Hello,
I am using ITK5 to build an automated multi-resolution rigid registration for multi-modality 3D MR images, basically T1 and T2 registration. The results are quite good on most of my subjects, but there are a few subjects on those my registration algorithm does not converge. Here are a part of the source code and one result that went crazy during the iteration. I want to understand why it happens and how to improve the stability.
For information, the smoothing sigmas I use are 4, 2 and 1 for a 3-level multi-resolution registration. 4 is for the very coarse level, and 1 is for the very fine level (the values of sigmas are also given in the source code). The reason that I choose small sigmas is because that I have found using a small sigma or no gaussian smoothing (sigma=1 or 0) at the finest level generally gets better results (the mis-alignments between the moving and the fixed images are smaller) than bigger sigmas (2 or 3…).
#include "itkImageRegistrationMethodv4.h"
#include "itkVersorRigid3DTransform.h
#include "itkMattesMutualInformationImageToImageMetricv4.h"
#include "itkRegularStepGradientDescentOptimizerv4.h"
#include "itkCommand.h"
// ...
template <typename TRegistration>
class RegistrationInterfaceCommand : public itk::Command
{
// ...
if (registration->GetCurrentLevel() == 0)
{
optimizer->SetLearningRate(16.00);
optimizer->SetMinimumStepLength(1); //2.5
}
else
{
optimizer->SetLearningRate(optimizer->GetCurrentStepLength());
optimizer->SetMinimumStepLength(optimizer->GetMinimumStepLength() * 0.1); //0.2
}
// ...
}
int main(int argc, const char *argv[])
{
// ...
using TransformType = itk::VersorRigid3DTransform<double>;
using RegistrationType = itk::ImageRegistrationMethodv4<FixedImageType, MovingImageType, TransformType>;
using OptimizerType = itk::RegularStepGradientDescentOptimizerv4<double>;
using MetricType = itk::MattesMutualInformationImageToImageMetricv4<FixedImageType, MovingImageType>;
// ...
using OptimizerScalesType = OptimizerType::ScalesType;
OptimizerScalesType optimizerScales(Transform->GetNumberOfParameters());
const double translationScale = 1.0 / 1000.0;
optimizerScales[0] = 1.0;
optimizerScales[1] = 1.0;
optimizerScales[2] = 1.0;
optimizerScales[3] = translationScale;
optimizerScales[4] = translationScale;
optimizerScales[5] = translationScale;
optimizer->SetScales(optimizerScales);
optimizer->SetNumberOfIterations(200);
optimizer->SetRelaxationFactor(0.5);
metric->SetNumberOfHistogramBins(50);
registration->SetNumberOfLevels(3);
RegistrationType::ShrinkFactorsArrayType shrinkFactorsPerLevel;
shrinkFactorsPerLevel[0]=4;
shrinkFactorsPerLevel[1]=2;
shrinkFactorsPerLevel[2]=1
registration->SetShrinkFactorsPerLevel(shrinkFactorsPerLevel);
registration->SetSmoothingSigmasAreSpecifiedInPhysicalUnits(false);
RegistrationType::SmoothingSigmasArrayType smoothingSigmasPerLevel;
smoothingSigmasPerLevel.SetSize(3);
smoothingSigmasPerLevel[0]=4;
smoothingSigmasPerLevel[1]=2;
smoothingSigmasPerLevel[2]=1;
registration->SetSmoothingSigmasPerLevel(smoothingSigmasPerLevel);
// ...
}
And one failed result I got is this:
-------------------------------------
Current level = 0
Shrink factor = [4, 4, 4]
Smoothing sigma = 4
0 -0.733149 [-0.9263068972697296, -0.36179856746411254, 0.07263498269129506, 5.332439363952538, -6.637601332183772, -13.212873107993977] 0
1 -0.191829 [-0.8759868251199792, -0.45856679931259603, 0.04274679556310132, 1.912725536287918, -0.64078318603611, -9.200531745698711] 1
2 -0.235488 [-0.8429528976766242, -0.5375091101512786, -0.021693675940054925, -2.800149010626315, 4.484608455513287, -5.278417288183214] 2
3 -0.279343 [0.5810137381977183, 0.4027944740920511, -0.009592710017768104, -6.601922401165744, 9.704019816707206, -5.258936274885786] 3
4 -0.244462 [0.6363684292657169, 0.3249588551518063, -0.08165876371218779, -7.813217359800395, 8.777643017993581, -1.5688622817441833] 4
5 -0.280338 [0.7125188955524352, 0.22221747628069877, -0.14099002119462142, -8.203371636861585, 8.432349574928773, 2.386009694637051] 5
6 -0.308272 [0.8631588611445928, 0.0657707944573068, -0.14334855768845234, -5.926626969163246, 8.12008811751936, 5.612716041046605] 6
7 -0.350938 [0.924737467971267, -0.14108239669337416, -0.017663182258158272, -2.281900535667566, 8.374170697770245, 4.08441530998319] 7
8 -0.379674 [0.9613330592905334, -0.07936569759944935, 0.04944499862555255, 1.5416077615615738, 7.650227073820257, 3.1997642194963296] 8
9 -0.394592 [0.9839639701995025, 0.17241030226052198, 0.024402675805923743, 4.839994041916466, 9.80421181028754, 3.043914387855261] 9
10 -0.366561 [0.9784011268024441, 0.2017283172792666, -0.013840060741934047, 3.1426348108360247, 10.841560079489865, 2.861178959103724] 10
11 -0.37658 [0.9712492333360878, 0.20787272473954113, -0.058111771949200655, 1.3589289855171487, 11.686358056603218, 2.7424388570758698] 11
12 -0.393754 [0.9764159713159172, 0.17896991069535495, -0.10858867303628511, -0.5086515983058342, 12.28739372045914, 2.949968315106795] 12
13 -0.394075 [0.9624974677148777, 0.10374942931182482, -0.14028604644447795, -2.128730133293009, 13.320395674553204, 3.035890901903846] 13
14 -0.393914 [0.9658325709637364, -0.05425982851936116, -0.11015595964355138, -3.8274594710263306, 13.281566558026809, 3.5185818194795284] 14
15 -0.393761 [0.9874717891613721, -0.09361251147613073, -0.07519642837481721, -2.896708134588527, 13.07800105411728, 3.3927558919831227] 15
16 -0.414078 [0.9892155820867167, -0.1076811604995671, -0.045397371227273005, -2.01335649367855, 13.278361831980904, 3.2216160000074265] 16
17 -0.417239 [0.9900488944279731, -0.11020620077789288, -0.017250173778628218, -1.1128733585858912, 13.513015879997907, 3.12508220734304] 17
18 -0.419076 [0.9889079727253617, -0.09841772588997635, 0.007564451481912156, -0.23758819400318754, 13.787060594177838, 3.1065301161055436] 18
19 -0.421628 [0.9933731695929913, -0.06782217581991092, 0.02725866835262499, 0.6523916065831211, 13.974137614213646, 3.019906456152648] 19
20 -0.42274 [0.9866332376011676, -0.02151503189601338, 0.038964348126677165, 1.4734281161366554, 14.246538738497657, 3.0109785202109234] 20
21 -0.42239 [0.9665891621169802, 0.06818214721107235, 0.0288295084653986, 2.0281167110336797, 14.214837414026166, 3.027235418644008] 21
-------------------------------------
Current level = 1
Shrink factor = [2, 2, 2]
Smoothing sigma = 2
0 -0.165818 [-0.925357805270639, -0.3678443324508694, 0.07003382321146866, 5.104457053027096, -6.258609962438153, -12.982499148092636] 22
1 -0.170225 [-0.9242723196322958, -0.37395533615702053, 0.06744078600633185, 4.872553438174363, -5.875925015593804, -12.764476879907527] 23
2 -0.175174 [-0.9228678423531748, -0.3795302083014648, 0.06515496691732986, 4.6373307546655385, -5.493018805703098, -12.554766331503036] 24
