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-435.99800 (and) -437.02000 (indoor) ] TJ -11.95510 -11.95590 Td [ (scenes\054) -388.00700 (consist) -361.00600 (of) -360.99700 (a) -359.98400 (set) -360.99000 (of) -360.99700 (parallel) -360.00900 (and) -360.99400 (orthogonal) -361.00100 (planes\056) ] TJ 11.95510 TL T* [ (These) -293.00400 (structures) -292.98900 (are) -292.98300 (commonly) -293.00100 (approximated) -293.01500 (by) -294.02000 (the) -293.00300 (Man\055) ] TJ T* [ (hattan) -391.01700 (W) 79.98730 (orld) -391.01900 (\050MW\051) -390.98900 (assumption) -391.01800 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 188.30400 255.03800 Tm (5) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 193.28500 255.03800 Tm [ (\135) -390.99700 (in) -390.98100 (the) -390.98600 <02656c6473> -391.00300 (of) -390.99100 (com\055) ] TJ -143.17300 -11.95470 Td [ (puter) -233.01000 (vision) -232.98400 (and) -233.01400 (robotics\056) -303.99700 (Under) -233.01500 (the) -233.01300 (MW) -233.00800 (assumption\054) -237.00200 (three) ] TJ 11.95510 TL T* [ (orthogonal) -374.99900 (directions) -373.98500 (are) -375.00800 (used) -374.98400 (to) -374.98400 (represent) -374.01100 (a) -375.00100 (scene) -374.99900 (struc\055) ] TJ 11.95590 TL T* [ (ture\054) -392.00600 (which) -364.00200 (are) -363.99100 (referred) -364 (to) -364.00500 (as) -364.01600 (the) -364.01000 (Manhattan) -363.99100 (Frame) -364.00300 (\050MF\051) ] TJ 11.95510 TL T* [ (in) -344.00900 (pre) 25.01300 (vious) -343.99300 (studies) -343.98900 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 133.20000 207.21700 Tm (27) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 143.16200 207.21700 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 149.07000 207.21700 Tm (9) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 154.05200 207.21700 Tm [ (\135\056) -592.02000 (Recent) -344.00900 (studies) -343.98900 (ha) 19.99670 (v) 14.98280 (e) -343.98700 (proposed) ] TJ -103.93900 -11.95510 Td [ (a) -357.00400 (v) 24.98110 (ariety) -356.99200 (of) -356.99700 (MF) -355.99300 (estimation) -356.99100 (methods) -357.00300 (for) -357.00200 (scene) -357.00200 (representa\055) ] TJ 11.95510 TL T* [ (tion) -401.00700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 72.92660 183.30700 Tm (8) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 77.90780 183.30700 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 84.38360 183.30700 Tm (25) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 94.34610 183.30700 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 100.83200 183.30700 Tm (13) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 110.79400 183.30700 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 117.27000 183.30700 Tm (21) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 127.23200 183.30700 Tm [ (\135\056) -761.99200 (In) -400.99100 (addition) -400.99400 (to) -400 (scene) -400.99400 (representation\054) ] TJ -77.12030 -11.95510 Td [ (an) -362.99800 (accurate) -363.01100 (estimation) -362.99000 (of) -362.99700 (MF) -363.01200 (is) -362.98500 (important) -362.99600 (as) -362.99600 (a) -363.98300 (k) 10.00320 (e) 15.01220 (y) -362.99300 (mod\055) ] TJ 11.95470 TL T* [ (ule) -362.01000 (for) -363 (man) 14.99080 (y) -362.01300 (computer) -361.99600 (vision) -363.00200 (applications\054) -390.00800 (such) -362.00600 (as) -362.99600 (scene) ] TJ 11.95630 TL T* [ (understanding) -273.00800 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 112.59800 147.44100 Tm (24) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 122.56000 147.44100 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 127.77100 147.44100 Tm (4) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 132.75200 147.44100 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 137.95200 147.44100 Tm (11) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 147.91500 147.44100 Tm [ (\135\054) -279.01300 (SLAM) -272.98100 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 190.21600 147.44100 Tm (6) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 195.19700 147.44100 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 200.40800 147.44100 Tm (30) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 