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[(,)]TJ -11.955 -11.955 Td [(which)-366(includes)-366(feature)-365(encoder)]TJ/F14 9.9626 Tf 131.32 0 Td [(F)]TJ/F73 9.9626 Tf 8.15 0 Td [(,)-395(feature)-366(modulator)]TJ/F14 9.9626 Tf 82.325 0 Td [(M)]TJ/F73 9.9626 Tf 11.964 0 Td [(,)]TJ -233.759 -11.955 Td [(descriptor)-228(e)15(xtractor)]TJ/F14 9.9626 Tf 79.646 0 Td [(P)]TJ/F73 9.9626 Tf 7.749 0 Td [(,)-233(and)-228(uncertainty-aided)-228(grid-based)-228(lo-)]TJ -87.395 -11.955 Td [(cator)]TJ/F14 9.9626 Tf 23.307 0 Td [(G)]TJ/F73 9.9626 Tf 9.91 0 Td [(\(UC-GBL\).)-340(Moreo)15(v)15(er)40(,)-364(we)-340(also)-341(learn)-340(the)-341(semantic)]TJ -33.217 -11.955 Td [(distincti)25(v)15(eness)-282(\(SD\))-283(by)-282(adding)-283(a)-282(side)-282(branch)]TJ/F14 9.9626 Tf 181.994 0 Td [(D)]TJ/F73 9.9626 Tf 10.776 0 Td [(\(SD)-282(head\).)]TJ -192.77 -11.956 Td [(In)-250(the)-250(follo)25(wing,)-250(we)-250(will)-250(describe)-250(each)-250(module)-250(in)-250(detail.)]TJ/F72 10.9589 Tf 0 -19.014 Td [(3.2.)-250(K)25(eypoint)-250(Pr)18(ototypes)-250(and)-250(Descriptors)-250(Building)]TJ/F72 9.9626 Tf 0 -17.932 Td [(K)25(eypoint)-382(Embedding:)]TJ/F73 9.9626 Tf 101.182 0 Td [(Let)-382(support)-383(and)-382(query)-383(images)]TJ/F83 9.9626 Tf 127.512 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.495 Td [(s)]TJ/F73 9.9626 Tf -233.039 -10.461 Td [(and)]TJ/F83 9.9626 Tf 18.909 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F73 9.9626 Tf 8.509 1.494 Td [(be)-454(mapped)-454(to)]TJ/F14 9.9626 Tf 62.267 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(s)]TJ/F8 9.9626 Tf 3.211 1.494 Td [(\))]TJ/F73 9.9626 Tf 8.398 0 Td [(and)]TJ/F14 9.9626 Tf 18.909 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.875 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\))]TJ/F73 9.9626 Tf 8.397 0 Td [(in)-454(feature)-454(space)]TJ/F70 9.9626 Tf -169.669 -11.955 Td [(R)]TJ/F10 6.9738 Tf 7.195 3.616 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(l)]TJ/F13 6.9738 Tf 2.56 0 Td [<02>]TJ/F10 6.9738 Tf 6.226 0 Td [(C)]TJ/F73 9.9626 Tf 11.028 -3.616 Td [(using)-434(a)-435(weight-shared)-434(con)40(v)20(olutional)-434(encoder)]TJ/F14 9.9626 Tf 189.813 0 Td [(F)]TJ/F73 9.9626 Tf 8.15 0 Td [(.)]TJ -233.759 -11.955 Td [(Gi)25(v)15(en)-350(a)-350(support)-350(k)10(e)15(ypoint)-350(at)-350(location)]TJ/F83 9.9626 Tf 153.098 0 Td [(u)]TJ/F8 9.9626 Tf 10.978 0 Td [(=)-463([)]TJ/F11 9.9626 Tf 15.13 0 Td [(x;)-167(y)]TJ/F8 9.9626 Tf 15.363 0 Td [(])]TJ/F69 6.9738 Tf 2.768 3.615 Td [(|)]TJ/F73 9.9626 Tf 5.009 -3.615 Td [(,)-375(we)-350(e)15(x-)]TJ -202.346 -11.955 Td [(tract)-315(the)-314(k)10(e)15(ypoint)-315(representation)]TJ/F83 9.9626 Tf 133.471 0 Td [(\b)]TJ/F8 9.9626 Tf 12.233 0 Td [(=)]TJ/F14 9.9626 Tf 11.707 0 Td [(A)]TJ/F8 9.9626 Tf 7.955 0 Td [(\()]TJ/F14 9.9626 Tf 3.875 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.495 Td [(s)]TJ/F8 9.9626 Tf 3.211 1.495 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(;)]TJ/F83 9.9626 Tf 4.428 0 Td [(u)]TJ/F8 9.9626 Tf 6.365 0 Td [(\))]TJ/F73 9.9626 Tf 7.008 0 Td [(via)]TJ/F14 9.9626 Tf 15.308 0 Td [(A)]TJ/F73 9.9626 Tf 7.955 0 Td [(.)]TJ -233.759 -11.955 Td [(Operator)]TJ/F14 9.9626 Tf 38.773 0 Td [(A)]TJ/F73 9.9626 Tf 11.321 0 Td [(could)-338(be)-338(inte)15(ger)20(-based)-338(inde)15(xing)-338([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(36)]TJ
0 g 0 G
[(],)-360(bil)1(inear)]TJ -50.094 -11.955 Td [(interpolation)-312([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(18)]TJ
0 g 0 G
[(,)]TJ
0 0.6 0 rg 0 0.6 0 RG
[-172(21)]TJ
0 g 0 G
[(],)-328(or)-312(Gaussian)-312(pooling.)-497(Feature)-313(repre-)]TJ 0 -11.956 Td [(sentations)]TJ/F83 9.9626 Tf 43.215 0 Td [(\b)]TJ/F73 9.9626 Tf 11.64 0 Td [(must)-338(contain)-338(s)1(ome)-338(local)-338(conte)15(xt)-338(of)-338(k)10(e)15(ypoint)]TJ -54.855 -11.955 Td [(to)-346(be)-345(suf)25(\002ciently)-346(discriminati)25(v)15(e)-345(during)-346(the)-345(matching)-346(step.)]TJ 0 -11.955 Td [(Therefore,)-369(we)-344(emplo)10(y)-345(Gaussian)-345(pooling.)