%PDF-1.3 1 0 obj << /Kids [ 3 0 R 4 0 R 5 0 R 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R 11 0 R ] /Type /Pages /Count 9 >> endobj 2 0 obj << /Title (Beyond Covariance\072 Feature Representation With Nonlinear Kernel Matrices) /Producer (PyPDF2) /Author (Lei Wang\054 Jianjia Zhang\054 Luping Zhou\054 Chang Tang\054 Wanqing Li) /Subject (2015 IEEE International Conference on Computer Vision) >> endobj 3 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 13 0 R /Resources << /XObject << /x8 14 0 R /x6 17 0 R /x12 20 0 R /x10 23 0 R >> /ExtGState << /s9 26 0 R /s11 29 0 R /a0 << /CA 1 /ca 1 >> /R20 32 0 R /s5 33 0 R /s7 36 0 R >> /Font << /F2 39 0 R /R29 40 0 R /F1 44 0 R /R21 45 0 R /R23 49 0 R /R25 53 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 61 0 R 62 0 R 63 0 R 64 0 R 65 0 R 66 0 R 67 0 R 68 0 R 69 0 R 70 0 R 71 0 R 72 0 R ] >> endobj 4 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 73 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /F2 74 0 R /R58 75 0 R /R54 78 0 R /R56 82 0 R /R70 87 0 R /R52 91 0 R /F1 94 0 R /R29 40 0 R /R64 95 0 R /R66 100 0 R /R60 103 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R68 113 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 117 0 R 118 0 R 119 0 R 120 0 R 121 0 R 122 0 R 123 0 R 124 0 R 125 0 R 126 0 R 127 0 R 128 0 R 129 0 R 130 0 R 131 0 R 132 0 R ] >> endobj 5 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 133 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R54 78 0 R /R56 82 0 R /R52 91 0 R /F2 134 0 R /R89 135 0 R /F1 138 0 R /R83 139 0 R /R87 142 0 R /R85 145 0 R /R29 40 0 R /R64 95 0 R /R66 100 0 R /R60 103 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R25 53 0 R /R68 113 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 148 0 R 149 0 R 150 0 R 151 0 R 152 0 R 153 0 R ] >> endobj 6 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 154 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R70 87 0 R /R54 78 0 R /R56 82 0 R /R52 91 0 R /R127 155 0 R /R125 160 0 R /F1 163 0 R /R123 164 0 R /R121 168 0 R /R129 172 0 R /F2 177 0 R /R119 178 0 R /R113 182 0 R /R111 185 0 R /R117 188 0 R /R115 191 0 R /R29 40 0 R /R64 95 0 R /R66 100 0 R /R85 145 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R68 113 0 R /R60 103 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 196 0 R 197 0 R 198 0 R 199 0 R 200 0 R 201 0 R 202 0 R 203 0 R 204 0 R 205 0 R 206 0 R 207 0 R 208 0 R 209 0 R 210 0 R ] >> endobj 7 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 211 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R54 78 0 R /R56 82 0 R /R52 91 0 R /F2 212 0 R /R89 135 0 R /F1 213 0 R /R159 214 0 R /R87 142 0 R /R157 218 0 R /R161 223 0 R /R115 191 0 R /R29 40 0 R /R64 95 0 R /R66 100 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R25 53 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 226 0 R 227 0 R 228 0 R 229 0 R 230 0 R 231 0 R 232 0 R 233 0 R 234 0 R 235 0 R 236 0 R 237 0 R 238 0 R 239 0 R 240 0 R 241 0 R 242 0 R 243 0 R 244 0 R 245 0 R 246 0 R ] >> endobj 8 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 247 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /F2 248 0 R /R54 78 0 R /R25 53 0 R /R115 191 0 R /R29 40 0 R /R64 95 0 R /F1 249 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R87 142 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 250 0 R 251 0 R 252 0 R 253 0 R 254 0 R 255 0 R 256 0 R 257 0 R 258 0 R 259 0 R 260 0 R 261 0 R 262 0 R 263 0 R 264 0 R 265 0 R 266 0 R 267 0 R 