3 -0.181715 [-0.9002126411609571, -0.3729385858294942, 0.06255691686672964, 4.526627981032414, -5.3191263196865215, -12.460240610914896] 25
4 -0.166954 [-0.8988147741059745, -0.37820380837469186, 0.058684380239440496, 4.332656941697785, -4.9680207257434414, -12.162077931410956] 26
5 -0.169421 [-0.8974372116369461, -0.383163607742936, 0.05454913996986776, 4.144184626795788, -4.613284441135864, -11.864671468866156] 27
6 -0.171992 [-0.8960294461573377, -0.3880078407515677, 0.0506052794555148, 3.954124113352406, -4.256021098219392, -11.57130885869079] 28
7 -0.17452 [-0.8945329413529126, -0.3927940851103804, 0.04654438110667645, 3.7565462966897605, -3.8974977237901602, -11.284520819041582] 29
8 -0.177228 [-0.893073260495885, -0.3982703951042737, 0.04270336502680604, 3.54694625720387, -3.5441117364591066, -10.999996593588236] 30
9 -0.179887 [-0.8917511459782593, -0.402988724120896, 0.038672574747297746, 3.3433000521152207, -3.1887345432212735, -10.713560888525159] 31
10 -0.182599 [-0.8907572166808908, -0.4080763343356853, 0.03500111757664416, 3.1283769203972276, -2.8359114940749586, -10.432396362798384] 32
11 -0.185375 [-0.8897144806413659, -0.41234870469471696, 0.03170403608800336, 2.920159703160874, -2.477397612485587, -10.153220888600227] 33
12 -0.188227 [-0.8895069704613835, -0.4163908090888854, 0.028359245159709393, 2.695386125890537, -2.1165774910106894, -9.890617439521083] 34
13 -0.191164 [-0.8899451969489741, -0.41941946185259477, 0.024826806411803702, 2.4669359785716853, -1.7528708334162935, -9.635382018656843] 35
14 -0.194149 [-0.8899849883770795, -0.4222436983881426, 0.021376244369684223, 2.2215281542697514, -1.3934443054590209, -9.38974963087036] 36
15 -0.197016 [-0.8902905083577677, -0.4246791647800027, 0.018085283389813363, 1.9610480857416466, -1.0367226593601728, -9.15605594017561] 37
16 -0.200109 [-0.8911790506866288, -0.4268636532161478, 0.014601540714027658, 1.6987011304274675, -0.6782774807194962, -8.92763269742938] 38
17 -0.20338 [-0.892609971313073, -0.4289708256956284, 0.011205424426267138, 1.4368362652633277, -0.3180131731590729, -8.702456232986432] 39
18 -0.207198 [-0.8948186503199645, -0.43068581821958923, 0.007439807193324334, 1.1792349394289712, 0.05425310153903656, -8.494571103551753] 40
19 -0.211672 [-0.8962831081961655, -0.43170871400106947, 0.0036241160866411, 0.9282332126620418, 0.44228118259744825, -8.30653216158485] 41
20 -0.215567 [-0.8979578016971458, -0.4325239302827552, 0.00012611599773141137, 0.6745792819605017, 0.8330938974757329, -8.129828463101125] 42
21 -0.219986 [-0.8993297522411758, -0.43300070679577385, -0.0034295940388321946, 0.42428745739645846, 1.235629692442797, -7.976190797822581] 43
22 -0.224458 [-0.9007931442073573, -0.43284151326304304, -0.007623228141168549, 0.18182142517369806, 1.6497935103071022, -7.846843722895878] 44
23 -0.230441 [-0.9017218652813284, -0.43177597351274905, -0.011923069098106621, -0.042625547697304395, 2.0703892287599213, -7.738331630297215] 45
24 -0.235023 [-0.9001617249717538, -0.4279121087901158, -0.016833032158279648, -0.23901114189993375, 2.478872133323959, -7.658656893669951] 46
25 -0.228304 [-0.9040621749932988, -0.42463791667625456, -0.02155825859725272, -0.493314729492467, 2.883906663923926, -7.532576796152746] 47
26 -0.235289 [-0.906797236082112, -0.42064106092626263, -0.026635128836558282, -0.7099755412182263, 3.319837483122768, -7.443672928356708] 48
27 -0.242654 [-0.9012187974459399, -0.41231234058907185, -0.030912190408688058, -0.87416074585958, 3.7001626725063685, -7.406122563997332] 49
28 -0.226219 [-0.909628741476757, -0.40525189726308697, -0.03635132665987023, -1.1546888503008423, 4.065655359408644, -7.236832959709584] 50
29 -0.23549 [-0.9162597171934478, -0.39663914657533816, -0.04214937208722823, -1.3978107398313029, 4.47635688381423, -7.123518829496737] 51
30 -0.244331 [-0.9205228276029965, -0.3876485001464969, -0.04823340854653245, -1.5774947880691668, 4.931866851232399, -7.0768956287230464] 52
31 -0.250684 [-0.9171489410460895, -0.3752978647077677, -0.05368213562216609, -1.7012674139375772, 5.339684803923876, -7.05055470834848] 53
32 -0.2337 [-0.9281366410328409, -0.36163038868929465, -0.060102546266258876, -1.9336199069107947, 5.741130904159817, -6.9096525362799825] 54
33 -0.246485 [-0.9356778677927674, -0.3462680102835435, -0.06736822700720943, -2.1059768590070234, 6.188809836192489, -6.833785636126782] 55
34 -0.25745 [-0.9406958188416923, -0.33064091413730823, -0.0755098396942315, -2.223945769532191, 6.669634383251642, -6.783954314480191] 56
35 -0.259537 [-0.946212694907357, -0.312122543770429, -0.08417468755887808, -2.3273443899603232, 7.153714389774761, -6.72848622554401] 57
36 -0.260884 [-0.9519821377278442, -0.29118521232997696, -0.09271267001867436, -2.391865404154327, 7.638191930248697, -6.658603443485945] 58
37 -0.262504 [-0.9575823021252302, -0.26819418939376605, -0.10057191384818075, -2.4201037649934816, 8.117537150554696, -6.575546904442142] 59
38 -0.263229 [-0.9637983850095505, -0.2422849799874104, -0.10870742623282147, -2.429858556138909, 8.588217107428903, -6.461740574678728] 60
39 -0.266665 [-0.9697361221544298, -0.21306034895581893, -0.11555871246797618, -2.378756094183432, 9.053594326734553, -6.33649073226307] 61
40 -0.268846 [-0.9756466635127031, -0.18266096780584146, -0.12126685717100173, -2.304219663612551, 9.515263150649709, -6.187583886525595] 62
41 -0.275248 [-0.9782429381622855, -0.14863409006545836, -0.12733182811300656, -2.1507065323327077, 9.947876254098734, -6.049892338423588] 63
42 -0.269738 [-0.9840604741567089, -0.11437438809783523, -0.13068383185182905, -1.9922702606690412, 10.37040766739417, -5.855576068060787] 64
43 -0.278805 [-0.987824902891459, -0.07978119946507067, -0.13349608288137932, -1.7767606338381747, 10.77217022694567, -5.675143957272761] 65
44 -0.286237 [-0.9861571870577481, -0.0465540663651426, -0.1344036856688025, -1.497885506195055, 11.112376675235712, -5.515055589971861] 66
45 -0.279441 [-0.9896194584149618, -0.015209989866006933, -0.13358717374473358, -1.2171327281268156, 11.457376962576307, -5.306679763003057] 67
46 -0.287929 [-0.9904669785975865, 0.016715894345531432, -0.13277929827778154, -0.898819009029671, 11.782041044126492, -5.112068907282296] 68
47 -0.292555 [-0.989171249203694, 0.048207894970332524, -0.13110706236159023, -0.5403243939057008, 12.06888732827803, -4.9260525901896495] 69
48 -0.293751 [-0.987481166483558, 0.07929218908071525, -0.12792641186715073, -0.1855230434777863, 12.355302532457625, -4.730742270539382] 70
49 -0.29571 [-0.9851294260635808, 0.10873198349287472, -0.12345039402271298, 0.17534725576035382, 12.633926341698055, -4.5344014987318655] 71
50 -0.297586 [-0.9822093419644586, 0.13630112897437185, -0.11834232802811712, 0.544569576875381, 12.901895842362428, -4.337757978643693] 72