-594(Let)]TJ/F83 9.9626 Tf 189.242 0 Td [(u)]TJ/F10 6.9738 Tf 6.365 -1.494 Td [(k)-24(;n)]TJ/F73 9.9626 Tf 15.629 1.494 Td [(be)-345(the)]TJ/F11 9.9626 Tf -211.236 -11.955 Td [(n)]TJ/F73 9.9626 Tf 5.98 0 Td [(-th)-349(k)10(e)15(ypoint)-349(in)-349(t)1(h)-1(e)]TJ/F11 9.9626 Tf 79.515 0 Td [(k)]TJ/F73 9.9626 Tf 5.5 0 Td [(-th)-349(support)-349(image)]TJ/F83 9.9626 Tf 75.731 0 Td [(I)]TJ/F10 6.9738 Tf 4.345 3.615 Td [(k)]TJ/F73 6.9738 Tf 0 -6.078 Td [(s)]TJ/F73 9.9626 Tf 8.377 2.463 Td [(and)]TJ/F14 9.9626 Tf 17.861 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.875 0 Td [(I)]TJ/F10 6.9738 Tf 4.344 3.615 Td [(k)]TJ/F73 6.9738 Tf 0 -6.078 Td [(s)]TJ/F8 9.9626 Tf 4.902 2.463 Td [(\)\()]TJ/F83 9.9626 Tf 7.749 0 Td [(x)]TJ/F8 9.9626 Tf 6.047 0 Td [(\))]TJ/F73 9.9626 Tf -232.376 -11.955 Td [(be)-260(the)-259(feature)-260(v)15(ector)-260(at)-259(po)-1(s)1(ition)]TJ/F83 9.9626 Tf 128.808 0 Td [(x)]TJ/F14 9.9626 Tf 8.993 0 Td [(2)]TJ/F70 9.9626 Tf 9.589 0 Td [(R)]TJ/F7 6.9738 Tf 7.195 3.615 Td [(2)]TJ/F73 9.9626 Tf 4.469 -3.615 Td [(.)-339(The)-260(k)10(e)15(ypoint)-260(rep-)]TJ -159.054 -11.956 Td [(resentation)]TJ/F83 9.9626 Tf 46.206 0 Td [(\b)]TJ/F10 6.9738 Tf 8.275 -1.494 Td [(k)-24(;n)]TJ/F73 9.9626 Tf 14.683 1.494 Td [(can)-250(be)-250(obtained)-250(as)]TJ/F83 9.9626 Tf -64.183 -21.991 Td [(\b)]TJ/F10 6.9738 Tf 8.275 -1.495 Td [(k)-24(;n)]TJ/F8 9.9626 Tf 14.96 1.495 Td [(=)]TJ/F1 9.9626 Tf 10.516 9.464 Td [(X)]TJ/F84 6.9738 Tf 14.39 -15.442 Td [(x)]TJ/F8 9.9626 Tf 6.92 5.978 Td [(exp\()]TJ/F14 9.9626 Tf 19.095 0 Td [<00>-278(k)]TJ/F83 9.9626 Tf 18.265 0 Td [(x)]TJ/F14 9.9626 Tf 7.875 0 Td [<00>]TJ/F83 9.9626 Tf 9.577 0 Td [(u)]TJ/F10 6.9738 Tf 6.365 -1.495 Td [(k)-24(;n)]TJ/F14 9.9626 Tf 14.96 1.495 Td [(k)]TJ/F7 6.9738 Tf 4.981 4.113 Td [(2)]TJ 0 -6.576 Td [(2)]TJ/F11 9.9626 Tf 7.237 2.463 Td [(=)]TJ/F8 9.9626 Tf 4.981 0 Td [(2)]TJ/F11 9.9626 Tf 4.982 0 Td [<18>]TJ/F7 6.9738 Tf 4.817 4.113 Td [(2)]TJ/F8 9.9626 Tf 4.469 -4.113 Td [(\))]TJ/F14 9.9626 Tf 5.703 0 Td [<01>-183(F)]TJ/F8 9.9626 Tf 12.745 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F10 6.9738 Tf 4.345 4.113 Td [(k)]TJ/F73 6.9738 Tf 0 -6.576 Td [(s)]TJ/F8 9.9626 Tf 4.902 2.463 Td [(\)\()]TJ/F83 9.9626 Tf 7.749 0 Td [(x)]TJ/F8 9.9626 Tf 6.047 0 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(;)]TJ/F73 9.9626 Tf 7.749 0 Td [(\(1\))]TJ -224.634 -21.577 Td [(where)]TJ/F11 9.9626 Tf 27.768 0 Td [<18>]TJ/F73 9.9626 Tf 8.247 0 Td [(is)-344(the)-344(standard)-345(de)25(viation.)-592(F)15(ollo)25(wing)-345(prototypical)]TJ -36.015 -11.955 Td [(netw)10(orks)-302([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(42)]TJ
0 g 0 G
[(],)-315(each)-302(support)-302(k)10(e)15(ypoint)-302(prototype)-302(\(SKP\))]TJ/F83 9.9626 Tf 222.553 0 Td [(\b)]TJ/F10 6.9738 Tf 8.274 -1.495 Td [(n)]TJ/F73 9.9626 Tf -230.827 -10.46 Td [(can)-211(be)-212(obtained)-211(by)-211(a)20(v)15(eraging)-211(the)-212(same)-211(type)-211(of)-211(k)10(e)15(ypoint)-212(rep-)]TJ 0 -11.956 Td [(resentations)-250(across)-250(support)-250(images)-250(as)]TJ/F83 9.9626 Tf 70.885 -23.997 Td [(\b)]TJ/F10 6.9738 Tf 8.274 -1.495 Td [(n)]TJ/F8 9.9626 Tf 8.19 1.495 Td [(=)]TJ 13.808 6.739 Td [(1)]TJ
ET
q
1 0 0 1 149.173 153.634 cm
[]0 d 0 J 0.398 w 0 0 m 9.174 0 l S
Q
BT
/F11 9.9626 Tf 149.173 144.309 Td [(K)]TJ/F1 9.9626 Tf 12.03 16.299 Td [(X)]TJ/F10 6.9738 Tf 14.39 -1.467 Td [(K)]TJ 0 -13.976 Td [(k)]TJ/F7 6.9738 Tf 4.404 0 Td [(=1)]TJ/F83 9.9626 Tf 12.246 5.978 Td [(\b)]TJ/F10 6.9738 Tf 8.274 -1.494 Td [(k)-24(;n)]TJ/F11 9.9626 Tf 12.193 1.494 Td [(;)]TJ/F73 9.9626 Tf 62.036 0 Td [(\(2\))]TJ -224.634 -22.322 Td [(where)]TJ/F11 9.9626 Tf 27.125 0 Td [(n)]TJ/F8 9.9626 Tf 9.294 0 Td [(=)-333(1)]TJ/F11 9.9626 Tf 16.044 0 Td [(;)]TJ/F14 9.9626 Tf 4.428 0 Td [<01>-167<01>-166<01>]TJ/F11 9.9626 Tf 14.944 0 Td [(;)-167(N)]TJ/F73 9.9626 Tf 13.519 0 Td [(.)-399(Thus)-280(we)-279(ha)20(v)15(e)]TJ/F11 9.9626 Tf 64.825 0 Td [(N)]TJ/F73 9.9626 Tf 11.877 0 Td [(SKPs)-280(generated)-279(in)]TJ -162.056 -11.955 Td [(the)]TJ/F11 9.9626 Tf 14.665 0 Td [(N)]TJ/F73 9.9626 Tf 9.091 0 Td [(-w)10(ay)]TJ/F11 9.9626 Tf 22.306 0 Td [(K)]TJ/F73 9.9626 Tf 9.174 0 Td [(-shot)-250(learning)-250(process.)]TJ/F72 9.9626 Tf -55.236 -11.956 Td [(Support)-251(and)-250(Query)-251(Corr)18(elation:)]TJ/F73 9.9626 Tf 141.59 0 Td [(In)-251(order)-250(to)-251(guide)-251(FSKD)]TJ -141.59 -11.955 Td [(to)-388(disco)15(v)15(er)-388(the)-388(corresponding)-388(k)10(e)15(ypoints)-388(in)-389(the)-388(query)-388(im-)]TJ 0 -11.955 Td [(age,)-350(SKP)]TJ/F83 9.9626 Tf 41.361 0 Td [(\b)]TJ/F10 6.9738 Tf 8.275 -1.494 Td [(n)]TJ/F73 9.9626 Tf 8.709 1.494 Td [(needs)-330(to)-330(be)-330(correlated)-330(ag)5(ainst)-329(query)-330(feature)]TJ
