX_SO3', diffY_SO3', diffX_trans', diffY_trans']) ./ errMean(:,1)' * 100
%% Plot Results 3 - Box plots
close all
titles = {'Errors in rotation of X', 'Errors in rotation of Y';...
'Errors in translation of X', 'Errors in translation of Y'};
data = {[distX_geometric_SO3', distX_prob_SO3']*180/pi, [distY_geometric_SO3', distY_prob_SO3']*180/pi,...
[distX_geometric_trans', distX_prob_trans'], [distY_geometric_trans', distY_prob_trans']};
figure('Position', [100, 100, 700, 500])
% figure
for j = 1:2 % over X and Y
for i = 1:2 % over rotation and translation
x = 1:2;
subplot(2,2,2*(j-1)+i)
bp = boxplot(data{2*(j-1)+i},'Whisker',100);
grid on
title(titles{j,i})
ax = gca();
if j < 2
ylabel('Rotational error (^o)')
ax.YLim = [0, 2.0];
else
ylabel('Translational error')
ax.YLim = [0, 0.06];
end
% xticklabels({' Distance\newlineminimization', 'Proposed\newline method'})
xticklabels({'Dist. Min.', 'Proposed'})
pos = get(gca, 'Position');
pos(1) = 0.08 + 0.51*(i-1);
pos(2) = 0.08 + 0.51*(2-j);
pos(3) = 0.405;
pos(4) = 0.37;
set(gca, 'Position', pos)
end
end