51 -0.299129 [-0.9787853646218182, 0.16214059052084812, -0.11188154088548058, 0.9090802819423833, 13.179981030350504, -4.145837267101502] 73
52 -0.299918 [-0.9758597319275882, 0.1860272616657608, -0.1033518863636072, 1.2673673034444217, 13.461214162384818, -3.9465346428502435] 74
53 -0.301249 [-0.9717428754914894, 0.20927699120333404, -0.0930259185978707, 1.620751941468307, 13.732249369176625, -3.7257555833675795] 75
54 -0.301127 [-0.9677997109300885, 0.23049866333492047, -0.08084832581062627, 1.9630607240842861, 14.011662080690108, -3.4971893878539473] 76
55 -0.3012 [-0.9636460685087992, 0.2513745479265786, -0.06676703289906473, 2.309927879614788, 14.276407078254413, -3.258469252789649] 77
56 -0.301314 [-0.9590926676099415, 0.27103956639191545, -0.052297711079512026, 2.6670113899452375, 14.53413719236776, -3.026977767952518] 78
57 -0.301063 [-0.9545323996752234, 0.28938300551040297, -0.03736703264787272, 3.05523156876583, 14.761352928256446, -2.8140807000727075] 79
58 -0.300867 [-0.9492325577819646, 0.30673522332412295, -0.020807744010985844, 3.4686916882363943, 14.955142433103898, -2.616699604762967] 80
59 -0.299372 [-0.9463969225244658, 0.31953977294541147, -0.003068544643698528, 3.908779185984713, 15.113762962059672, -2.4502948018627926] 81
60 -0.299224 [-0.9430150116403059, 0.32556208434289613, 0.01891645652074097, 4.390978287398183, 15.207068280821632, -2.3781632832921757] 82
61 -0.296299 [-0.9461141414714858, 0.3194929803558318, 0.045058020824795784, 4.881147124727425, 15.231987938752942, -2.394087670227974] 83
62 -0.2978 [-0.922624193928644, 0.29195995473355885, 0.06648890482088528, 5.070966028965843, 15.273629012854064, -2.5304930091225373] 84
63 -0.258637 [-0.9457395575478134, 0.2724674462826168, 0.08441279954457773, 5.288952614864694, 15.584451766335075, -2.265403667437342] 85
64 -0.28049 [-0.9689332278103917, 0.22134475771007298, 0.10922404013287773, 5.346021953224784, 15.965518784518984, -2.176326668141574] 86
65 -0.306255 [-0.9396225706556334, 0.19634291901155326, 0.11345840220206552, 5.249527301919962, 16.00088768371235, -2.2010747324449618] 87
66 -0.263439 [-0.9614448330856479, 0.16225154420333326, 0.12211431860255369, 5.133278801013146, 16.343336299593453, -1.897325464159635] 88
67 -0.285498 [-0.9780489918746654, 0.11574261959866906, 0.1308557192034924, 4.877636210171303, 16.684916939807813, -1.7043574780541884] 89
68 -0.305678 [-0.9849467134941096, 0.07229829919321373, 0.1353196345005947, 4.451881341682758, 16.865412817360102, -1.5503395238885411] 90
69 -0.314721 [-0.9863535624503112, 0.03543029757464442, 0.13727438016894208, 3.9932786386333023, 16.995384296196693, -1.418948016634683] 91
70 -0.317296 [-0.9867936604874552, 0.002220349859455982, 0.13719576011729487, 3.5294055479902875, 17.098548316983408, -1.2784363416792575] 92
71 -0.319324 [-0.9868898832753977, -0.027608843508004646, 0.13397993752679252, 3.065246340838182, 17.19590983199931, -1.1318914583668422] 93
72 -0.322172 [-0.9872616648795368, -0.05478915943181845, 0.1292713353684114, 2.6008985571287586, 17.29588890437029, -0.9874137635625656] 94
73 -0.325586 [-0.98561485421978, -0.07829758515051997, 0.12305347400979604, 2.1270529799026563, 17.37753910869945, -0.8609907130470374] 95
74 -0.32626 [-0.9851227642479249, -0.09856665550285064, 0.11601710371857357, 1.6567397339107242, 17.459009463745463, -0.7188713338306301] 96
75 -0.328892 [-0.9839876652516821, -0.11605639350774523, 0.10762283289009375, 1.1809352864477423, 17.544985697065705, -0.597677668377306] 97
76 -0.330356 [-0.9834929659982574, -0.13118208166535264, 0.09798589756559949, 0.703893235426408, 17.63374314757983, -0.4829264652228358] 98
77 -0.332381 [-0.9827360972097647, -0.14457905872650056, 0.08719482155496162, 0.22363636760574823, 17.71831361158019, -0.3780087135175008] 99
78 -0.333909 [-0.9825425226981144, -0.15684289603739604, 0.07481724883604722, -0.2584663567573885, 17.791667083156177, -0.27485278567435917] 100
79 -0.335741 [-0.9816559636255555, -0.16809581307901098, 0.06118141426403543, -0.7493432776583788, 17.838171255124625, -0.19986653861733464] 101
80 -0.336239 [-0.9813338477700431, -0.17604127713663037, 0.04599689556610882, -1.246508597213061, 17.85862295695849, -0.16553944235579526] 102
81 -0.336745 [-0.9809804794180044, -0.178939929038977, 0.028461805012938005, -1.7448133574679232, 17.84457116883423, -0.16173688662932614] 103
82 -0.336101 [-0.9819451144461997, -0.17318393169327378, 0.006115929015089821, -2.2372254491198853, 17.77564066268309, -0.18387451033796925] 104
83 -0.334863 [-0.9894411024485972, -0.12238052427032531, -0.03681351578210678, -2.6733125944486575, 17.636976973277157, -0.3337040974849663] 105
84 -0.33174 [-0.9923507093912546, -0.07587690768776686, -0.04730644783324176, -2.4547467524894193, 17.638682042809336, -0.40061502956759887] 106
85 -0.33287 [-0.9951081671074995, -0.04473706115732764, -0.049397749664795605, -2.21784662796679, 17.681677027446316, -0.4034791072610586] 107
86 -0.336092 [-0.9953104322177813, -0.017811646747828615, -0.05057775562125523, -1.9780493017217196, 17.721609846932203, -0.38714750704325385] 108
87 -0.337519 [-0.9960891634292374, 0.005737232801412855, -0.050338673224213454, -1.7391236565272334, 17.760267023280132, -0.34926481098361384] 109
88 -0.339279 [-0.9955953439101791, 0.025072164752853694, -0.04854208196371605, -1.4972301468387874, 17.797476697084715, -0.3170820530165164] 110
89 -0.339986 [-0.9955176072744911, 0.04168433913383707, -0.04554121457239799, -1.255741484246355, 17.832320891140476, -0.27529017998591665] 111
90 -0.341166 [-0.9948869144812309, 0.05539821383186175, -0.042016187430160105, -1.012354520858942, 17.861071322587566, -0.2350123746359741] 112
91 -0.341829 [-0.9941009959803208, 0.06710654963327162, -0.037782756339504356, -0.7687711699216543, 17.891232808890706, -0.19506223838264924] 113
92 -0.342521 [-0.9935485285478766, 0.07761942208498515, -0.03317837888940019, -0.5269973973779716, 17.93212976731783, -0.1521302328615623] 114
93 -0.343195 [-0.9931688334082606, 0.08688016862772206, -0.02779313009265569, -0.28643501611476074, 17.974322357084553, -0.1036053099492819] 115
94 -0.343955 [-0.9930221679155986, 0.09559919351026479, -0.02179222253478049, -0.046334817965160674, 18.0198999870175, -0.05760238868976635] 116
95 -0.344948 [-0.9928854585780849, 0.10341816614169913, -0.015239739712948085, 0.19478720036689173, 18.058891922155677, -0.011404931298047788] 117
96 -0.345721 [-0.9920741992961812, 0.10986928952799302, -0.007699365735547873, 0.4368915038994132, 18.100601770900496, 0.029840527183275317] 118
97 -0.345814 [-0.9918201649797718, 0.11470244525457665, 0.0011207731264449494, 0.6755788030006297, 18.152782644047672, 0.0780056431163029] 119
98 -0.34635 [-0.9914625922045586, 0.11845244989240648, 0.010923903628145316, 0.9146083669117342, 18.202475041902673, 0.12727576133399082] 120