0 g 0 G
0 g 0 G
200.405 629.037 Td [(map)]TJ/F14 9.9626 Tf 19.98 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\))]TJ/F73 9.9626 Tf 3.874 0 Td [(.)-410(T)80(o)-284(this)-283(end,)-292(we)-284(adopt)-283(a)-284(feat)1(ure)-284(modulator)]TJ/F14 9.9626 Tf 177.587 0 Td [(M)]TJ/F73 9.9626 Tf 11.964 0 Td [(,)]TJ -233.759 -11.955 Td [(which)-276(tak)10(es)-275(both)]TJ/F83 9.9626 Tf 70.671 0 Td [(\b)]TJ/F10 6.9738 Tf 8.274 -1.494 Td [(n)]TJ/F73 9.9626 Tf 8.168 1.494 Td [(and)]TJ/F14 9.9626 Tf 17.131 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.875 0 Td [(I)]TJ/F73 6.9738 Tf 4.344 -1.494 Td [(q)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\))]TJ/F73 9.9626 Tf 6.62 0 Td [(as)-276(input)-275(to)-276(produce)-275(the)-276(at-)]TJ -131.218 -11.955 Td [(tenti)25(v)15(e)-358(features)]TJ/F83 9.9626 Tf 65.384 0 Td [(A)]TJ/F10 6.9738 Tf 8.662 -1.494 Td [(n)]TJ/F8 9.9626 Tf 10.182 1.494 Td [(=)]TJ/F14 9.9626 Tf 12.508 0 Td [(M)]TJ/F8 9.9626 Tf 11.964 0 Td [(\()]TJ/F14 9.9626 Tf 3.875 0 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(;)]TJ/F83 9.9626 Tf 4.428 0 Td [(\b)]TJ/F10 6.9738 Tf 8.275 -1.494 Td [(n)]TJ/F8 9.9626 Tf 5.423 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(;)-167(n)]TJ/F8 9.9626 Tf 15.167 0 Td [(=)-478(1)]TJ/F11 9.9626 Tf 17.49 0 Td [(;)]TJ/F8 9.9626 Tf 4.428 0 Td [(2)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F14 9.9626 Tf 4.428 0 Td [<01>-167<01>-166<01>]TJ/F11 9.9626 Tf 14.944 0 Td [(;)-167(N)]TJ/F73 9.9626 Tf 13.518 0 Td [(.)]TJ -233.759 -11.955 Td [(F)15(or)]TJ/F14 9.9626 Tf 17.19 0 Td [(M)]TJ/F73 9.9626 Tf 15.466 0 Td [(we)-351(could)-352(choose)-351(simple)-352(correlation,)-376(spatial)-352(atten-)]TJ -32.656 -11.955 Td [(tion,)-404(channel)-373(attention,)]TJ/F77 9.9626 Tf 98.101 0 Td [(etc)]TJ/F73 9.9626 Tf 11.616 0 Td [(.)-679(In)-374(this)-373(paper)40(,)-404(we)-373(use)-373(simple)]TJ -109.717 -11.956 Td [(correlation)-366(for)-366(its)-366(ef)25(\002cienc)15(y)65(,)-395(whi)1(ch)-366(is)-366(gi)25(v)15(en)-366(as)]TJ/F83 9.9626 Tf 195.397 0 Td [(A)]TJ/F10 6.9738 Tf 8.662 -1.494 Td [(n)]TJ/F8 9.9626 Tf 5.423 1.494 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(p)]TJ/F8 9.9626 Tf 6.365 0 Td [(\))-492(=)]TJ/F14 9.9626 Tf -219.721 -11.955 Td [(F)]TJ/F8 9.9626 Tf 8.15 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\)\()]TJ/F83 9.9626 Tf 7.749 0 Td [(p)]TJ/F8 9.9626 Tf 6.365 0 Td [(\))]TJ/F14 9.9626 Tf 4.926 0 Td [(\f)]TJ/F83 9.9626 Tf 8.801 0 Td [(\b)]TJ/F10 6.9738 Tf 8.274 -1.494 Td [(n)]TJ/F73 9.9626 Tf 5.423 1.494 Td [(,)-225(where)]TJ/F83 9.9626 Tf 31.246 0 Td [(p)]TJ/F14 9.9626 Tf 9.132 0 Td [(2)]TJ/F70 9.9626 Tf 9.409 0 Td [(R)]TJ/F7 6.9738 Tf 7.195 3.616 Td [(2)]TJ/F73 9.9626 Tf 6.647 -3.616 Td [(runs)-218(o)15(v)15(er)-219(the)-218(feature)-219(map)-218(of)]TJ -125.521 -11.955 Td [(size)]TJ/F11 9.9626 Tf 17.806 0 Td [(l)]TJ/F14 9.9626 Tf 4.73 0 Td [<02>]TJ/F11 9.9626 Tf 9.31 0 Td [(l)]TJ/F73 9.9626 Tf 3.168 0 Td [(,)-236(and)]TJ/F14 9.9626 Tf 21.541 0 Td [(\f)]TJ/F73 9.9626 Tf 10.063 0 Td [(is)-232(the)-233(channel-wise)-232(multiplication.)-304(Feature)]TJ -66.618 -11.955 Td [(correlation)-397(performs)-398(the)-397(similarity)-398(learning)-397(between)-398(sup-)]TJ 0 -11.955 Td [(port)-390(and)-390(query)65(,)-424(which)-390(`acti)25(v)25(ates')-390(the)-389(local)-390(re)15(gions)-390(in)-390(the)]TJ 0 -11.955 Td [(query)-250(feature)-250(map)-250(that)-250(signi\002cantly)-250(correlate)-250(with)-250(SKP)111(.)]TJ/F72 9.9626 Tf 0 -12.399 Td [(K)25(eypoint)-396(Descriptor)-397(Extraction:)]TJ/F73 9.9626 Tf 147.026 0 Td [(After)-396(performing)-397(fea-)]TJ -147.026 -11.955 Td 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[-347(4)]TJ
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[-346(relies)-346(on)-347(the)-346(computation)-346(of)-347(the)]TJ -68.354 -11.956 Td [(in)40(v)15(erse)-296(of)-296(co)15(v)25(ariance)-297(matrix)]TJ/F83 9.9626 Tf 117.087 0 Td [<06>]TJ/F73 9.9626 Tf 8.275 0 Td [(,)-308(which)-296(is)-296(costly)-296(and)-296(unsta-)]TJ -125.362 -11.955 Td [(ble)-304(in)-303(back-propag)5(ation)-304(especially)-303(when)]TJ/F11 9.9626 Tf 166.136 0 Td [(k)]TJ/F14 9.9626 Tf 9.256 0 Td [<15>]TJ/F8 9.9626 Tf 11.505 0 Td [(4)]TJ/F73 9.9626 Tf 4.981 0 Td [(.)-471(Thus,)-317(we)]TJ -191.878 -11.955 Td [(replace)]TJ/F83 9.9626 Tf 31.252 0 Td [<06>]TJ/F73 9.9626 Tf 10.765 0 Td [(with)-250(the)-250(precision)-250(matrix)]TJ/F83 9.9626 Tf 102.385 0 Td [(\n)]TJ/F8 9.9626 Tf 11.042 0 Td [(=)]TJ/F83 9.9626 Tf 10.516 0 Td [<06>]TJ/F13 6.9738 Tf 8.275 3.615 Td [<00>]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F73 9.9626 Tf 4.47 -3.615 Td [(,)-250(and)-250(obtain)]TJ/F14 9.9626 Tf -173.724 -27.684 Td [(L)]TJ/F73 6.9738 Tf 6.871 -1.494 Td [(os-nll)]TJ/F8 9.9626 Tf 19.152 1.494 Td [(=)]TJ 11.711 6.74 Td [(1)]TJ