210.37000 147.44100 Tm [ (\135\054) -277.99300 (focal) -273.01300 (length) -272.98900 (esti\055) ] TJ -160.25800 -11.95510 Td [ (mation) -317.99300 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 84.27380 135.48600 Tm (27) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 94.23630 135.48600 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 99.89490 135.48600 Tm (2) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 104.87600 135.48600 Tm [ (\135\054) -335.98400 (and) -317.98000 (3D) -318.01800 (reconstruction) -319.01200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 210.41000 135.48600 Tm (8) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 215.40100 135.48600 Tm [ (\135) 1.01699 (\056) -515.01000 (Since) -318.98800 (MF) -318 (esti\055) ] TJ -165.28900 -11.95470 Td [ (mation) -256.98300 (is) -257.00200 (typically) -256.98000 (used) -257.00400 (as) -257.01500 (an) -257.01500 (early) -257.01600 (phase) -257.00900 (module) -258.00600 (in) -257.00400 (such) -257.00400 (a) ] TJ 11.95510 TL T* [ (wide) -283.98100 (range) -283.01300 (of) -283.99100 (applications\054) -291.98600 (its) -282.99100 (o) 14.98280 (v) 14.98280 (erall) -283.98900 (performance) -283.01200 (is) -284.01900 (criti\055) ] TJ T* [ (cal) -249.99900 (for) -249.99900 (the) -249.99000 (viability) -249.99000 (of) -249.99600 (the) -249.99000 (application) -250.00100 (as) -249.99500 (a) -250.00200 (whole\056) ] TJ ET Q 3.98000 w 0 G 501.12100 904.14800 m 1446.11000 904.14800 l S q 10 0 0 10 0 0 cm BT /R41 5.97760 Tf 1 0 0 1 60.14100 83.81290 Tm [ <03> -0.90058 ] TJ /R31 7.97010 Tf 4.31680 -2.81289 Td [ (The) -249.98800 <02727374> -250.01700 (and) -249.97800 (the) -250.00500 (second) -249.98700 (authors) -250.01700 (pro) 14.98830 (vided) -249.98400 (equal) -250.01300 (contrib) 19.99660 (utions\056) ] TJ /R31 9.96260 Tf 256.35900 487.26800 Td [ (In) -343 (order) -343.00200 (to) -344.00900 (ensure) -342.99700 (the) -342.99200 (v) 14.98280 (ersatile) -342.99200 (applicability) -342.99200 (to) -344.01100 (a) -343.00700 (broad) ] TJ -11.95510 -11.95510 Td [ (range) -398.99500 (of) -398.99000 (applications\054) -436 (a) -398.99700 (gi) 24.98600 (v) 14.98280 (en) -398.99200 (MF) -399.00700 (estimation) -398.98200 (method) -399.00200 (re\055) ] TJ 11.95590 TL T* [ (quires) -268.01900 (tw) 10.00810 (o) -267.00900 (properties\072) ] TJ /R39 9.96260 Tf 90.57300 0 Td (stability) Tj /R31 9.96260 Tf 34.77380 0 Td (and) Tj /R39 9.96260 Tf 17.05200 0 Td [ (ef) 18.00190 <026369656e6379> ] TJ /R31 9.96260 Tf 37.44020 0 Td [ (\056) -362.99300 (F) 14.99260 (or) -267.01400 (stability) 65.01860 (\054) ] TJ -179.83900 -11.95510 Td [ (the) -221.01500 (rob) 20.00400 (ustness) -220.01000 (ag) 5.01877 (ainst) -221 (noise) -219.98300 (and) -221.01700 (outliers) -220.01200 (is) -221.00700 (essential\054) -226.01100 (as) -220.98300 (well) ] TJ 11.95510 TL T* [ (as) -275.99100 (the) -275.98600 (estimation) -275.00300 (method\047) 54.99570 (s) -275.98800 (insensiti) 24.98110 (vity) -276.00800 (to) -275.98300 (its) -276.01300 (initialization\056) ] TJ T* [ (As) -300.99900 (for) -301.01100 (ef) 25.00810 <026369656e63> 14.99260 (y) 65.01370 (\054) -313.00400 (the) -301.00100 (computational) -300.99400 (comple) 14.99750 (xity) -300.98400 (of) -301.00900 (the) -300.99900 (MF) ] TJ T* [ (estimation) -209.01400 (has) -209.01700 (to) -209.01200 (remain) -209.01200 (reasonable\056) -296.01900 (Ev) 14.98770 (en) -208.98500 (when) -209.01400 (its) -209.00400 (stability) ] TJ T* [ (is) -219.99000 (guara) 1.01699 (nteed\054) -225.99200 (an) -220.00300 (MF) -218.99800 (estimation) -219.99300 (with) -218.99800 (a) -220.00700 (high) -218.99800 (order) -220.00300 (comple) 14.99750 (x\055) ] TJ 11.95590 TL T* [ (ity) -233 (is) -233.00800 (undesirable) -232.99500 (for) -232.00300 (time) -232.99500 (critical) -233.00500 (applications\054) ] TJ /R39 9.96260 Tf 187.00200 0 Td [ (e) 15.01220 (\056g) ] TJ /R31 9.96260 Tf 11.74610 0 Td [ (\056\054) -235.99500 (SLAM\056) ] TJ -186.79300 -11.95510 Td [ (In) -241.99600 (this) -242.01400 (research\054) -242.98900 (we) -242.00100 (propose) -242.01800 (a) -242.00400 (rob) 20.00160 (ust) -241.97900 (and) -241.99400 (real\055time) -241.98400 (Man\055) ] TJ -11.95510 -11.95510 Td [ (hattan) -364.98300 (Frame) -364.00300 (\050MF\051) -365.01800 (esti) 0.99738 (mation) -365.00300 (approach) -364.99300 (that) -364.00300 (guarantees) -364.98800 (a) ] TJ 11.95510 TL T* [ (globally) -263.99800 (optimal) -263.01500 (solution) -263.98800 (with) -264.01000 (high) -262.99000 (stability) -263.98500 (and) -263.99000 (ef) 25.00560 <026369656e63> 14.99260 (y) 65.01370 (\056) ] TJ T* [ (W) 79.98660 (e) -369.00200 (pose) -368.00500 (the) -368.99000 (MF) -367.99300 (estimation) -368.98700 (problem) -367.99300 (as) -368.99700 (that) -368.98300 (of) -368.01700 (a) -369.00200 (consen\055) ] TJ 11.95630 TL T* [ (sus) -381.99800 (set) -382.98500 (maximization\054) -415.01200 (and) -382.99000 (solv) 15.00240 (e) -382.02000 (it) -382.98000 (through) -381.98500 (a) -383 (branch\055and\055) ] TJ 11.95510 TL T* [ (bound) -349.99600 (\050BnB\051) -349.01500 (frame) 25.01300 (w) 10 (ork) -350.01300 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 415.80100 400.89500 Tm (15) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 425.76300 400.89500 Tm [ (\135\056) -608.01600 (T) 79.99160 (ypically) 64.99900 (\054) -374.99100 (the) -348.99100 (bound) -349.99600 (com\055) ] TJ -116.90100 -11.95470 Td [ (putation) -277.01500 (is) -276.02000 (the) -277.00500 (most) -276.98300 (time\055consuming) -276.98800 (part) -275.98800 (in) -277.00300 (a) -277.01700 (con) 39.99820 (v) 14.98280 (entional) ] TJ 11.95510 TL T* [ (BnB) -284 (frame) 25.01300 (w) 10 (ork) -283.00400 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 379.45700 376.98500 Tm (19) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 389.42000 376.98500 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 394.73900 376.98500 Tm (12) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 404.70200 376.98500 Tm [ (\135\056) -410.99000 (T) 79.99160 (o) -283.00700 (combat) -284.01100 (this\054) -292 (we) -283.01200 (suggest) -284.00200 (a) -283.99700 (re\055) ] TJ -95.83980 -11.95510 Td [ (laxation) -371.98900 (of) -372.99400 (the) -372.98900 (original) -371.98700 (problem) -373.01100 (and) -372.01100 (a) -373.00100 (ne) 25.01540 (w) -372.01100 (bound) -373.01100 <6465026e692d> ] TJ 11.95510 TL T* [ (tion) -288.00600 (that) -288.01600 (can) -287.99400 (be) -287.99100 (ef) 25.00810 <026369656e746c79> -287.99100 (computed) -288 (on) -287.98100 (a) -289.01600 (2D) -287.98100 (domain) -288 (\050) ] TJ /R39 9.96260 Tf 221.58500 0 Td (i\056e) Tj /R31 9.96260 Tf 9.68437 0 Td (\056\054) Tj -231.26900 -11.95590 Td [ (EGI\051\056) -323.98300 (This) -324.00200 (allo) 24.99090 (ws) -324.01500 (the) -322.99800 (bounds) -323.99500 (to) -324.01500 (be) -323.98500 (computed) -323.99500 (using) -323.99500 (a) -323.99000 (fe) 25.00560 (w) ] TJ T* [ (simple) -311.01200 (arithmetic) -309.99700 (operations) -311.01700 (with) -310.00200 (linear) -310.99700 (comple) 14.99750 (xity) 64.99410 (\054) -325.98000 (while) ] TJ T* [ (still) -359.00400 (preserving) -358.98200 (the) -358.01100 (global) -359.01400 (optimality) -359.01900 (and) -358.99400 (the) -358.98900 (con) 39.99820 (v) 14.98280 (er) 17.98720 (gence) ] TJ T* [ (property) -300.01100 (of) -299.98700 (the) -301.00100 (BnB) -299.99700 (frame) 25.01050 (w) 10.00320 (ork\056) -459.99200 (The) -301.00400 (propos) 1.00473 (ed) -301.00900 (frame) 25.01050 (w) 10.00320 (ork) ] TJ T* [ (is) -386.00200 (illustrated) -386.01400 (in) -386.98200 (Fig\056) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 394.28100 293.29900 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R31 9.96260 Tf 1 0 0 1 399.26300 293.29900 Tm [ (\056) -719.01500 (Our) -386.00900 (method) -385.98500 (is) -386 (quantitati) 25.02030 (v) 14.98280 (ely) -386.98400 (and) ] TJ -90.40040 -11.95510 Td [ (qualitati) 25.01300 (v) 14.98280 (ely) -233.99300 (v) 24.98110 (alidated) -235 (with) -234.01500 (real) -234.98500 (and) -233.99500 (synthetic) -234.00500 (data\056) -305.00300 (W) 79.98660 (e) -234.98500 (also) ] TJ 11.95590 TL T* [ (demonstrate) -256.98400 (the) -257.00900 <0365> 14.98770 (xibility) -257.00600 (of) -257.99600 (our) -257.01100 (method) -256.98700 (by) -257.00600 (using) -256.98700 (it) -257.98100 (i) 0.98513 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