99 -0.346532 [-0.9906295479051428, 0.11899168152594636, 0.022354909626129363, 1.1508528395118223, 18.26104668613265, 0.17572267433318112] 121
100 -0.346103 [-0.9908493166430918, 0.11561441334652976, 0.035199036319845486, 1.3899307009045068, 18.31090651443882, 0.2216747257760759] 122
101 -0.346244 [-0.9897266687184523, 0.10468057760952654, 0.05096045146518653, 1.6207839737887468, 18.375074243575334, 0.2606303235473561] 123
102 -0.344811 [-0.9925521883618272, 0.07226898670133464, 0.07557825764654816, 1.8256090012921975, 18.46193364433264, 0.3289174648731861] 124
103 -0.346942 [-0.9914798303305697, 0.0431616099726984, 0.08601557053236995, 1.736437026982794, 18.48510659466566, 0.3562557832314204] 125
104 -0.345028 [-0.9913301028952016, 0.024093417554861836, 0.08967291337508619, 1.6309831856874157, 18.49461616803232, 0.4091574520817015] 126
105 -0.345089 [-0.991551174204955, 0.00809521615338267, 0.09080511643387419, 1.5205564454872815, 18.491111226523067, 0.4580208693927873] 127
106 -0.345551 [-0.9915762116040893, -0.005862881272009594, 0.09062239000426509, 1.4101637120800938, 18.494305856103292, 0.5094868861834465] 128
107 -0.345862 [-0.9917492011205299, -0.017496596962102623, 0.08970680904440884, 1.2963511289934442, 18.50146702963317, 0.554777067921959] 129
108 -0.346436 [-0.99183415762465, -0.02752158409630273, 0.08856397418960253, 1.1810912879533535, 18.51046760329863, 0.597554435256704] 130
109 -0.346905 [-0.991778922349373, -0.03644706129975344, 0.08709362934148684, 1.065150390177914, 18.518468751389886, 0.6398145333944504] 131
110 -0.347348 [-0.9917838690399674, -0.044618241784555354, 0.085632263277202, 0.9501565127539198, 18.53014702817237, 0.6841439791378359] 132
111 -0.347838 [-0.9917380883174906, -0.05187384940065049, 0.08399488563824842, 0.8330678393977832, 18.540791150587637, 0.7236995697819083] 133
112 -0.348248 [-0.991705786248508, -0.05841432072330708, 0.08215939331964148, 0.7155654868843113, 18.55017702196133, 0.7627701548308277] 134
113 -0.348654 [-0.9917202553181078, -0.064495009200278, 0.08014729493456946, 0.5981256381222355, 18.561088152657877, 0.8017159690921236] 135
114 -0.349113 [-0.9916095461114857, -0.07031505520521805, 0.07797091270313974, 0.4800450632156195, 18.569909947650732, 0.8396797382730988] 136
115 -0.349404 [-0.9914601685320859, -0.07564885081900792, 0.075587855917701, 0.3610368649497796, 18.57776811258179, 0.8751943657939545] 137
116 -0.3496 [-0.9913480591913695, -0.0805307468139973, 0.07292625858572827, 0.24180236359585927, 18.586553338241448, 0.9098846684010452] 138
117 -0.349802 [-0.9911684801757772, -0.08504588868673839, 0.07004677490697223, 0.12226531583104558, 18.596282733967836, 0.9434453255605056] 139
118 -0.3499 [-0.990901401575419, -0.08907249173999272, 0.06692903796870811, 0.0029127923371791847, 18.6071319274808, 0.9773060925368862] 140
119 -0.349854 [-0.9907869308111794, -0.09249220841550619, 0.06358185816863714, -0.11742674015490076, 18.617467016711625, 1.0080407310920063] 141
120 -0.349935 [-0.9908328634310787, -0.09541590698581041, 0.05996628073645356, -0.23796745168104816, 18.629758113260777, 1.0372080094117715] 142
121 -0.350109 [-0.9909553239624105, -0.09809627926579473, 0.05620399605829597, -0.3592085393652746, 18.641057962008183, 1.0635323305022857] 143
122 -0.350358 [-0.9912925858741657, -0.10032016296852397, 0.05214678770086569, -0.4803591246289213, 18.653013637660084, 1.0885636817087114] 144
123 -0.350766 [-0.9914325775767654, -0.10210297900911867, 0.04776259300139092, -0.6028455535810507, 18.662042325934966, 1.1095842233605056] 145
124 -0.350821 [-0.9914679185838994, -0.1028999426652362, 0.04266394440158776, -0.7258409584213791, 18.669332220925277, 1.1276359315578939] 146
125 -0.350704 [-0.9917798191489938, -0.10273970844449642, 0.03697733439549115, -0.848907403449012, 18.67652784088932, 1.144786135177181] 147
126 -0.35072 [-0.992152059046925, -0.10095707022486194, 0.030430077712838753, -0.9724136818789267, 18.68424730817072, 1.1560069317600008] 148
127 -0.350625 [-0.9930287497638056, -0.0966124393242517, 0.022158533031042357, -1.094758845543175, 18.682971174176338, 1.1720128717651932] 149
128 -0.350747 [-0.9942147488955216, -0.08617363895245142, 0.010010222668966685, -1.2129139432438147, 18.65928225246178, 1.1804108733945187] 150
129 -0.350571 [-0.9957297333621415, -0.0565033584815487, -0.008090468030291119, -1.2726313543771932, 18.583581135330544, 1.1465532821859685] 151
-------------------------------------
Current level = 2
Shrink factor = [1, 1, 1]
Smoothing sigma = 1
0 -0.319092 [-0.9916412031540319, -0.1026783804299, 0.0403079792456647, -0.7832780576961592, 18.66246777287566, 1.1507717569752787] 152
1 -0.319166 [-0.9917942238048439, -0.1022244371400659, 0.0378299282386451, -0.8408019806975299, 18.655021532196955, 1.1734930534633192] 153
2 -0.31921 [-0.9919561125007952, -0.10150871337735523, 0.03521342575982704, -0.8982830209387778, 18.646641718919103, 1.195906548519548] 154
3 -0.319253 [-0.9921307201295896, -0.10053095680602717, 0.032453167801532457, -0.9557312096269195, 18.636327718446747, 1.2174665994180887] 155
4 -0.319302 [-0.9923379382232574, -0.09916964432437052, 0.029495084457304834, -1.0132136090165396, 18.62434135180817, 1.2378465147558895] 156
5 -0.319358 [-0.9926149519902928, -0.0973500883252101, 0.026429802572508095, -1.0702107885765573, 18.609679272349442, 1.2576294725039114] 157
6 -0.319436 [-0.9929500560064127, -0.09501749850082582, 0.02322152297413979, -1.1261876113455067, 18.591770356192292, 1.2773272209179733] 158
7 -0.319558 [-0.9932886793387474, -0.09217750467463429, 0.019854466387672375, -1.1812323010402994, 18.571675632213495, 1.2971882670478307] 159
8 -0.319665 [-0.9935968294847648, -0.08851922148740711, 0.016266637698220385, -1.235757424203174, 18.549423891234454, 1.3152372154999439] 160
9 -0.31974 [-0.9939485019775812, -0.08378903217917547, 0.0124738385906644, -1.2886453124336303, 18.522962840952864, 1.3310736411005688] 161
10 -0.319808 [-0.9944120373273782, -0.07758271411050804, 0.008576996899106279, -1.3373474389950437, 18.489358947597825, 1.3446450754141883] 162
11 -0.31994 [-0.9949316868087391, -0.07004378847889972, 0.004732517387317282, -1.3803802650966333, 18.449938890724777, 1.3591233623629826] 163
12 -0.320104 [-0.9954904851833989, -0.06022762486642237, 0.0007591679616269767, -1.4166602652082312, 18.40651465220695, 1.3748647819699484] 164
13 -0.320322 [-0.9958688213328384, -0.0482629897436435, -0.0028876038431538227, -1.4397320034973735, 18.35660151814749, 1.3891858266623833] 165
14 -0.320511 [-0.9962472986140676, -0.03466989275308006, -0.006288895380404431, -1.443942567012919, 18.303613642566276, 1.4057868851703765] 166
15 -0.320704 [-0.9964969137214319, -0.022338106433382098, -0.008554617289404463, -1.4218492707368897, 18.256098939825755, 1.4287376685688105] 167