ET
q
1 0 0 1 99.053 387.322 cm
[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S
Q
BT
/F8 9.9626 Tf 99.053 377.997 Td [(2)]TJ/F70 9.9626 Tf 6.177 6.834 Td [(E)]TJ/F8 9.9626 Tf 6.642 0 Td [([\()]TJ/F83 9.9626 Tf 6.642 0 Td [(x)]TJ/F14 9.9626 Tf 8.26 0 Td [<00>]TJ/F83 9.9626 Tf 9.963 0 Td [(v)]TJ/F13 6.9738 Tf 6.206 4.114 Td [<03>]TJ/F8 9.9626 Tf 4.58 -4.114 Td [(\))]TJ/F69 6.9738 Tf 3.874 4.114 Td [(|)]TJ/F83 9.9626 Tf 5.009 -4.114 Td [(\n)]TJ/F8 9.9626 Tf 8.275 0 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(x)]TJ/F14 9.9626 Tf 8.261 0 Td [<00>]TJ/F83 9.9626 Tf 9.962 0 Td [(v)]TJ/F13 6.9738 Tf 6.206 4.114 Td [<03>]TJ/F8 9.9626 Tf 4.58 -4.114 Td [(\))]TJ/F14 9.9626 Tf 6.088 0 Td [<00>]TJ/F8 9.9626 Tf 9.963 0 Td [(log)-181(d)1(e)-1(t\()]TJ/F83 9.9626 Tf 32.24 0 Td [(\n)]TJ/F8 9.9626 Tf 8.275 0 Td [(\)])]TJ/F11 9.9626 Tf 6.642 0 Td [(:)]TJ/F73 9.9626 Tf 13.974 0 Td [(\(5\))]TJ -224.634 -26.008 Td [(As)-368(a)-368(result,)-397(the)]TJ/F14 9.9626 Tf 67.252 0 Td [(L)]TJ/F73 6.9738 Tf 6.871 -1.495 Td [(os-nll)]TJ/F73 9.9626 Tf 20.051 1.495 Td [(can)-368(be)-368(easily)-368(computed)-368(as)-368(long)-368(as)]TJ/F83 9.9626 Tf -94.174 -11.956 Td [(\n)]TJ/F14 9.9626 Tf 13.652 0 Td [<1f>]TJ/F83 9.9626 Tf 13.126 0 Td [(0)]TJ/F73 9.9626 Tf 5.729 0 Td [(.)-734(T)80(o)-392(guarantee)-391(this,)-427(we)-392(let)]TJ/F83 9.9626 Tf 117.122 0 Td [(\n)]TJ/F8 9.9626 Tf 13.652 0 Td [(=)]TJ/F7 6.9738 Tf 14.41 3.923 Td [(1)]TJ
ET
q
1 0 0 1 227.715 349.358 cm
[]0 d 0 J 0.398 w 0 0 m 4.147 0 l S
Q
BT
/F10 6.9738 Tf 227.715 343.432 Td [(d)]TJ/F83 9.9626 Tf 5.343 3.435 Td [(QQ)]TJ/F69 6.9738 Tf 17.213 3.616 Td [(|)]TJ/F73 9.9626 Tf 5.009 -3.616 Td [(,)-427(where)]TJ/F83 9.9626 Tf -205.168 -11.955 Td [(Q)]TJ/F14 9.9626 Tf 13 0 Td [(2)]TJ/F70 9.9626 Tf 11.036 0 Td [(R)]TJ/F10 6.9738 Tf 7.195 3.616 Td [(k)]TJ/F13 6.9738 Tf 4.404 0 Td [<02>]TJ/F10 6.9738 Tf 6.226 0 Td [(d)]TJ/F73 9.9626 Tf 8.015 -3.616 Td [(\()]TJ/F11 9.9626 Tf 3.317 0 Td [(d)]TJ/F14 9.9626 Tf 9.579 0 Td [<15>]TJ/F11 9.9626 Tf 12.143 0 Td [(k)]TJ/F73 9.9626 Tf 5.5 0 Td [(\))-338(is)-338(the)-338(latent)-339(matrix)-338(learned)-338(from)-338(our)]TJ -80.415 -11.955 Td [(co)15(v)25(ariance)-253(branch)-253(netw)10(ork.)-319(In)-253(e)15(xtreme)-253(case,)-254(a)-253(small)]TJ/F11 9.9626 Tf 211.615 0 Td [<0f>]TJ/F14 9.9626 Tf 6.868 0 Td [(!)]TJ/F8 9.9626 Tf 12.786 0 Td [(0)]TJ/F73 9.9626 Tf -231.269 -11.955 Td [(can)-250(be)-250(added)-250(to)-250(ensure)]TJ/F8 9.9626 Tf 93.23 0 Td [(det\()]TJ/F83 9.9626 Tf 17.711 0 Td [(\n)]TJ/F8 9.9626 Tf 8.275 0 Td [(\))]TJ/F11 9.9626 Tf 6.641 0 Td [(>)]TJ/F8 9.9626 Tf 10.516 0 Td [(0)]TJ/F73 9.9626 Tf 4.982 0 Td [(.)]TJ -129.4 -12.659 Td [(Firstly)65(,)-372(we)-348(in)40(v)15(estig)5(ate)-348(learning)-347(the)-348(co)15(v)25(ariance)-348(per)-348(k)10(e)15(y-)]TJ -11.955 -11.956 Td [(point)-371(by)-370(adding)-371(a)-371(co)15(v)25(ariance)-370(branch)]TJ/F14 9.9626 Tf 154.003 0 Td [(G)]TJ/F73 6.9738 Tf 5.927 -1.494 Td [(v)]TJ/F73 9.9626 Tf 7.678 1.494 Td [(to)-371(GBL)-370(\(Fig.)]TJ
1 0 0 rg 1 0 0 RG
[-371(4)]TJ
0 g 0 G
[(\),)]TJ -167.608 -11.955 Td [(whose)-534(output)-535(is)-534(the)-534(latent)-535(co)15(v)25(ariance)-534<02656c64>]TJ/F14 9.9626 Tf 189.601 0 Td [(G)]TJ/F73 6.9738 Tf 5.926 -1.494 Td [(v)]TJ/F8 9.9626 Tf 3.985 1.494 Td [(\()]TJ/F83 9.9626 Tf 3.875 0 Td [(\t)]TJ/F10 6.9738 Tf 8.911 -1.494 Td [(n)]TJ/F8 9.9626 Tf 5.423 1.494 Td [(\))]TJ/F14 9.9626 Tf 11.887 0 Td [(2)]TJ/F70 9.9626 Tf -229.608 -11.955 Td [(R)]TJ/F10 6.9738 Tf 7.195 3.615 Td [(S)]TJ/F13 6.9738 Tf 5.274 0 Td [<02>]TJ/F10 6.9738 Tf 6.226 0 Td [(S)]TJ/F13 6.9738 Tf 5.273 0 Td [<02>]TJ/F7 6.9738 Tf 6.227 0 Td [(2)]TJ/F10 6.9738 Tf 3.971 0 Td [(d)]TJ/F73 9.9626 Tf 4.646 -3.615 Td [(.)