268 0 R 269 0 R 270 0 R 271 0 R 272 0 R 273 0 R 274 0 R 275 0 R 276 0 R ] >> endobj 9 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 277 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R54 78 0 R /R25 53 0 R /R56 82 0 R /R115 191 0 R /F2 278 0 R /R64 95 0 R /F1 279 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R87 142 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 280 0 R 281 0 R 282 0 R 283 0 R 284 0 R 285 0 R 286 0 R 287 0 R 288 0 R 289 0 R 290 0 R 291 0 R 292 0 R 293 0 R ] >> endobj 10 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 294 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R157 218 0 R /R161 223 0 R /R54 78 0 R /R25 53 0 R /R52 91 0 R /R227 295 0 R /F2 299 0 R /R64 95 0 R /R125 160 0 R /F1 300 0 R /R62 108 0 R /R21 45 0 R /R23 49 0 R /R115 191 0 R /R87 142 0 R /R27 56 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ 301 0 R 302 0 R 303 0 R 304 0 R 305 0 R 306 0 R 307 0 R 308 0 R ] >> endobj 11 0 obj << /Parent 1 0 R /Rotate 0 /Type /Page /Contents 309 0 R /Resources << /ExtGState << /R20 32 0 R >> /Font << /R21 45 0 R /R29 40 0 R /R23 49 0 R /F1 310 0 R /F2 311 0 R >> /ProcSet [ /ImageC /Text /PDF /ImageI /ImageB ] >> /MediaBox [ 0 0 612 792 ] /Annots [ ] >> endobj 12 0 obj << /Type /Catalog /Pages 1 0 R >> endobj 13 0 obj << /Length 21114 >> stream q q q 0.10000 0 0 0.10000 0 0 cm /R20 gs 0 g q 10 0 0 10 0 0 cm BT /R21 14.34620 Tf 1 0 0 1 62.15000 675.06700 Tm [ (Bey) 24.99660 (ond) -249.99100 (Co) 10.00650 (v) 9.99625 (ariance\072) -309.99000 (F) 24.98890 (eatur) 17.99120 (e) -250 (Repr) 18.00140 (esentation) -250.01300 (with) -250.01300 (Nonlinear) -250.01200 (K) 24.99570 (er) 15 (nel) -250.00800 (Matrices) ] TJ /R23 11.95520 Tf 64.21600 -37.85820 Td [ (Lei) -249.99300 (W) 80 (ang) ] TJ /R25 7.97010 Tf 46.51680 4.33906 Td (1) Tj /R23 11.95520 Tf 4.73320 -4.33906 Td [ (\054) -250.01200 (Jianjia) -250.00600 (Zhang) ] TJ /R25 7.97010 Tf 70.72620 4.33906 Td (1) Tj /R23 11.95520 Tf 4.73164 -4.33906 Td [ (\054) -250.01200 (Luping) -249.99700 (Zhou) ] TJ /R25 7.97010 Tf 68.74220 4.33906 Td (1) Tj /R23 11.95520 Tf 4.73203 -4.33906 Td [ (\054) -250.01200 (Chang) -250.00600 (T) 80.01470 (ang) ] TJ /R25 7.97010 Tf 63.79300 4.33906 Td (1) Tj /R27 7.97010 Tf 4.23398 0 Td (\073) Tj /R25 7.97010 Tf 2.35312 0 Td (2) Tj /R23 11.95520 Tf 4.73203 -4.33906 Td [ (\054) -250.01200 (W) 79.99840 (anqing) -250.00200 (Li) ] TJ /R25 7.97010 Tf 62.46480 4.33906 Td (1) Tj /R23 11.95520 Tf -380.04200 -18.28590 Td [ (School) -250.00400 (of) -250.01500 (Computing) -250.00600 (and) -249.98700 (Information) -250.00400 (T) 70.01640 (echnology) 65.01320 (\054) -250.01200 (Uni) 24.99570 (v) 14.98510 (ersity) -249.98900 (of) -250.01400 (W) 80 (ollongong\054) -250.00600 (Australia) ] TJ /R25 7.97010 Tf 422.32500 4.33789 Td (1) Tj /R23 11.95520 Tf -384.48700 -18.28590 Td [ (School) -250.00400 (of) -250.01500 (Electronic) -249.99500 (Information) -250.00400 (Engineering\054) -249.98500 (T) 34.98980 (ianjin) -249.99300 (Uni) 24.99570 (v) 14.98510 (ersity) 64.98870 (\054) -250.01000 (China) ] TJ /R25 7.97010 Tf 346.64900 4.33789 Td (2) Tj /R21 11.95520 Tf -322.57500 -45.38400 Td (Abstract) Tj /R29 9.96260 Tf -83.92810 -23.91090 Td [ (Co) 10.01670 (variance) -338.00700 (matrix) -337.99800 (has) -338.00600 (r) 37.01960 (ecently) -337.98000 (r) 37.01960 (eceived) -337.99300 (incr) 36.98890 (easing) -337.99800 (at\055) ] TJ -11.95470 -11.95510 Td [ (tention) -212.99100 (in) -211.99200 (computer) -213.00100 (vision) -212.99800 (by) -212.00300 (le) 14.98030 (ver) 15.01470 (a) 10.00320 (ging) -213.00100 (Riemannian) -212.98200 (g) 10.00320 (eom\055) ] TJ 11.95510 TL T* [ (etry) -362.99400 (of) -364.00500 (symmetric) -363.01800 <706f7369746976652d6465026e697465> -364.01000 (\050SPD\051) -362.99300 (matrices\056) -651 (Orig\055) ] TJ T* [ (inally) -448.01600 (pr) 44.98390 (oposed) -449.00100 (as) -447.99300 (a) -449.01800 (r) 37.01960 (e) 39.98840 (gion) -447.98200 (descriptor) 111.00100 (\054) -497.99300 (it) -449.00800 (has) -447.98700 (now) -449.00100 (been) ] TJ T* [ (used) -485.98600 (as) -485.98600 (a) -485.99200 (g) 10.00320 (eneric) -485.99200 (r) 37.01960 (epr) 36.98160 (esentation) -485.99700 (in) -485.98500 (various) -486.00700 (r) 37.01830 (eco) 9.99588 (gnition) ] TJ 11.95630 TL T* [ (tasks\056) -502.99100 (Howe) 14.99440 (ver) 110.99900 (\054) -329.98200 (co) 10 (variance) -314.01100 (matrix) -314.00200 (has) -314.00900 (shortcomings) -314.98900 (suc) 14.98520 (h) ] TJ 11.95470 TL T* [ (as) -386.00300 (being) -385.99600 (pr) 44.98390 (one) -386.00800 (to) -386.00200 (be) -386.01300 (singular) 111.00800 (\054) -420.00600 (limited) -387.00200 (capabilit) 0.98513 (y) -387 (in) -386.00200 (mod\055) ] TJ T* [ (eling) -336.00200 (complicated) -335.99100 (featur) 37 (e) -335.98800 (r) 37.01960 (elationship\054) -356.98000 (and) -336.00800 (having) -336 (a) -336.01700 <02786564> ] TJ T* [ (form) -383.01300 (of) -382.98300 (r) 37.01960 (epr) 36.98100 (esentation\056) -709.01600 (This) -383.00100 (paper) -383.01700 (ar) 36.98650 (gues) -382.98300 (that) -383.01000 (mor) 36.98890 (e) -383 (ap\055) ] TJ T* [ (pr) 44.98390 (opriate) -460.01000 (SPD\055matrix\055based) -459.99400 (r) 37.01960 (epr) 36.98160 (esentations) -459.99700 (shall) -460.01100 (be) -460.00200 (e) 19.99180 (x\055) ] TJ T* [ (plor) 36.99750 (ed) -351 (to) -350.98800 (ac) 15.01770 (hie) 14.98520 (ve) -351.00900 (better) -350.98300 (r) 37.01960 (eco) 9.99466 (gnition\056) -612.99100 (It) -350.99500 (pr) 44.98510 (oposes) -351.01700 (an) -350.99000 (open) ] TJ 11.95630 TL T* [ (fr) 14.99140 (ame) 14.98160 (work) -455.00200 (to) -453.99000 (use) -455.01500 (the) -455.01500 (k) 9.99343 (ernel) -455.01200 (matrix) -454.01700 (o) 10.00320 (ver) -454.98500 (featur) 37.00120 (e) -454.98800 (dimen\055) ] TJ 11.95510 TL T* [ (sions) -295.01900 (as) -296.01800 (a) -295.00500 (g) 10.00320 (eneric) -295.98500 (r) 37.01960 (epr) 36.98160 (esentation) -295.01000 (and) -296.01400 (discusses) -295.01700 (its) -296.00900 (pr) 44.98510 (oper) 20.00890 (\055) ] TJ T* [ (ties) -264.01800 (and) -264.01900 (advanta) 9.98730 (g) 10.00320 (es\056) -350.99700 (The) -264.02000 (pr) 44.98390 (oposed) -264.01200 (fr) 14.99140 (ame) 14.98030 (work) -264.01500 <7369676e690263616e746c79> ] TJ T* [ (ele) 15.01590 (vates) -306.01800 (co) 9.99894 (variance) -306.01300 (r) 37.01960 (epr) 36.98160 (esentation) -305.98800 (to) -306.01500 (the) -306.02000 (unlimited) -305.98600 (oppor) 19.98440 (\055) ] TJ T* [ (tunities) -380.99400 (pr) 44.98390 (o) 10.00320 (vided) -380.98700 (by) -382.01300 (this) -381.00900 (ne) 15.01830 (w) -380.98200 (r) 37.01960 (epr) 36.98160 (esentation\056) -703.99800 (Experimen\055) ] TJ T* [ (tal) -242.01800 (study) -243 (s) 0.98635 (hows) -242.98900 (that) -242.01400 (this) -242.01200 (r) 37.01960 (epr) 36.98160 (esentation) -241.99900 (consistently) -243.01300 (outper) 19.98200 (\055) ] TJ 11.95590 TL T* [ (forms) -228.99400 (its) -230.02000 (co) 9.99894 (variance) -229.00600 (counterpart) -229.99700 (on) -229.01100 (various) -228.99100 (visual) -230.01300 (r) 37.01830 (eco) 9.99588 (gni\055) ] TJ 11.95510 TL T* [ (tion) -212.01900 (tasks\056) -296.98700 (In) -212.98200 (particular) 111.01100 (\054) -218.98100 (it) -211.98900 (ac) 15.01830 (hie) 14.98520 (ves) -212.98700 <7369676e690263616e74> -211.99400 (impr) 44.99490 (o) 10.00320 (vement) ] TJ T* [ (on) -193.99700 (sk) 10 (eleton\055based) -194.01700 (human) -193.98400 (action) -193.98200 (r) 37.01960 (eco) 9.99466 (gnition\054) -206 (demonstr) 15.00980 (ating) ] TJ T* [ (the) -354.01100 (state\055of\055the\055art) -354.98900 (performance) -353.99000 (o) 10.00320 (ver) -355.00200 (both) -353.99700 (the) -354.99200 (co) 9.99833 (variance) ] TJ T* [ (and) -249.98200 (the) -249.99000 (e) 19.99240 (xisting) -250.00400 (non\055co) 10.01060 (variance) -249.98300 (r) 37.01960 (epr) 36.98160 (esentations\056) ] TJ /R21 11.95520 Tf 35.12620 TL T* [ (1\056) -249.99000 (Intr) 18.01460 (oduction) ] TJ /R23 9.96260 Tf 11.95470 -18.92890 Td [ (Co) 14.99630 (v) 24.98110 (ariance) -337.01100 (matrix) -337.99800 (w) 10 (as) -337.00100 (proposed) -337.99900 (as) -337 (a) -337.00700 (re) 15.00980 (gion) -338 (descriptor) ] TJ -11.95470 -11.95510 Td [ (around) -280.01900 (ten) -279.00400 (years) -279.99400 (ago) ] TJ ET Q 1 0 0 rg q 10 0 0 10 0 0 cm BT /R23 6.97380 Tf 1 0 0 1 133.71400 230.90400 Tm (1) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 140.48400 227.28900 Tm (\133) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 143.80200 227.28900 Tm (22) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 153.76400 227.28900 Tm [ (\135\056) -398.99300 (It) -279.00900 (can) -279.99600 (ef) 25.00810 (fecti) 25.01790 (v) 14.98280 (ely) -279.00500 (fuse) -279.99000 (multiple) ] TJ -103.65200 -11.95470 Td [ (features) -390.01500 (and) -390.00800 (be) -390.99200 (ef) 25.00810 <026369656e746c79> -390.01600 (calculated) -390.00400 (via) -390.00600 (inte) 14.99260 (gral) -390.98900 (images\056) ] TJ 11.95630 TL T* [ (Also\054) -347.99600 (it) -328.99000 (is) -328.01000 (partially) -327.99700 (in) 40.00560 (v) 24.98110 (ariant) -328.99700 (to) -328.01100 (rotation) -329.01400 (and) -328.01900 (scale) -329.00400 (changes) ] TJ 11.95510 TL T* [ (and) -285.00600 (rob) 20.00340 (ust) -286.01200 (ag) 5.02000 (ainst) -284.99000 (outliers\056) -416.99500 (Due) -285.00800 (to) -286.01800 (these) -285.00100 (properties\054) -294.98800 (re) 15.00980 (gion) ] TJ T* [ (co) 15.01770 (v) 24.98110 (ariance) -270.00300 (descriptor) -268.99300 (has) -269.98700 (sho) 24.99220 (wn) -269.00700 (promising) -269.98400 (performance) -269.99400 (in) ] TJ T* [ (object) -249.98200 (detection\054) -250.01100 (recognition) -250.00200 (and) -249.99100 (tracking) -250.02000 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 221.65800 167.51300 Tm (22) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 231.62100 167.51300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 236.60200 167.51300 Tm (18) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 246.56400 167.51300 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 251.54600 167.51300 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 261.50800 167.51300 Tm (\135\056) Tj -199.44100 -11.95510 Td [ (The) -245.01400 (past) -245.00400 (se) 25.01670 (v) 14.98280 (eral) -246.00300 (years) -245.01900 (ha) 19.99790 (v) 14.98280 (e) -244.98400 (seen) -245.01500 (an) -245.01700 (e) 15.01220 (xpansion) -246.00300 (of) -245.01500 (co) 15.01710 (v) 24.98110 (ari\055) ] TJ -11.95510 -11.95510 Td [ (ance) -321.01300 (matrix) -320.98100 (in) -320.99300 (vision) -321.00900 (applications\056) -523.00600 (In) -321.00400 (addition) -321.98800 (to) -320.99300 (a) -321.01000 (re) 15.00980 (gion) ] TJ 11.95590 TL T* [ (descriptor) 40.01350 (\054) -382.99200 (it) -356.98500 (has) -356.01200 (no) 24.98600 (w) -356.99700 (been) -356.01800 (used) -356.98700 (as) -356.01800 (a) -357.00400 (generic) -356.01900 (feature) -357.00700 (rep\055) ] TJ 11.95510 TL T* [ (resentation) -407.00400 (and) -408.00400 (applied) -407.99000 (to) -407.01800 (v) 24.98110 (arious) -407.99400 (tasks) -407.01000 (including) -408.00800 (pedes\055) ] TJ T* [ (trian) -439.99300 (detection) -439.98200 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 116.98100 107.73700 Tm (23) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 126.94300 107.73700 Tm [ (\135\054) -487.01800 (f) 9.99466 (ace) -440.01800 (recognition) -440.01000 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 211.55600 107.73700 Tm (15) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 221.51900 107.73700 Tm [ (\135\054) -487.99700 (action) -439.99000 (recog\055) ] TJ ET Q 3.98000 w 0 G 501.12100 1001.43000 m 1446.11000 1001.43000 l S q 10 0 0 10 0 0 cm BT /R23 5.97760 Tf 1 0 0 1 60.97110 93.27700 Tm (1) Tj /R23 7.97010 Tf 3.48672 -2.81211 Td [ (As) -234.01800 (a) -235.00200 (basic) -234.02400 (statistical) -234.99700 (concept\054) -236.99000 (co) 14.99130 (v) 24.98200 (ariance) -235.02000 (matrix) -234.00800 (has) -235.01800 (long) -234.01400 (been) -235.02100 (used) -234.00100 (in) ] TJ -14.34570 -9.46484 Td [ (all) -249.98400 (sorts) -250 (of) -250.00300 (areas) -250.02100 (of) -250.00400 (computer) -250.01400 (vision\054) -249.99100 (which) -250.00500 (is) -250.00200 (not) -249.97600 (the) -250.00700 (focus) -250.01300 (of) -250.00400 (this) -250.00700 (paper) 54.99380 (\056) ] TJ /R23 9.96260 Tf 258.75000 487.26800 Td [ (nition) -369 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 339.10900 568.26800 Tm (30) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 349.07100 568.26800 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 355.24800 568.26800 Tm (5) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 360.22900 568.26800 Tm (\054) Tj ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 366.39600 568.26800 Tm (10) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 376.35900 568.26800 Tm [ (\135\054) -398.99200 (image) -370.00200 (set) -368.98700 <636c6173736902636174696f6e> -368.98700 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 487.93900 568.26800 Tm (27) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 497.90200 568.26800 Tm [ (\135\054) -398.99200 (shape) -370.00700 (re\055) ] TJ -189.04000 -11.95510 Td [ (trie) 24.98360 (v) 24.98110 (al) -218 (\133) ] TJ ET Q 0 1 0 rg q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 339.30800 556.31300 Tm (20) Tj ET Q 0 g q 10 0 0 10 0 0 cm BT /R23 9.96260 Tf 1 0 0 1 349.27100 556.31300 Tm [ (\135\054) -224.00200 (etc\056) -299.00900 (A) -218 (dri) 24.98600 (ving) -217.97800 (force) -218.01300 (to) -217.99300 (this) -218.01800 (trend) -217.99300 (is) -217.98800 (the) -217.99300 (po) 24.98600 (werful) ] TJ -40.40860 -11.95590 Td [ (mathematical) -240.00200 (theory) -239.98400 (of) -239.01600 (Riemannian) -239.99400 (manifold) -240.00400 (of) -240 (symmetric) ] TJ 11.95510 TL T* [ (positi) 25.01300 (v) 14.98280 <652d6465026e697465> -250.01500 (\050SPD\051) -250.01200 (matrices\056) ] TJ 11.95510 -14.97500 Td [ (The) -313.98200 (transition) -315.00400 (from) -314.01600 (re) 15.00730 (gion) -314.98200 (descriptor) -314.00600 (to) -314.01600 (generic) -315.00600 (feature) ] TJ -11.95510 -11.95510 Td [ (representation) -322 (brings) -321.02000 (forth) -322.01500 (ne) 25.01540 (w) -321.98100 (issues\056) -524.98100 (Fi) 1 (rstly) 64.99410 (\054) -340.01700 (the) -322.01500 (dimen\055) ] TJ 11.95590 TL T* [ (sions) -309.99700 (of) -309.00500 (co) 15.01710 (v) 24.98110 (ariance) -309.99500 (matrix) -310.00200 (become) -310.01700 (higher) 40.00800 (\054) -323.98000 (while) -310.00700 (the) -310.01700 (num\055) ] TJ 11.95510 TL T* [ (ber) -242.00100 (of) -241.99600 (samples) -242.01100 (a) 19.99180 (v) 24.98110 (ailable) -241.98400 (for) -241.99900 (co) 15.01710 (v) 24.98110 (ariance) -242.00900 (estimation) -241.98900 (becomes) ] TJ T* [ (smaller) 40.01290 (\054) -224 (as) -216.98100 (observ) 14.99260 (ed) -216.98300 (in) -217.99100 (human) -216.99800 (action) -217.00800 (recognition) -216.98800 (and) -217.99800 (image) ] TJ T* [ (set) -249.98800 <636c6173736902636174696f6e2e> -310.99500 (This) -250.01500 (results) -250.01200 (in) -249.98800 (unreliable) -250.01700 (or) -251.01700 (e) 25.01050 (v) 14.98280 (en) -249.99700 (singular) ] TJ T* [ (co) 15.01710 (v) 24.98110 (ariance) -339.01000 (estimate\054) -361.98900 (and) -338.99700 (the) -338.99200 (Riemannian) -338.99700 (metrics) -338.98300 (for) -339.98200 (SPD) ] TJ 11.95590 TL T* [ (matrix) -197.98200 (cannot) -197.99100 (be) -198.00600 (directly) -197.98700 (applied\056) -292.00500 (Secondly) 65.00390 (\054) -208.98000 (co) 15.01710 (v) 24.98110 (ariance) -198.01600 (ma\055) ] TJ 11.95510 TL T* [ (trix) -229.00300 (only) -228.99900 (e) 25.01050 (v) 24.98110 (aluates) -229.00800 (linear) -229.01300 (correlation) -229.00600 (of) -230 (features\056) -303.00800 (This) -228.99600 (might) ] TJ T* [ (bring) -244.99800 (the) -245.01100 (adv) 24.98110 (antages) -245.98800 (of) -245.01500 (simplicity) -244.99800 (and) -245.01300 (ef) 25.00560 <026369656e63> 14.99260 (y) 65.01370 (\054) -245.99300 (when) -245.98800 (it) -245.00300 (is) ] TJ T* [ (used) -282.01900 (as) -281.00900 (a) -281.99700 (re) 15.00980 (gion) -280.99000 (descriptor) 54.99080 (\056) -404.98600 (Ne) 25.01540 (v) 14.98280 (ertheless\054) -288.99100 (as) -281.99200 (a) -281.01700 (generic) -281.99200 (rep\055) ] TJ T* [ (resentation\054) -236.99000 (the) -233.01300 (capability) -232.99100 (of) -233.02000 (modeling) -233.01500 (nonlinear) -234.01500 (feat) 1.01454 (ure) -234.00500 (re\055) ] TJ T* [ (lationship) -263.98300 (becomes) -265 (essential\056) -353.01000 (Last) -265 (b) 20.00160 (ut) -263.98500 (not) -264.99500 (least\054) -268.01900 (co) 15.01710 (v) 24.98110 (ariance) ] TJ 11.95630 TL T* [ (matrix) -327.01900 (has) -326.99700 (a) -327.00900 (single\054) -345.99100 <0278> 14.99750 (ed) -327.00400 (form\056) -540.99300 (It) -327 (cannot) -326.99000 (be) -327.00400 (con) 39.99820 (v) 14.98280 (eniently) ] TJ 11.95470 TL T* [ (altered) -249.99500 (to) -249.98500 (model) -250.01200 (dif) 24.98600 (ferent) -250.00200 (feature) -250.00200 (relationships\056) ] TJ 11.95510 -14.97500 Td [ (T) 79.99160 (o) -249.99300 (address) -249.00700 (these) -249.98800 (issues\054) -250.00700 (we) -249.01700 (propose) -250.01700 (to) -249.00700 (use) -249.99300 (k) 10.00320 (ernel) -249.99700 (matrix) ] TJ -11.95510 -11.95510 Td [ (as) -259.01300 (a) -258.98100 (generic) -259.01600 (feature) -260.00300 (representation\056) -337.01700 (Each) -259.01600 (of) -259.01600 (its) -260.01500 (entries) -259 (e) 25.01050 (v) 24.98110 (al\055) ] TJ 11.95590 TL T* [ (uates) -215.01300 (a) -214.00800 (k) 10.00320 (ernel) -214.98400 (function) -214.99600 (between) -215.01800 (a) -214.00800 (pair) -215.01800 (of) ] TJ /R29 9.96260 Tf 161.42400 0 Td [ (featur) 36.99870 (e) -214.98900 (dimensions) ] TJ /R23 9.96260 Tf -161.42400 -11.95510 Td [ (\050rather) -274 (than) -275 (between) -273.98600 (a) -275.01800 (pair) -273.98900 (of) ] TJ /R29 9.96260 Tf 121.51900 0 Td (samples) Tj /R23 9.96260 Tf 32.09920 0 Td [ (\054) -281.00700 (as) -273.99300 (we) -273.99300 (usually) -274.98400 (do) -273.98400 (in) ] TJ -153.61800 -11.95510 Td [ (k) 10.00320 (ernel) -247.01800 (methods\051\056) -309.01200 (As) -247.00800 (will) -248.01300 (be) -247.01800 (sho) 24.99090 (wn\054) -247.98800 (for) -247.01800 (a) -246.98300 (lar) 17.99700 (ge) -247.01800 (set) -247.00800 (of) -247.99800 (k) 10.00320 (ernel) ] TJ 11.95510 TL T* [ (functions\054) -220.00700 (the) -213.01600 (k) 10.00320 (ernel) -214.00400 (m) 0.99248 (atrix) -213.99400 (is) -213.00900 (guaranteed) -213.01800 (to) -213.01300 (be) -212.98400 (nonsingular) 39.99820 (\054) ] TJ T* [ (e) 25.01050 (v) 14.98280 (en) -243.99900 (if) -243.99400 (samples) -244.99100 (are) -244.01100 (scarce\054) -244.98900 (which) -243.98400 (ensures) -245.00800 (Riemannian) -243.99400 (met\055) ] TJ T* [ (rics) -277.98800 (to) -277.98100 (be) -279.01200 (readi) 0.98023 (ly) -279 (applicable\056) -393.99300 (More) -277.98300 (importantly) 64.98430 (\054) -285.98700 (k) 10.00320 (ernel) -277.99300 (ma\055) ] TJ 11.95660 TL T* [ (trix) -205.00700 (gi) 24.98850 (v) 14.98280 (es) -206.00200 (us) -205.01200 (unlimited) -205.99300 (opportunities) -205.00500 (to) -205.99500 (model) -205 (nonlinear) -205.98000 (fea\055) ] TJ 11.95470 TL T* [ (ture) -229.99600 (relationship) -229.99600 (in) -231.00800 (an) -230 (ef) 25.00810 <026369656e74> -230.01600 (manner) 54.98100 (\056) -303.98400 (Extra) 0.99003 (cting) -231 (dif) 24.98600 (ferent) ] TJ T* [ (relationship) -231.99600 (is) -231.98800 (just) -232.01500 (a) -232.00500 (matter) -231.98600 (of) -232 (changing) -232.01500 (the) -231.99100 (k) 10.00320 (ernel) -232 (function\056) ] TJ T* [ (In) -265.01200 (addition\054) -269.01400 (this) -266.01000 (ne) 25.01540 (w) -265.01200 (representation) -264.99000 (can) -266 (w) 10.00320 (ork) -265.01000 (well) -265 (with) -266.01000 (co\055) ] TJ T* [ (v) 24.98110 (ariance) -266.98200 (representation) -266.99000 (by) -267.00400 (pro) 14.98280 (viding) -267.01900 (complementary) -267.01400 (infor) 20.00650 (\055) ] TJ 11.95590 TL T* [ (mation\056) -476.98400 (Combining) -306.00300 (them) -306.00800 (together) -304.98800 (can) -305.99300 (ef) 25.00560 (fecti) 25.01540 (v) 14.98280 (ely) -306.01800 (impro) 15.00240 (v) 14.98280 (e) ] TJ 11.95510 TL T* [ (recognition) -250.00200 (performance\056) ] TJ 11.95510 -14.97500 Td [ (This) -286.00900 (paper) -287.01300 <02> 0.99493 (rst) -287.00100 (describes) -286.01600 (the) -285.98200 (background) -286.00600 (on) -287.00100 (co) 15.01710 (v) 24.98110 (ariance) ] TJ -11.95510 -11.95510 Td [ (matrix) -232.99500 (and) -233.01500 (then) -233.98800 (discusses) -232.98600 (its) -233 (ne) 25.01540 (wly) -233.00500 (encountered) -233.01000 (issues\056) -305.01800 (Af\055) ] TJ 11.95590 TL T* [ (ter) -208.98500 (that\054) -215.98600 (we) -208.98700 (propose) -207.98500 (k) 10.00320 (ernel) -208.98500 (matrix) -209 (as) -208.00500 (a) -208.99000 (generic) -208.00500 (feature) -208.99000 (repre\055) ] TJ 11.95510 TL T* [ (sentation) -303.01300 (and) -303.00300 (elaborate) -303.00300 (its) -302.00800 (properties) -302.98900 (and) -303.00300 (adv) 24.98110 (antages\056) -469.00500 (F) 14.99260 (ol\055) ] TJ T* [ (lo) 24.98850 (wing) -205.00500 (that\054) -213.98600 (a) -204.99000 (frame) 25.01300 (w) 10 (ork) -205.01700 (of) -204.98500 (combining) -205.01500 (dif) 24.98600 (ferent) -204.99000 (representa\055) ] TJ T* [ (tions) -264.98500 (is) -265.00200 (presented\056) -356.00400 (At) -265.00500 (last\054) -268.01400 (we) -265.99500 (discuss) -264.98500 (computational) -265 (issues) ] TJ T* [ (and) -251.01200 (the) -251.01000 (dif) 24.98600 (ferences) -252.00900 (of) -251.01400 (our) -251.01200 (w) 10.00320 (ork) -251.01200 (from) -251.98700 (the) -251.00700 (e) 15.01220 (xisting) -251.01200 (ones\056) -314.01100 (Ex\055) ] TJ ET Q Q Q q q 1 1 1 rg /a0 gs 48.40600 786.42200 515.18800 -52.69900 re f q /s5 gs /x6 Do Q q /s7 gs /x8 Do Q q /s9 gs /x10 Do Q q /s11 gs /x12 Do Q Q Q Q q 1 0 0 1 0 0 cm BT /F1 12 Tf 14.40000 TL ET 1 1 1 rg n 270 32 72 14 re f* 0.50000 0.50000 0.50000 rg BT /F2 9 Tf 10.80000 TL ET BT 1 0 0 1 297 35 Tm (4570) Tj T* ET Q endstream endobj 14 0 obj << /Filter /FlateDecode /Resources << /ExtGState << /a0 << /CA 1 /ca 1 >> >> /XObject << /x18 15 0 R >> >> /Length 28 /Group << /Type /Group /S /Transparency /CS /DeviceRGB /I true >> /BBox [ 78 746 96 765 ] /Type /XObject /Subtype /Form >> stream x+O4PH/VЯ0Pp 0 endstream endobj 15 0 obj << /Filter /FlateDecode /Resources 16 0 R /Length 107 /Type /XObject /BBox [ 78 746 96 765 ] /Subtype /Form >> stream xe AC̬wʠ =p,?]%+H-
Jc "82w8VSnGW;"
endstream
endobj
16 0 obj
<<
/ExtGState <<
/a0 <<
/CA 1
/ca 1
>>
>>
>>
endobj
17 0 obj
<<
/Filter /FlateDecode
/Resources <<
/ExtGState <<
/a0 <<
/CA 1
/ca 1
>>
>>
/XObject <<
/x15 18 0 R
>>
>>
/Length 28
/Group <<
/Type /Group
/S /Transparency
/CS /DeviceRGB
/I true
>>
/BBox [ 67 752 84 775 ]
/Type /XObject
/Subtype /Form
>>
stream
x+O4PH/VЯ04Up
0
endstream
endobj
18 0 obj
<<
/Filter /FlateDecode
/Resources 19 0 R
/Length 228
/Type /XObject
/BBox [ 67 752 84 775 ]
/Subtype /Form
>>
stream
xeQKn!s ?FPav6R٪TS.
b];15YyR
{7QL.\:Rv/x9l+L7h%1!}i/AI(kz"U&,YO![R hg{3}4/GyYF:!w}Gn+'xJcO9i뽼_-:`
endstream
endobj
19 0 obj
<<
/ExtGState <<
/a0 <<
/CA 1
/ca 1
>>
>>
>>
endobj
20 0 obj
<<
/Filter /FlateDecode
/Resources <<
/ExtGState <<
/a0 <<
/CA 1
/ca 1
>>
>>
/XObject <<
/x24 21 0 R
>>
>>
/Length 28
/Group <<
/Type /Group
/S /Transparency
/CS /DeviceRGB
/I true
>>
/BBox [ 133 751 479 772 ]
/Type /XObject
/Subtype /Form
>>
stream
x+O4PH/VЯ02Qp
0
endstream
endobj
21 0 obj
<<
/Filter /FlateDecode
/Resources 22 0 R
/Length 53008
/Type /XObject
/BBox [ 133 751 479 772 ]
/Subtype /Form
>>
stream
xlK8,8?DKs9mavd
{f-8*2Y@H >חk}y}uf`v)_s}1z#*Gw_gX jow\o'1c|Z^G<
A̺X}ay?IT|y~L.[ {Ȟb\3-3]_'X\竵0{+_۾oY-wj+ B;)Aa=/
1~a(>}m_K' >*Q1:?OPnGsQ_`?mzN
?WBB!lU n'S 1Ipzχ1xF_09,}?e){:̹~Gu7g {0mD`pdS)>;ys`Pµx'O
+혝 oI~!p7̵&m=dC+>5ALV"I1"S*CKha#03L4|@p灟vMRQ==*/m"r>@uqo9ͻ;Vz 'ȳ;IBzWR~ihwa8PlT>]fZ8y52)r빃W{B7G/q)}M]elS(k=5^A] сڸc'w!Ll'M=Ȥ뎓z;#կN>\q6r>|8}}Lr$Mo5:>syls+Ǵ`C?/9{Y||jD u#i^\rJ8a|oY+Rxl<{[؏s迨nYaյ[?/^u;+ ,bhL}wrj:ɴdM8^q|m'aQ6;0k_ar|E8HɃpN('&r`V;Rs볩Nk\&W=DDG#5]~M{VyCSRH9ܜXˏt7߾i9ADگ
USڝ|{(hbIRZXg @6Hɹ0Dq;si\Tv<1?mUŏV7bF
p7Y9sƨ*.uz_LբřsB݃ɹ^'_Yae91f+n%A̶d
Ċc#q
CF=Mt'\&ξ)z;L-4:n}41j:mӶ_)\݇ |T@uAƓxAN6Ql;}Ɲ{~_y"g%]nCi']I~,xa?feoɌr0u?V=phldx.Y;~nZL603> \`ęܓ