16 -0.320909 [-0.9964090646879686, -0.012111018144424605, -0.009806069320949249, -1.3840240746693673, 18.21760224057793, 1.4517745687818964] 168
17 -0.321091 [-0.9964175174923795, -0.0034166819251363455, -0.01067644716952688, -1.3420390240914977, 18.18274625275676, 1.476708968717383] 169
18 -0.32128 [-0.9966062632698699, 0.0037903548524694723, -0.01079471175741654, -1.2950010797910734, 18.155738096382663, 1.5038196891497033] 170
19 -0.321566 [-0.9966095417988432, 0.009691721966747549, -0.010474328958449622, -1.2431965642694098, 18.133631365175866, 1.5281747175751874] 171
20 -0.32175 [-0.9965791777806454, 0.014818617402532909, -0.009831307172500204, -1.18898510243976, 18.115493647612237, 1.551222011087254] 172
21 -0.321911 [-0.9965380489541291, 0.01947461973870432, -0.008994459881054625, -1.1326694620945592, 18.102712142615985, 1.5731609795157084] 173
22 -0.322066 [-0.9964925668466985, 0.023493258025270178, -0.007988745221613896, -1.0750644096380635, 18.09328909523815, 1.5938927187359735] 174
23 -0.322221 [-0.9964257456487594, 0.026985679472946306, -0.0068501880534143356, -1.0165562927536298, 18.08646937631101, 1.6134488571325176] 175
24 -0.32236 [-0.9963526565764085, 0.03011022247480589, -0.005605167384654802, -0.9576054038609274, 18.08096442355631, 1.6323014061345706] 176
25 -0.3225 [-0.996310018497647, 0.03291942232625954, -0.00431820841487186, -0.8983388411389333, 18.0767176619454, 1.650645137108431] 177
26 -0.322659 [-0.9962985635797527, 0.035479756197495216, -0.0030200809035903662, -0.8388404368007955, 18.07353271992381, 1.6685278629311697] 178
27 -0.322825 [-0.9962668770938863, 0.037817483306547155, -0.001707716028607217, -0.7791942429418713, 18.071198056186027, 1.6862101588389924] 179
28 -0.32298 [-0.9962123790995648, 0.039956813777842326, -0.00035330752455142397, -0.7195109558781154, 18.069056403201966, 1.7039134648666234] 180
29 -0.323122 [-0.9961823888741268, 0.041915782721514874, 0.0010217515292145877, -0.6597296556593815, 18.067687280919447, 1.7214037661132702] 181
30 -0.323273 [-0.99618311160041, 0.04371715815781243, 0.0024450846314269803, -0.5999299150806466, 18.06717210260492, 1.7388516825524136] 182
31 -0.323434 [-0.996194523880867, 0.04537524001080007, 0.0038531381746146087, -0.5400459676326401, 18.06786770625148, 1.756027849832353] 183
32 -0.323612 [-0.9962172264775198, 0.04690086969725138, 0.0052276198672624495, -0.48017033686562777, 18.06935825407447, 1.7731976715983637] 184
33 -0.323792 [-0.996231447295931, 0.048273940223347904, 0.0066146817701852, -0.42044698769336136, 18.0715073325163, 1.790907465138616] 185
34 -0.32396 [-0.9962417503640686, 0.04953204410596337, 0.008032511752234319, -0.36092199927026963, 18.074200610653904, 1.8092396240264783] 186
35 -0.324125 [-0.9962535530118547, 0.05069083070278457, 0.009482510565368075, -0.3016052269330352, 18.077246442539675, 1.8281909822876774] 187
36 -0.324291 [-0.996273373079593, 0.051729897443296424, 0.01097450460202386, -0.24245960627365315, 18.080670930414932, 1.8475949451980618] 188
37 -0.324451 [-0.9962917609538628, 0.05265893837323176, 0.012498856055921739, -0.1833836500232646, 18.084325093664074, 1.8671878998746414] 189
38 -0.324601 [-0.9963278605765139, 0.05347266866369995, 0.014025831801517931, -0.1246563745651323, 18.08843917298499, 1.887667518607806] 190
39 -0.324759 [-0.996341254178279, 0.05411765230451132, 0.015592537188868452, -0.06628110793636662, 18.09286049000975, 1.909178376077267] 191
40 -0.32489 [-0.9963380535250018, 0.054569419225904275, 0.017213581982544787, -0.008239880165644316, 18.09769380729698, 1.9315508004518944] 192
41 -0.325 [-0.9963291284845393, 0.05484126116595535, 0.01889828426618134, 0.049491963424848545, 18.10312961903492, 1.9545890848101373] 193
42 -0.325108 [-0.9963290968734719, 0.05492783830145441, 0.020644721305665394, 0.1066465234147791, 18.109138852564882, 1.9788727195927294] 194
43 -0.325207 [-0.9963265550504539, 0.05479835179728632, 0.02249282236287178, 0.16302535298904655, 18.11613990847747, 2.0046406421386513] 195
44 -0.325302 [-0.9962826222019006, 0.05439257505638011, 0.024476683225087167, 0.21838801380984144, 18.123408538314262, 2.032418235285639] 196
45 -0.325363 [-0.9962781742246798, 0.053641464341828766, 0.026559747870701665, 0.27183108954467383, 18.131926087336794, 2.06336749495553] 197
46 -0.325437 [-0.9962330240648347, 0.05245955260818818, 0.02876040319945567, 0.3235281538386039, 18.141443765040645, 2.096771967465291] 198
47 -0.325477 [-0.9962218083784847, 0.050771181316540244, 0.031025598150545366, 0.3722734557873156, 18.152552213002608, 2.133837814966623] 199
48 -0.325535 [-0.9961957019657434, 0.048419374371421256, 0.03346533048362027, 0.4168086910878763, 18.16573475034471, 2.175058206488189] 200
49 -0.325561 [-0.9962092656510433, 0.045115774010732114, 0.03597587196322294, 0.4537878431605798, 18.18155176852527, 2.222142994424637] 201
50 -0.325596 [-0.9962454585531454, 0.040802175486558484, 0.03852436904469896, 0.48325625807955885, 18.19814507634394, 2.2737119885319355] 202
51 -0.325637 [-0.9963537230532812, 0.035444749362588165, 0.040863288007376077, 0.5003131277440694, 18.214900023800915, 2.330261399789681] 203
52 -0.325723 [-0.996527054986816, 0.02970242848000208, 0.04293333477777046, 0.5072415239562689, 18.2335246029181, 2.388203752069577] 204
53 -0.325901 [-0.9966075381754523, 0.023708366922316083, 0.04463939493933944, 0.5060143660928476, 18.254487043787154, 2.4457355759533153] 205
54 -0.325997 [-0.9966691156756334, 0.017665567245960023, 0.0459982953716073, 0.49211234654380653, 18.277241466278475, 2.500887659362999] 206
55 -0.326083 [-0.9969247235778618, 0.012149622285284371, 0.04678089534311625, 0.46882935510502105, 18.29604822641716, 2.5542031448747644] 207
56 -0.326437 [-0.9970490938610065, 0.006910228601389411, 0.04753380491084879, 0.4395487204395185, 18.31261718667517, 2.605673831355057] 208
57 -0.326668 [-0.9970630451698781, 0.001960068804554102, 0.04808896129595806, 0.403112558299175, 18.326926011422053, 2.653363241371075] 209
58 -0.326763 [-0.997117667778149, -0.0026202852000437684, 0.048324537100182134, 0.3632741686189783, 18.34075907519064, 2.698512296861627] 210
59 -0.326914 [-0.9971468948761685, -0.006991865458268423, 0.04843241140122256, 0.3209811054403995, 18.355157144607983, 2.7412919399390043] 211
60 -0.327027 [-0.9972040032610069, -0.010987739573747244, 0.048264261923333426, 0.2766336147954856, 18.36738678588247, 2.7827294400532376] 212
61 -0.327171 [-0.9971487470098572, -0.014578505017992464, 0.04787117826751574, 0.23012173121822493, 18.380097405261818, 2.821820765330817] 213
62 -0.327124 [-0.9970840598385896, -0.017929766665171005, 0.0474081570438598, 0.1827145925493424, 18.39258398370303, 2.859976004897376] 214