-432(Then)]TJ/F83 9.9626 Tf 30.166 0 Td [(Q)]TJ/F14 9.9626 Tf 12.125 0 Td [(2)]TJ/F70 9.9626 Tf 10.161 0 Td [(R)]TJ/F7 6.9738 Tf 7.195 3.615 Td [(2)]TJ/F13 6.9738 Tf 3.971 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(d)]TJ/F73 9.9626 Tf 7.542 -3.615 Td [(which)-291(encodes)-290(the)-291(co)15(v)25(ariance)]TJ -116.199 -11.955 Td [(information)-243(for)-243(a)-243(gi)25(v)15(en)-243(k)10(e)15(ypoint)-243(can)-243(be)-244(e)15(xtracted)-243(from)-243(grid)]TJ/F83 9.9626 Tf 0 -11.955 Td [(g)]TJ/F73 9.9626 Tf 5.888 0 Td [(.)-759(Secondly)65(,)-437(we)-400(in)40(v)15(estig)5(ate)-400(learning)-399(relations)-400(for)-400(multi-)]TJ -5.888 -11.955 Td [(ple)-250(k)10(e)15(ypoints)-250(within)-250(group)-249(\()]TJ/F77 9.9626 Tf 112.651 0 Td [(i.e)]TJ/F73 9.9626 Tf 9.683 0 Td [(.,)]TJ/F11 9.9626 Tf 7.471 0 Td [(m)]TJ/F73 9.9626 Tf 11.237 0 Td [(k)10(e)15(ypoints)-250(per)-250(group\))-250(by)]TJ -141.042 -11.956 Td [(a)-381(multi-k)10(e)15(ypoint)-382(co)15(v)25(ariance)-381(branch)]TJ/F14 9.9626 Tf 148.461 0 Td [(G)]TJ/F73 6.9738 Tf 5.926 -1.494 Td [(mkv)]TJ/F73 9.9626 Tf 16.698 1.494 Td [(whose)-382(output)-381(is)]TJ/F83 9.9626 Tf -171.085 -11.955 Td [(Q)]TJ/F73 6.9738 Tf 8.606 -1.494 Td [(mkv)]TJ/F14 9.9626 Tf 15.665 1.494 Td [(2)]TJ/F70 9.9626 Tf 9.409 0 Td [(R)]TJ/F7 6.9738 Tf 7.196 3.616 Td [(2)]TJ/F10 6.9738 Tf 3.971 0 Td [(m)]TJ/F13 6.9738 Tf 7.07 0 Td [<02>]TJ/F7 6.9738 Tf 6.226 0 Td [(2)]TJ/F10 6.9738 Tf 3.971 0 Td [(m)]TJ/F73 9.9626 Tf 7.568 -3.616 Td [(.)]TJ -57.727 -12.659 Td [(In)-380(addition)-380(to)]TJ/F83 9.9626 Tf 60.065 0 Td [<06>]TJ/F73 9.9626 Tf 12.061 0 Td [(which)-380(re\003ects)-380(the)-380(localization)-380(uncer)20(-)]TJ -84.081 -11.955 Td [(tainty)-420(o)15(v)15(er)-420(k)10(e)15(ypoints,)-462(follo)25(wing)-420([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(23)]TJ
0 g 0 G
[(,)]TJ
0 0.6 0 rg 0 0.6 0 RG
[-243(36)]TJ
0 g 0 G
[(],)-463(we)-420(also)-420(model)]TJ 0 -11.955 Td [(the)-235(semantic)-236(uncertainty)]TJ/F90 9.9626 Tf 99.45 0 Td [<1b>]TJ/F73 9.9626 Tf 9.549 0 Td [(by)-235(learning)-236(a)-235(single-channel)-236(SD)]TJ -108.999 -11.955 Td [(map)]TJ/F90 9.9626 Tf 20.204 0 Td [<1b>]TJ/F13 6.9738 Tf 7.202 3.615 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -6.227 -6.078 Td [(s)]TJ/F14 9.9626 Tf 14.498 2.463 Td [(2)]TJ/F70 9.9626 Tf 10.442 0 Td [(R)]TJ/F10 6.9738 Tf 7.196 3.615 Td [(H)]TJ/F13 6.9738 Tf 7.058 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(W)]TJ/F13 6.9738 Tf 8.565 0 Td [<02>]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F73 9.9626 Tf 7.519 -3.615 Td [(via)-306(SD)-306(head)]TJ/F14 9.9626 Tf 52.861 0 Td [(D)]TJ/F73 9.9626 Tf 11.011 0 Td [(\(Fig.)]TJ
1 0 0 rg 1 0 0 RG
[-306(4)]TJ
0 g 0 G
[(\))-306(whose)-306(v)25(al-)]TJ -159.009 -11.956 Td [(ues)-279(are)-278(in)-279(range)]TJ/F8 9.9626 Tf 66.423 0 Td [(\(0)]TJ/F11 9.9626 Tf 8.856 0 Td [(;)]TJ/F8 9.9626 Tf 4.428 0 Td [(1\))]TJ/F73 9.9626 Tf 8.855 0 Td [(.)-396(The)-278(higher)-279(the)-278(v)25(alue,)-286(the)-279(more)-278(dis-)]TJ -88.562 -11.955 Td [(tincti)25(v)15(e)-373(perceptually)-373(a)-372(k)10(e)15(ypoint)-373(is.)-678(Let)]TJ/F90 9.9626 Tf 165.521 0 Td [<1b>]TJ/F13 6.9738 Tf 7.202 3.616 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -6.227 -6.079 Td [(s)]TJ/F73 9.9626 Tf 14.41 2.463 Td [(and)]TJ/F90 9.9626 Tf 18.1 0 Td [<1b>]TJ/F13 6.9738 Tf 7.202 3.616 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F10 6.9738 Tf -6.227 -6.079 Td [(q)]TJ/F73 9.9626 Tf 14.41 2.463 Td [(be)]TJ -226.845 -11.955 Td [(the)-348(support)-347(and)-348(query)-348(SD)-347(maps.)-603(Thus,)-372(for)-348(each)-348(k)10(e)15(ypoint)]TJ 0 -11.955 Td [(descriptor)]TJ/F83 9.9626 Tf 43.258 0 Td [(\t)]TJ/F10 6.9738 Tf 8.911 -1.495 Td [(n)]TJ/F73 9.9626 Tf 5.423 1.495 Td [(,)-366(we)-344(e)15(xtra)1(ct)-344(the)-343(corresponding)-343(SD)-343(scalar)-343(as)]TJ/F11 9.9626 Tf -57.592 -11.955 Td [(w)]TJ/F10 6.9738 Tf 7.132 -1.495 Td [(n)]TJ/F8 9.9626 Tf 8.191 1.495 Td [(=)]TJ/F7 6.9738 Tf 11.711 3.922 Td [(1)]TJ
ET
q
1 0 0 1 77.146 96.891 cm
[]0 d 0 J 0.398 w 0 0 m 3.971 0 l S
Q
BT
/F7 6.9738 Tf 77.146 90.965 Td [(2)]TJ/F8 9.9626 Tf 5.167 3.436 Td [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [<1b>]TJ/F13 6.9738 Tf 6.051 3.615 Td [<00>]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F73 6.9738 Tf -6.584 -6.078 Td [(s)]TJ/F10 6.9738 Tf 2.713 0 Td [(;)]TJ/F84 6.9738 Tf 2.366 0 Td [(u)]TJ/F9 4.9813 Tf 5.009 -0.996 Td [(n)]TJ/F8 9.9626 Tf 7.515 3.459 Td [(+)]TJ/F11 9.9626 Tf 9.881 0 Td [<1b>]TJ/F13 6.9738 Tf 6.05 4.262 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F73 6.9738 Tf -6.585 -7.184 Td [(q)]TJ/F10 6.9738 Tf 3.487 0 Td [(;)]TJ/F84 6.9738 Tf 2.367 0 Td [(u)]TJ/F12 4.9813 Tf 5.009 1.992 Td [(0)]TJ/F9 4.9813 Tf 0 -3.985 Td [(n)]TJ/F8 9.9626 Tf 5.383 4.915 Td [(\))]TJ/F73 9.9626 Tf 3.875 0 Td [(,)-248(where)]TJ/F11 9.9626 Tf 31.77 0 Td [<1b>]TJ/F13 6.9738 Tf 6.05 3.615 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F73 6.9738 Tf -6.584 -6.078 Td [(s)]TJ/F10 6.9738 Tf 2.713 0 Td [(;)]TJ/F84 6.9738 Tf 2.366 0 Td [(u)]TJ/F9 4.9813 Tf 5.009 -0.996 Td [(n)]TJ/F73 9.9626 Tf 7.852 3.459 Td [(and)]TJ/F11 9.9626 Tf 16.855 0 Td [<1b>]TJ/F13 6.9738 Tf 6.05 4.262 Td [<00>]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F73 6.9738 Tf -6.584 -7.184 Td [(q)]TJ/F10 6.9738 Tf 3.487 0 Td [(;)]TJ/F84 6.9738 Tf 2.366 0 Td [(u)]TJ/F12 4.9813 Tf 5.009 1.992 Td [(0)]TJ/F9 4.9813 Tf 0 -3.985 Td [(n)]TJ/F73 9.9626 Tf 7.853 4.915 Td [(are)-248(support)]TJ -191.73 -13.401 Td [(and)-259(query)-260(SD)-259(map)-260(v)25(alues)-259(at)-260(k)10(e)15(ypoint)-259(locations)]TJ/F83 9.9626 Tf 190.628 0 Td [(u)]TJ/F10 6.9738 Tf 6.365 -1.494 Td [(n)]TJ/F73 9.9626 Tf 8.008 1.494 Td [(and)]TJ/F83 9.9626 Tf 16.97 0 Td [(u)]TJ/F13 6.9738 Tf 6.365 3.615 Td [(0)]TJ/F10 6.9738 Tf 0 -6.078 Td [(n)]TJ/F73 9.9626 Tf 5.423 2.463 Td [(.)]TJ
0 g 0 G
0 g 0 G
24.991 367.381 Td [(Let)]TJ/F83 9.9626 Tf 15.811 0 Td [(W)]TJ/F8 9.9626 Tf 14.846 0 Td [(=)]TJ/F11 9.9626 Tf 10.591 0 Td [(diag)]TJ/F8 9.9626 Tf 18.993 0 Td [(\([)]TJ/F11 9.9626 Tf 6.642 0 Td [(w)]TJ/F7 6.9738 Tf 7.132 -1.495 Td [(1)]TJ/F11 9.9626 Tf 4.469 1.495 Td [(;)-167(w)]TJ/F7 6.9738 Tf 11.561 -1.495 Td [(1)]TJ/F11 9.9626 Tf 4.469 1.495 Td [(;)]TJ/F14 9.9626 Tf 4.428 0 Td [<01>-167<01>-166<01>]TJ/F11 9.9626 Tf 14.944 0 Td [(;)-167(w)]TJ/F10 6.9738 Tf 11.56 -1.495 Td [(m)]TJ/F11 9.9626 Tf 7.568 1.495 Td [(;)-167(w)]TJ/F10 6.9738 Tf 11.56 -1.495 Td [(m)]TJ/F8 9.9626 Tf 7.568 1.495 Td [(]\))]TJ/F14 9.9626 Tf 9.484 0 Td [(2)]TJ/F70 9.9626 Tf 9.483 0 Td [(S)]TJ/F7 6.9738 Tf 5.535 3.615 Td [(2)]TJ/F10 6.9738 Tf 3.972 0 Td [(m)]TJ/F7 6.9738 Tf -3.972 -6.078 Td [(++)]TJ/F73 9.9626 Tf 15.261 2.463 Td [(be)-254(a)-254(diago-)]TJ -191.905 -11.956 Td [(nal)-250(matrix)-250(with)-250(entries)]TJ/F11 9.9626 Tf 92.422 0 Td [(w)]TJ/F10 6.9738 Tf 7.132 -1.494 Td [(n)]TJ/F73 9.9626 Tf 5.423 1.494 Td [(.)-310(W)80(e)-250(introduce)]TJ/F83 9.9626 Tf 61.22 0 Td [(W)]TJ/F73 9.9626 Tf 14.495 0 Td [(into)-250(Eq.)]TJ
1 0 0 rg 1 0 0 RG
[-250(5)]TJ
0 g 0 G
[(:)]TJ/F14 9.9626 Tf -180.692 -22.489 Td [(L)]TJ/F73 6.9738 Tf 6.871 -1.494 Td [(uc)]TJ/F8 9.9626 Tf 9.849 1.494 Td [(=)]TJ 11.712 6.74 Td [(1)]TJ
ET
q
1 0 0 1 337.294 416.427 cm
[]0 d 0 J 0.398 w 0 0 m 4.981 0 l S
Q
BT
/F8 9.9626 Tf 337.294 407.102 Td [(2)]TJ/F70 9.9626 Tf 6.177 6.834 Td [(E)]TJ/F8 9.9626 Tf 6.641 0 Td [([\()]TJ/F83 9.9626 Tf 6.642 0 Td [(x)]TJ/F14 9.9626 Tf 6.047 0 Td [<00>]TJ/F83 9.9626 Tf 7.749 0 Td [(v)]TJ/F13 6.9738 Tf 6.206 4.114 Td [<03>]TJ/F8 9.9626 Tf 4.58 -4.114 Td [(\))]TJ/F69 6.9738 Tf 3.874 4.114 Td [(|)]TJ/F8 9.9626 Tf 5.009 -4.114 Td [(\()]TJ/F83 9.9626 Tf 3.874 0 Td [(\n)]TJ/F8 9.9626 Tf 8.275 0 Td [(+)]TJ/F11 9.9626 Tf 7.749 0 Td [(\f)]TJ/F83 9.9626 Tf 6.161 0 Td [(W)]TJ/F8 9.9626 Tf 12.003 0 Td [(\)\()]TJ/F83 9.9626 Tf 7.749 0 Td [(x)]TJ/F14 9.9626 Tf 6.047 0 Td [<00>]TJ/F83 9.9626 Tf 7.748 0 Td [(v)]TJ/F13 6.9738 Tf 6.206 4.114 Td [<03>]TJ/F8 9.9626 Tf 4.58 -4.114 Td [(\))]TJ/F14 9.9626 Tf 3.875 0 Td [<00>]TJ/F8 9.9626 Tf 7.748 0 Td [(log)-14(\(det\()]TJ/F83 9.9626 Tf 34.454 0 Td [(\nW)]TJ/F10 6.9738 Tf 20.279 4.114 Td [(\f)]TJ/F8 9.9626 Tf 5.373 -4.114 Td [(\)\)])]TJ/F11 9.9626 Tf 10.517 0 Td [(;)]TJ/F73 9.9626 Tf -9.361 -14.624 Td [(\(6\))]TJ -224.634 -11.956 Td [(where)]TJ/F11 9.9626 Tf 27.621 0 Td [(\f)]TJ/F73 9.9626 Tf 9.443 0 Td [(is)-329(a)-330(trade-of)25(f)-329(\(we)-330(set)]TJ/F11 9.9626 Tf 88.082 0 Td [(\f)]TJ/F8 9.9626 Tf 8.734 0 Td [(=)-258(1)]TJ/F73 9.9626 Tf 15.302 0 Td [(\).)-548(W)80(e)-330(also)-329(use)]TJ/F11 9.9626 Tf 63.479 0 Td [(w)]TJ/F10 6.9738 Tf 7.133 -1.494 Td [(n)]TJ/F73 9.9626 Tf 8.705 1.494 Td [(to)]TJ -228.499 -11.955 Td [(re)25(weight)-279(the)-279(cross-entrop)10(y)-279(grid)-280(classi\002cation)-279(loss)]TJ/F14 9.9626 Tf 201.173 0 Td [(L)]TJ/F73 6.9738 Tf 6.871 -1.494 Td [(cls-uc)]TJ/F8 9.9626 Tf 20.457 1.494 Td [(=)]TJ/F14 9.9626 Tf -228.501 -11.955 Td [<00>]TJ/F70 9.9626 Tf 7.749 0 Td [(E)]TJ/F8 9.9626 Tf 6.642 0 Td [([)]TJ/F14 9.9626 Tf 2.767 6.429 Td [(p)]TJ