63 -0.327077 [-0.9971074233662713, -0.021045543302212977, 0.04682427815346036, 0.13491862469822968, 18.4043054489775, 2.8979261118385993] 215
64 -0.327155 [-0.9971178102411488, -0.02398330789915025, 0.04606305258481181, 0.08740491312698355, 18.416436732971945, 2.9361688191827002] 216
65 -0.327191 [-0.9970680004286583, -0.026711917191597788, 0.04516993089740013, 0.03967785671447476, 18.42752244105413, 2.9745343941690003] 217
66 -0.327117 [-0.9970326468183087, -0.029113109372188483, 0.04412610673128555, -0.009581128034061415, 18.4365334990757, 3.011559990081602] 218
67 -0.327065 [-0.9970810183034498, -0.03121860235887168, 0.04297063943783801, -0.05869697185459339, 18.444728420400494, 3.048959565226416] 219
68 -0.327122 [-0.9971939064591566, -0.03303340505057672, 0.04163468583748233, -0.10723311041740652, 18.452209741223264, 3.087118153987195] 220
69 -0.327256 [-0.997294835842965, -0.034613970679206504, 0.04007983409242977, -0.15411341249481247, 18.458803730663654, 3.1275297054313884] 221
70 -0.327343 [-0.9972429653917063, -0.03575530827928365, 0.03831913025793629, -0.20052980033904919, 18.465722684095137, 3.168475720759944] 222
71 -0.32716 [-0.9973051652754471, -0.036445941309626195, 0.03643846429370189, -0.24640929402155376, 18.469702639159483, 3.210535273782723] 223
72 -0.327124 [-0.9973297998859507, -0.036495940811539944, 0.03436978693355944, -0.29043814186162437, 18.472695051914325, 3.2545632200629213] 224
73 -0.326995 [-0.9974105434733961, -0.03575261765034475, 0.03203766290213115, -0.33203092281180113, 18.471796355516755, 3.3009388353271443] 225
74 -0.326902 [-0.9975242835242865, -0.03390315514832088, 0.029389537034777344, -0.3686457337470572, 18.46719605023781, 3.350951034393313] 226
75 -0.326788 [-0.9976646987146724, -0.030632330218752276, 0.026457741498470258, -0.39745546917781, 18.458848709093562, 3.4050464075974527] 227
76 -0.326661 [-0.9979965952149876, -0.025577711045433195, 0.023118537987951195, -0.41443123638729956, 18.448811378626225, 3.462965246055269] 228
77 -0.326688 [-0.9978819193198558, -0.01866200258558806, 0.019685256559921115, -0.4094308934106992, 18.44184005180418, 3.521671034088662] 229
78 -0.326312 [-0.9983584192812616, -0.010864170941065156, 0.016881167859533305, -0.3941076475016332, 18.42368948960345, 3.5759491644972163] 230
79 -0.326582 [-0.99782482176194, -0.003911529342526285, 0.015137829075920303, -0.35533688783446893, 18.418417326459238, 3.6176158688905735] 231
80 -0.326129 [-0.9981727202820264, 0.002857765061156263, 0.013931145744109827, -0.31801304973708744, 18.398437759643414, 3.6601776830648824] 232
81 -0.326448 [-0.9979007953034299, 0.00830882735723892, 0.013495636480844576, -0.26495046843454073, 18.386328534091348, 3.687709542491085] 233
82 -0.326356 [-0.9979923717620033, 0.012764900649657993, 0.013557095047953792, -0.21149729070206774, 18.37407021360611, 3.7159741930587313] 234
83 -0.326549 [-0.9977358987997964, 0.016511951581564436, 0.014144767805442758, -0.1555838451490227, 18.36235075758351, 3.7393442793257883] 235
84 -0.326521 [-0.997607248942934, 0.01980613642875968, 0.014879950124945012, -0.09969707066152869, 18.349485085726467, 3.7631874780411625] 236
85 -0.326584 [-0.9975854472467965, 0.022747594070888742, 0.015778685033286076, -0.04409851070919139, 18.336958132668617, 3.788034655729734] 237
86 -0.326717 [-0.9974033406316399, 0.025378703678170012, 0.016825861409596233, 0.01231790797450321, 18.32558918549218, 3.8115316438073066] 238
87 -0.326732 [-0.9974568375505127, 0.027626089908366278, 0.018019978109071424, 0.06806871782745615, 18.31328605367222, 3.836097262480453] 239
88 -0.326917 [-0.997285618087791, 0.029421299543550553, 0.019346086193854767, 0.1253865929070132, 18.30313690584186, 3.8582121474551463] 240
89 -0.32692 [-0.9972296982809089, 0.030788275792003612, 0.02086951336407509, 0.18224354183271585, 18.29191345410138, 3.881245921540991] 241
90 -0.326992 [-0.9972168435708785, 0.03169154847590816, 0.022537858836611822, 0.2389209444087252, 18.28213308989889, 3.9053554386059135] 242
91 -0.3271 [-0.9971792674675676, 0.032111181668936215, 0.02434406616173269, 0.29483888446266776, 18.27366905438806, 3.93169369182595] 243
92 -0.327173 [-0.9972167557463645, 0.031842811763547856, 0.02643035542731427, 0.3488066180002089, 18.26840046144508, 3.9623769515124283] 244
93 -0.327307 [-0.9972256096040572, 0.030605731867524005, 0.02892371922394254, 0.39956135391372216, 18.267668548134292, 3.9983917584645887] 245
94 -0.327423 [-0.9972071609508848, 0.027740681601570297, 0.031962801923071035, 0.4435578504865092, 18.27174862018351, 4.041797252518311] 246
95 -0.327501 [-0.9973104504954735, 0.02256888861689483, 0.03521312725904469, 0.47099108910563253, 18.28182214905108, 4.09560825824464] 247
96 -0.327704 [-0.9972206262475427, 0.015237419694956948, 0.03813365523433314, 0.4587400520109586, 18.293530494425926, 4.153524229734285] 248
97 -0.327667 [-0.9977170805027328, 0.009373394645111261, 0.039265600513754474, 0.4274798043054462, 18.305800698726728, 4.2022790914994745] 249
98 -0.328446 [-0.9974354745440217, 0.003793991631526131, 0.039774768834403985, 0.3868257979990891, 18.318673739447608, 4.2453139324629126] 250
99 -0.32805 [-0.9975502680598491, -0.0012403254462240764, 0.03970243649813168, 0.340249925166598, 18.325734186034875, 4.284971116714585] 251
100 -0.328217 [-0.9975376088894468, -0.005588622669752088, 0.03934316517822002, 0.29190560089447337, 18.33653482071911, 4.322066968905415] 252
101 -0.328201 [-0.9976156919971839, -0.009375527466045384, 0.03878738377128957, 0.24248327442069117, 18.34681437255573, 4.357992067827839] 253
102 -0.328319 [-0.9975967312733959, -0.012708791076527254, 0.03795307383779208, 0.19210448758823134, 18.353956400280648, 4.393625485315475] 254
103 -0.328256 [-0.9974741351819978, -0.015284145092159248, 0.03681523963451739, 0.1403702544827195, 18.355945392811158, 4.427891356274878] 255
104 -0.328003 [-0.9976659105678083, -0.017118336865519345, 0.035329405188093105, 0.08868161154725682, 18.355929745660365, 4.462213132436235] 256
105 -0.328205 [-0.9975776121130443, -0.018221851533847627, 0.03327342549701732, 0.03877679984436322, 18.352569025685607, 4.499076443370189] 257
106 -0.327892 [-0.998065469026932, -0.01810866446775994, 0.03087307178812477, -0.009440323922286803, 18.34498721796055, 4.534804699694509] 258
107 -0.328454 [-0.9971072243437977, -0.016891093861313745, 0.02827329161583844, -0.047733879135161715, 18.33440257282015, 4.56709644517444] 259
108 -0.326845 [-0.9983600058727906, -0.014520969193147427, 0.025938740993587124, -0.08537907726258093, 18.318845997655025, 4.592853477755555] 260
109 -0.328406 [-0.996735954043653, -0.010836158505937466, 0.02366607909986446, -0.09678814171702532, 18.31175387125771, 4.6176769968116655] 261