ET
q
1 0 0 1 334.322 370.074 cm
[]0 d 0 J 0.398 w 0 0 m 12.555 0 l S
Q
BT
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ET
q
1 0 0 1 50.112 572.989 cm
[]0 d 0 J 0.996 w 0 0 m 238.979 0 l S
Q
0 g 0 G
BT
/F73 9.9626 Tf 50.112 553.552 Td [(First,)-228(we)-222(modify)-222(our)-222(FSKD)-222(into)-222(a)-222(simple)-223(k)10(e)15(ypoint)-222(e)15(xtractor)]TJ 0 -11.955 Td [(by)-237(le)25(v)15(eraging)-236(the)-237(uni)25(v)15(ersal)-236(k)10(e)15(ypoint)-237(prototype)-236(\(UKP\))-237(com-)]TJ 0 -11.956 Td [(puted)-337(by)-337(a)20(v)15(eraging)-337(the)-336(SKPs)-337(on)-337(additional)-337(1000)-337(episodes)]TJ 0 -11.955 Td [(after)-331(t)1(raining.)-552(In)-331(testing,)-350(UKPs)-331(guide)-330(FSKD)-331(to)-330(detect)-331(the)]TJ 0 -11.955 Td [(k)10(e)15(ypoints,)-311(and)-298(thus)-299(FSKD)]TJ/F77 9.9626 Tf 109.46 0 Td [(no)-299(long)10(er)]TJ/F73 9.9626 Tf 42.053 0 Td [(needs)-298(the)-299(support)-299(in-)]TJ -151.513 -11.955 Td [(put)-194(as)-194(a)-195(reference.)-291(W)80(e)-194(use)-194(FGVR)-195(model)-194(from)-194([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(46)]TJ
0 g 0 G
[(],)-205(based)-195(on)]TJ 0 -11.955 Td [(ProtoNet)-204(\(Proto\))-204([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(42)]TJ
0 g 0 G
[(],)-213(whereas)-203(our)-204(FSKD)-204(supplies)-204(k)10(e)15(ypoint)]TJ 0 -11.955 Td [(predictions.)-528(Bilinear)-323(pooling)-323(\(BP\))-322([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(31)]TJ
0 g 0 G
[(])-323(and)-323(bounding)-323(box)]TJ 0 -11.956 Td [(normalization)-202(\(bbN\))-202([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(46)]TJ
0 g 0 G
[(])-202(based)-202(methods)-202(are)-202(also)-202(compared.)]TJ 0 -11.955 Td [(All)-313(models)-314(are)-313(e)25(v)25(aluated)-314(in)-313(all-w)10(ay)-314(setting,)-329(1-,)-330(5-)-313(and)-314(all-)]TJ 0 -11.955 Td [(shot)-240(results)-239(are)-240(reported.)-307(T)80(able)]TJ
1 0 0 rg 1 0 0 RG
[-240(4)]TJ
0 g 0 G
[-239(sho)25(ws)-240(our)-240(model)-240(achie)25(v)15(es)]TJ 0 -11.955 Td [(the)-209(best)-209(scores)-209(which)-209(v)25(alidates)-209(the)-209(quality)-209(of)-209(FSKD.)-209(Includ-)]TJ 0 -11.955 Td [(ing)-325(the)-324(features)-325(from)-325(auxiliary)-324(k)10(e)15(ypoints)-325(further)-325(impro)15(v)15(es)]TJ 0 -11.955 Td [(results)-250(by)-250(making)-250(the)-250(prototypes)-250(more)-250(discriminati)25(v)15(e.)]TJ/F72 10.9589 Tf 0 -18.934 Td [(5.2.)-250(Semantic)-250(Alignment)]TJ/F73 9.9626 Tf 11.955 -17.933 Td [(Semantic)-261(alignment)-261(\(SA\))-261(is)-261(used)-261(in)-261(tasks)-262(such)-261(as)-261(recog-)]TJ -11.955 -11.955 Td [(nition)-273(and)-272(graphics)-273([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(4)]TJ
0 g 0 G
[(,)]TJ
0 0.6 0 rg 0 0.6 0 RG
[-145(40)]TJ
0 g 0 G
[(].)-378(W)80(e)-272(demonstrate)-273(that,)-278(under)-273(the)]TJ 0 -11.956 Td [(imperfect)-323(k)10(e)15(ypoint)-323(predictions,)-341(the)-323(query)-323(image)]TJ/F83 9.9626 Tf 198.253 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(q)]TJ/F73 9.9626 Tf 7.202 1.494 Td [(can)-323(be)]TJ -209.8 -11.955 Td [(w)10(arped)-346(into)-346(the)-346(recti\002ed)-345(image)]TJ/F83 9.9626 Tf 131.12 0 Td [(I)]TJ/F13 6.9738 Tf 4.345 3.616 Td [(0)]TJ/F73 6.9738 Tf 0 -6.079 Td [(q)]TJ/F73 9.9626 Tf 7.43 2.463 Td [(which)-346(aligns)-346(well)-346(with)]TJ -142.895 -11.955 Td [(the)-250(support)-250(image)]TJ/F83 9.9626 Tf 73.882 0 Td [(I)]TJ/F73 6.9738 Tf 4.345 -1.494 Td [(s)]TJ/F73 9.9626 Tf 5.702 1.494 Td [(\(Fig.)]TJ
1 0 0 rg 1 0 0 RG
[-310(3)]TJ
0 g 0 G
[(\(b\)\).)]TJ/F72 9.9626 Tf -83.929 -11.955 Td [(Uncertainty-weighted)-456(Thin-plate-spline)-455(W)65(ar)10(p:)]TJ/F73 9.9626 Tf 209.232 0 Td [(Unlik)10(e)]TJ -209.232 -11.955 Td [(classic)-349(TPS)-349(w)10(arp)-350([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(3)]TJ
0 g 0 G
[(,)]TJ
0 0.6 0 rg 0 0.6 0 RG
[-196(12)]TJ
0 g 0 G
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1 0 0 rg 1 0 0 RG
/F73 6.9738 Tf 232.265 3.616 Td [(1)]TJ
0 g 0 G
/F83 9.9626 Tf -232.265 -15.571 Td [(T)]TJ/F14 9.9626 Tf 10.737 0 Td [(2)]TJ/F70 9.9626 Tf 9.409 0 Td [(R)]TJ/F7 6.9738 Tf 7.196 3.616 Td [(2)]TJ/F13 6.9738 Tf 3.971 0 Td [<02>]TJ/F7 6.9738 Tf 6.227 0 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(N)]TJ/F7 6.9738 Tf 7.058 0 Td [(+3\))]TJ/F73 9.9626 Tf 16.19 -3.616 Td [(of)-250(uncertainty-weighted)-250(TPS)-250(w)10(arp)-250(as)]TJ/F83 9.9626 Tf -49.259 -28.75 Td [(T)]TJ/F8 9.9626 Tf 10.737 0 Td [(=)]TJ/F1 9.9626 Tf 10.516 17.036 Td [( )]TJ 7.887 -2.989 Td [<14>]TJ/F83 9.9626 Tf 10.24 -7.97 Td [(R)]TJ/F8 9.9626 Tf 10.806 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [<15>]TJ/F83 9.9626 Tf 5.811 0 Td [(D)]TJ/F7 6.9738 Tf 8.787 3.616 Td [(2)]TJ/F8 9.9626 Tf 19.634 -1.07 Td [(^)]TJ/F83 9.9626 Tf -1.425 -2.546 Td [(P)]TJ/F69 6.9738 Tf 7.832 3.616 Td [(|)]TJ/F8 9.9626 Tf -43.981 -14.121 Td [(^)]TJ/F83 9.9626 Tf -1.425 -2.546 Td [(P)-2606(0)]TJ/F7 6.9738 Tf 39.525 3.615 Td [(3)]TJ/F13 6.9738 Tf 3.971 0 Td [<02>]TJ/F7 6.9738 Tf 6.227 0 Td [(3)]TJ/F1 9.9626 Tf 9.451 17.406 Td [<15>]TJ/F13 6.9738 Tf 5.258 -0.968 Td [<00>]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F1 9.9626 Tf 6.129 0.968 Td [<14>]TJ/F83 9.9626 Tf 12.869 -7.97 Td [(P)]TJ/F13 6.9738 Tf 7.832 3.616 Td [(0)]TJ/F69 6.9738 Tf 2.296 0 Td [(|)]TJ/F83 9.9626 Tf -12.757 -15.571 Td [(0)]TJ/F7 6.9738 Tf 5.728 3.615 Td [(3)]TJ/F13 6.9738 Tf 3.971 0 Td [<02>]TJ/F7 6.9738 Tf 6.227 0 Td [(2)]TJ/F1 9.9626 Tf 9.451 16.31 Td [<15>]TJ 5.258 2.989 Td [(!)]TJ/F69 6.9738 Tf 7.887 -1.926 Td [(|)]TJ/F11 9.9626 Tf 6.669 -15.11 Td [(;)]TJ/F73 9.9626 Tf 17.409 0 Td [(\(11\))]TJ -219.652 -29.315 Td [(Matrix)]TJ/F83 9.9626 Tf 30.293 0 Td [(R)]TJ/F14 9.9626 Tf 12.629 0 Td [(2)]TJ/F70 9.9626 Tf 10.677 0 Td [(R)]TJ/F10 6.9738 Tf 7.195 3.615 Td [(N)]TJ/F13 6.9738 Tf 7.058 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(N)]TJ/F73 9.9626 Tf 10.732 -3.615 Td [(has)-319(entries)]TJ/F11 9.9626 Tf 46.191 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.495 Td [(i;j)]TJ/F8 9.9626 Tf 13.418 1.495 Td [(=)]TJ/F11 9.9626 Tf 11.784 0 Td [(d)]TJ/F7 6.9738 Tf 5.185 3.615 Td [(2)]TJ/F10 6.9738 Tf 0 -6.208 Td [(i;j)]TJ/F8 9.9626 Tf 11.043 2.593 Td [(log)]TJ/F11 9.9626 Tf 14.529 0 Td [(d)]TJ/F7 6.9738 Tf 5.186 3.615 Td [(2)]TJ/F10 6.9738 Tf 0 -6.208 Td [(i;j)]TJ/F73 9.9626 Tf 9.382 2.593 Td [(,)]TJ/F11 9.9626 Tf 5.838 0 Td [(d)]TJ/F10 6.9738 Tf 5.185 -1.495 Td [(i;j)]TJ/F73 9.9626 Tf 12.558 1.495 Td [(is)]TJ -229.605 -11.955 Td [(the)-241(Euclidean)-240(distance)-241(between)]TJ/F83 9.9626 Tf 127.445 0 Td [(p)]TJ/F10 6.9738 Tf 6.365 -1.495 Td [(i)]TJ/F73 9.9626 Tf 5.714 1.495 Td [(and)]TJ/F83 9.9626 Tf 16.784 0 Td [(p)]TJ/F10 6.9738 Tf 6.365 -1.495 Td [(j)]TJ/F73 9.9626 Tf 4.198 1.495 Td [(,)-242(and)]TJ/F11 9.9626 Tf 21.689 0 Td [<15>]TJ/F14 9.9626 Tf 8.579 0 Td [<15>]TJ/F8 9.9626 Tf 10.516 0 Td [(0)]TJ/F73 9.9626 Tf 7.379 0 Td [(is)-241(the)]TJ
0 g 0 G
ET
q
1 0 0 1 50.112 90.679 cm
[]0 d 0 J 0.398 w 0 0 m 94.499 0 l S
Q
BT
/F73 5.9776 Tf 60.971 83.813 Td [(1)]TJ/F73 7.9701 Tf 3.487 -2.813 Td [(Uncertainty-weighted)-240(TPS)-240(w)10(arp)-240(is)-241(deri)25(v)15(ed)-240(in)-240]TJ
1 0 0 rg 1 0 0 RG
[(A)]TJ
0 g 0 G
[-240(of)]TJ/F72 7.9701 Tf 165.877 0 Td [(Suppl.)-307(Material)]TJ/F73 7.9701 Tf 54.034 0 Td [(.)]TJ
0 g 0 G
0 g 0 G
0 g 0 G
0 g 0 G
ET
1 0 0 1 308.862 616.961 cm
q
.16374 0 0 .16374 0 0 cm
q
1 0 0 1 0 0 cm
/Im13 Do
Q
Q
0 g 0 G
1 0 0 1 -308.862 -616.961 cm
BT
/F73 8.9664 Tf 308.862 603.62 Td [(Figure)-210(9.)-296(Comparison)-210(of)-210(semantic)-209(alignment)-210(approaches.)-297(The)-209<02727374>]TJ 0 -10.959 Td [(column)-254(sho)25(ws)-254(the)-254(support)-254(k)10(e)15(ypoints)-254(&)-254(image;)-256(the)-254(second)-254(column)]TJ 0 -10.959 Td [(sho)25(ws)-336(the)-336(query)-336(image)-336(with)-336(the)-336(predicted)-336(k)10(e)15(ypoints)-336(\()1(mark)10(ed)-336(by)]TJ 0 -10.958 Td [(tilted)-252(crosses\))-252(and)-252(unce)1(rtainty)-252(\(red)-252(shado)25(w)-252(ellipses\);)-253(the)-252(last)-251(three)]TJ 0 -10.959 Td [(columns)-319(are)-320(the)-320(result)1(s)-320(achie)25(v)15(ed)-320(by)]TJ/F77 8.9664 Tf 133.367 0 Td [(W)92(arp)-319(with)-320(GT)]TJ/F73 8.9664 Tf 55.291 0 Td [([)]TJ
0 0.6 0 rg 0 0.6 0 RG
[(3)]TJ
0 g 0 G
[(],)]TJ/F77 8.9664 Tf 15.717 0 Td [(Identical)]TJ -204.375 -10.959 Td [(UC)]TJ/F73 8.9664 Tf 12.454 0 Td [(,)-250(and)-250(our)-250(uncertainty-weighted)-250(TPS)-250(w)10(arp.)]TJ
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