110 -0.326191 [-0.9982689179255319, -0.007537660445341858, 0.021988780408626413, -0.1192044273060539, 18.28268000597665, 4.639776793905806] 262
111 -0.327852 [-0.9973028723626751, 0.000487930174431531, 0.019537405897344866, -0.08931243139818656, 18.26343934220975, 4.674973968078895] 263
112 -0.326681 [-0.9985699356064925, 0.0057930043757121125, 0.018489024544785203, -0.07366753617611559, 18.232238476064413, 4.70350435995651] 264
113 -0.328072 [-0.9972737361767936, 0.009240564510208011, 0.01855469851912859, -0.029835362570517, 18.231095319966542, 4.7164069727089935] 265
114 -0.326807 [-0.9982463671193026, 0.013849481829383586, 0.018738139099018374, 0.005539579614922088, 18.201623951392193, 4.741332015991891] 266
115 -0.327884 [-0.9971566628920602, 0.01710613465800021, 0.019419580727469247, 0.05596392900716499, 18.195325265599987, 4.755645158501503] 267
116 -0.326939 [-0.998006039206137, 0.02029150599335005, 0.020490412936100433, 0.10105539941702925, 18.17499448256701, 4.779219264612173] 268
117 -0.327959 [-0.9970860282527259, 0.02264719709899147, 0.02168065410517583, 0.15431061833730828, 18.168086482768793, 4.795741659103083] 269
118 -0.327179 [-0.9978989076387146, 0.024638662802681788, 0.023202778135446345, 0.20203498412783372, 18.154881214046732, 4.820416474711415] 270
119 -0.328215 [-0.9969748430178, 0.02551201683091797, 0.024923752748681412, 0.2549763844832133, 18.148564755481388, 4.8372178716789245] 271
120 -0.327328 [-0.9977120695261181, 0.025498363588183262, 0.027086725031953012, 0.3004575417780163, 18.137907476471902, 4.8698900218180965] 272
121 -0.328328 [-0.996765042475647, 0.024319667462362738, 0.02981046970013876, 0.35114314921938283, 18.13175658890011, 4.891427167516688] 273
122 -0.327312 [-0.9981020218150086, 0.021054077237231378, 0.03214256609678592, 0.37007697386868466, 18.12581450041111, 4.929196692974023] 274
123 -0.329336 [-0.996376451637505, 0.018132391312401963, 0.033985156691808724, 0.3855025897899764, 18.142912441530026, 4.9448703327508134] 275
124 -0.326905 [-0.9981108838502154, 0.013838475087453058, 0.03510543764629477, 0.3737819899561318, 18.133726590732575, 4.969414873823865] 276
125 -0.329491 [-0.996279349201433, 0.010672228447332859, 0.03623851318027634, 0.3702477915882465, 18.15046269063561, 4.983417688005283] 277
126 -0.326772 [-0.9979638804695897, 0.006598835595124731, 0.036598833922254256, 0.3468201939576743, 18.14144166017119, 5.007232476409578] 278
127 -0.329292 [-0.9965567847975186, 0.0017591544680041569, 0.036974830306006165, 0.31438007375221816, 18.15459803141559, 5.031237215791042] 279
128 -0.327103 [-0.9980537935651755, -0.0012827176228755845, 0.036823605296469275, 0.28366398068607385, 18.149423804472093, 5.0559026318678635] 280
129 -0.329455 [-0.9967104770514795, -0.0050854271709898195, 0.03647051413403366, 0.24897489672567863, 18.162464027007672, 5.07937759947659] 281
130 -0.327294 [-0.9979985662921647, -0.007426617557186464, 0.03603487005708872, 0.208585392892688, 18.154169413371427, 5.100639901113567] 282
131 -0.329315 [-0.9969545767175669, -0.0104247610385463, 0.03512012741149928, 0.16628134889949125, 18.16361413860664, 5.128406023919429] 283
132 -0.327567 [-0.9981040373478157, -0.01171051480107132, 0.03401595681513233, 0.12015548324215294, 18.15668481749985, 5.145274978200108] 284
133 -0.329366 [-0.9968639382434521, -0.01245362839529151, 0.03236480815010596, 0.08178350487454006, 18.16132431378173, 5.16970474145385] 285
134 -0.32725 [-0.998209854011833, -0.012322842389575433, 0.030887805514325843, 0.040704766974881554, 18.1502845705303, 5.1853702947633815] 286
135 -0.329239 [-0.9966579098055997, -0.011103479842873087, 0.028847512621708482, 0.013278267156423041, 18.152460473147173, 5.206177774271052] 287
136 -0.326751 [-0.9982279421099527, -0.009538067503669203, 0.027403159215211786, -0.01895460213164878, 18.13255569868509, 5.220440919539842] 288
137 -0.328874 [-0.9964107682722748, -0.005223440704178144, 0.024640156685263596, -0.02604577730231536, 18.13812681799805, 5.239784429671138] 289
138 -0.326266 [-0.9981238787375677, -0.00286184713655078, 0.02355989085033441, -0.0425705578873178, 18.10518993876214, 5.251308886352815] 290
139 -0.328319 [-0.9979574817883556, 0.0017474381295347176, 0.02259225298117358, -0.015973311399088298, 18.104907080355204, 5.263013234358774] 291
140 -0.328027 [-0.9979608509753186, 0.005665670403046849, 0.022152291911407152, 0.01195875157393475, 18.100845833673016, 5.273858112317914] 292
141 -0.328072 [-0.9977917242024062, 0.008648502674466901, 0.022028170848741924, 0.040662581770414055, 18.0979306487865, 5.283023927251229] 293
142 -0.327918 [-0.9977982494448427, 0.01135334176009576, 0.022178769664718937, 0.06872218687266397, 18.091395832212516, 5.293781932418422] 294
143 -0.328007 [-0.9977001977051486, 0.013649282380758325, 0.02256893116729404, 0.09732277586937518, 18.086399836454383, 5.304177798909395] 295
144 -0.327987 [-0.9977291219085395, 0.015568045829748172, 0.023145482581612913, 0.12582230240293005, 18.08086925803949, 5.314787368048717] 296
145 -0.328124 [-0.9976198114408928, 0.017085196057098514, 0.023859687133796097, 0.15490186158870306, 18.076528066684393, 5.3245872029830785] 297
146 -0.328097 [-0.9976224875282621, 0.01823871828454712, 0.02470469775404322, 0.1843116390025067, 18.071801331016648, 5.333482996954605] 298
147 -0.328216 [-0.9975390145345288, 0.019016500659278995, 0.025696989128254764, 0.21373377056419565, 18.067465350917267, 5.342633009609248] 299
148 -0.328211 [-0.997581611573443, 0.01933868520067864, 0.02693495830164724, 0.2428812587256476, 18.06342738651601, 5.35249210942006] 300
149 -0.328366 [-0.9973786332338491, 0.01897243528405698, 0.028473683189439134, 0.2706344155517432, 18.05977436188588, 5.364910996058993] 301
150 -0.328202 [-0.9977741984261782, 0.017612943028188388, 0.030275306292745274, 0.29428430978911735, 18.05518448222669, 5.378265240843649] 302
151 -0.328887 [-0.9970216594805247, 0.015794895477230238, 0.03173407730669402, 0.31007035696238466, 18.06208192922827, 5.388443614665577] 303
152 -0.327864 [-0.99789001111237, 0.013479545232681495, 0.03260229817741824, 0.30586794385338945, 18.05981868774446, 5.400434020590466] 304
153 -0.329209 [-0.997088331512151, 0.011219550630470823, 0.033861934912404176, 0.3125412913913053, 18.072883939994966, 5.4086362060254345] 305
154 -0.328003 [-0.9979120981132398, 0.008807121439539066, 0.03436454587637042, 0.3018982782280952, 18.07410094346607, 5.419306448687169] 306
155 -0.32935 [-0.9970830320478311, 0.006418879424787454, 0.03493794077696918, 0.29747106913625454, 18.08526539950569, 5.427522579417196] 307
156 -0.328017 [-0.9978653322461432, 0.004372632759226606, 0.035235380531714086, 0.28352185609080793, 18.08614665030472, 5.438104724197793] 308
157 -0.329289 [-0.9973645804005677, 0.0013017627863656607, 0.03541351047619138, 0.2691111352877279, 18.101548674681425, 5.452382394827086] 309
158 -0.328438 [-0.997836406600557, -0.0011291480979577862, 0.03523089389030179, 0.24627566559603942, 18.107855121675765, 5.464489805805888] 310
159 -0.329207 [-0.9976050737479251, -0.0035268148014835736, 0.034954411351709715, 0.2234510696001294, 18.120897469885097, 5.478464872525717] 311
160 -0.328794 [-0.9978673857808995, -0.005346487062564814, 0.03447711619242908, 0.19810679030349546, 18.126898469397613, 5.492813028730387] 312
161 -0.329203 [-0.9976597298342652, -0.006910202798953825, 0.03384577353690781, 0.17267144190141054, 18.135655784920136, 5.506318768909291] 313
162 -0.328804 [-0.9978750587179309, -0.008000596783225695, 0.033156498903621275, 0.14534289183970628, 18.137274863143002, 5.51941486022068] 314
163 -0.32911 [-0.9977004366928452, -0.00864805445801135, 0.032224905860373035, 0.11772239566478851, 18.14101801184789, 5.53149475612671] 315
164 -0.328731 [-0.9980074097403074, -0.008755463765878812, 0.03109449914855572, 0.09040871633634454, 18.13896429151179, 5.542841876261721] 316
165 -0.329142 [-0.9973825325377078, -0.007947938819989585, 0.02963818005879558, 0.06992218654015978, 18.13881227947552, 5.548845968172186] 317
166 -0.327982 [-0.9981567096114755, -0.006993889051209845, 0.028764794741062357, 0.05465455746563998, 18.129719059476688, 5.554092158056707] 318
167 -0.329165 [-0.9972809426594694, -0.005509438499734728, 0.027622754970632865, 0.049423796679189634, 18.13236634315802, 5.5573815159634945] 319
168 -0.327662 [-0.9980963315780299, -0.004222818022828151, 0.026832587448320063, 0.03817227199425688, 18.120011026924715, 5.563509972313603] 320
169 -0.328852 [-0.9977784965473928, -0.0019062755870109939, 0.02586818630693489, 0.04437944856363644, 18.11923049539006, 5.569495605872543] 321
170 -0.328264 [-0.9981781189200302, 0.00022790411024298934, 0.02517290406090805, 0.04670192790280608, 18.115006049601426, 5.574939270877709] 322
171 -0.328854 [-0.9979081825685077, 0.0016235410704112246, 0.024943449040382027, 0.058231872997816944, 18.115943544641205, 5.578167034764932] 323
172 -0.328409 [-0.9978968304012918, 0.0037959584752240262, 0.024662216004632437, 0.07207154884717883, 18.1128574036177, 5.5830365669998905] 324
173 -0.328407 [-0.9978096351515106, 0.005515796083539976, 0.024530631454373685, 0.08614390867346619, 18.109354945165183, 5.5868473380777965] 325
174 -0.328313 [-0.9978290613707435, 0.00710109500052061, 0.02447689755028835, 0.10002478285564438, 18.1043911734369, 5.590835956008005] 326
175 -0.328369 [-0.9978652018598593, 0.008469011229624545, 0.024480879201082648, 0.11417133496712462, 18.100731140552995, 5.595388140741755] 327
176 -0.328457 [-0.9978151687795181, 0.009691299896297894, 0.024562164510245746, 0.12879189938382474, 18.098616345330804, 5.599677697317937] 328
177 -0.328425 [-0.9978201156118147, 0.010813356229476925, 0.02474659914227113, 0.14342811810289885, 18.09634471458299, 5.60404874865308] 329
178 -0.328478 [-0.9977539076267921, 0.01179155966459417, 0.02504149740038315, 0.15817254427410934, 18.094040939972267, 5.607891693762574] 330
179 -0.328441 [-0.9977576117724656, 0.012644302015210334, 0.025384492066587418, 0.1728278943828135, 18.09062819069144, 5.611603129447805] 331
180 -0.328496 [-0.9977094180799482, 0.013349478654446661, 0.025807452534086672, 0.187536650811284, 18.08725169416911, 5.615184470293326] 332
181 -0.328487 [-0.9977019982114267, 0.013896543859251806, 0.026311134899186135, 0.20203938701452556, 18.083098186720935, 5.618947552066965] 333
182 -0.328538 [-0.9976674429887237, 0.01423336025353041, 0.026876624525221056, 0.21672006456616774, 18.079336280081645, 5.622482574755173] 334
183 -0.32855 [-0.9976474876227269, 0.014351980388234447, 0.02753161563345445, 0.23123420496510427, 18.075079986909184, 5.62616906709] 335
184 -0.328579 [-0.9976146942028096, 0.014156821958032095, 0.028312338062541857, 0.2456890009085579, 18.07087673901216, 5.630007979993603] 336
185 -0.328596 [-0.9976277483364442, 0.013528981061898867, 0.029232502324832085, 0.25979239666631915, 18.06651744591542, 5.634507975172578] 337
186 -0.32868 [-0.9975444180293487, 0.012137592603244629, 0.030402173263964945, 0.27377022392829653, 18.06485954926698, 5.639811526751728] 338
187 -0.328625 [-0.9978356549100964, 0.009599736357496258, 0.031594408543284956, 0.27741534829266257, 18.06085480280145, 5.6488118434329015] 339
188 -0.329149 [-0.9974662392837803, 0.008150163701208855, 0.032293059284503114, 0.27764056172017376, 18.068384699306105, 5.654517954120231] 340
189 -0.32858 [-0.9978001612285504, 0.006560688419375774, 0.03262102428415324, 0.2680943966280872, 18.068331212031968, 5.658979260949462] 341
190 -0.329138 [-0.9977172917104623, 0.004701443347259673, 0.03295530672890162, 0.26183363945601146, 18.07871701186006, 5.667625471749657] 342
191 -0.329003 [-0.9977792505702892, 0.0029720677914548185, 0.033177265458208476, 0.25144997025136073, 18.08663812298497, 5.67516118705311] 343
192 -0.329109 [-0.9977011337400666, 0.001415875374106352, 0.03324642954801077, 0.24000885192481414, 18.093478850028777, 5.682187882923784] 344
193 -0.328967 [-0.9978116488228801, 0.00009079428294273841, 0.03318891534992891, 0.22763509346113087, 18.098944483806477, 5.688545523141943] 345
194 -0.329143 [-0.9976971292170964, -0.0010215635677111108, 0.03308732760202188, 0.21526737093400874, 18.105116045067057, 5.694189026806784] 346
195 -0.328936 [-0.9978528276739366, -0.0019001877054706197, 0.03287735415010303, 0.20237980989576385, 18.10946070686266, 5.699581426132607] 347
196 -0.329183 [-0.9976785239290685, -0.0027094947114772853, 0.0325688979528428, 0.1901083602784944, 18.114925204821528, 5.70420362008804] 348
197 -0.328861 [-0.9979029361409855, -0.0032284018718885133, 0.03227031933257928, 0.177245056326962, 18.117420808167083, 5.708105280760299] 349
198 -0.329211 [-0.9976472782803707, -0.003721185838935605, 0.031872411488001746, 0.16571921970740355, 18.121252758234412, 5.711480019832107] 350
199 -0.328734 [-0.9979381262606579, -0.0039185981584585, 0.03152729321201497, 0.15385054057054554, 18.122308219197258, 5.71439833532196] 351
Generating output ...
Result =
Versor X = -0.996279
Versor Y = 0.0106722
Versor Z = 0.0362385
Translation X = 0.370248
Translation Y = 18.1505
Translation Z = 4.98342
Iterations = 200
Metric value = -0.329491
Matrix =
0.997146 -0.0268792 -0.070554
-0.0156508 -0.987772 0.155121
-0.0738607 -0.153574 -0.985373
Offset =
[-0.544034, -17.4274, -9.67461]
The problem is, at level 1 (the second level), the value of versor X changes drastically from 0.9665892 to -0.9253578 in the first iteration. After the big jump, the optimizer can not recover from it anymore. Is it because the discontinuity of the parameters between level 0 and 1, or should I increase the smoothing sigma at level 0 and 1? Any idea to improve the results?
Thanks.
Fang