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nod and
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sensor
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surface spot
amplitude modulated laser beam
( x, y )
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laser
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projector
c
CCD
camera
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X
(x , y , z )
w w w
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Zw
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c
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linear equations
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(x ,y ,z )
w w w
3D
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?@"TJEG:._.%8?@9A._9<PNBT?QC5.DBU%N=L=H2NGM0@.N[5dt0Ue325(+G+7M.OBF„cG:(+25._(+BT?U9>JM;<2N#MG:%q;AX5B\.K?U2u?U.DJEBF?].L?UB@.1=10U25*M0U.D;<#+Bt.‰?UG:|%ZG+?Q;AG^=HGl%qX5?U.O.DBF%!?](+B@=1#+25;A*M0U.K2E?@J+2%8(:9^B@,^.O.D9<%59<B\k‹B@?UG:G+%5.‰7^JE._J';AX)G:;AJ+;ABF;<#+?@2N[u[5=10H0@%8;<*p?@.D0@C8;A2525#:#a. d
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9A=H2ZG+|¤2)2NŒ XZB@%8.!*M0U?@;>.D%8G:%N#:.'BF=1(+JE.50Ud3;A.SX)Œ ;A28JE4\;A[5#+[50U[R0U2525(+=1(+7p0@7I;<?@|.DG+0@;<25?@;A25Gi*M#p2N9A2Z;>[5B|¤.1#:?UG:2&.125;<?T=H*MPWG+2)25;AB2N[NB@.1XZ.u#+%5.D0@%h;ƒ;>?T%8JEP&#:;AX)=1|.5;AJ+;<do9A;<9aŒ#+G:[&%q[5XNB@0U=1.2525(:G+0U7&.u;A[5|BFGi(:;<=H?@XZGpGp%80UG+?U;A%5G:;A[5#:%ZGp?‰=L.N?@G+d3G+2N‡‚.'*l#+0@2N._.-[5BF.D(+7^#+9<2c?@.1B@;A;<#+B@?T;<PW[h,:9<||K.u;<.1|39A;A9`[5%qG:GcPW%q?U.DXN?UJ2.
*M*WB@(+25%Z*™mE[N.1;A28*l#+4o.D;An1;ƒ?@?TG:._PNBK.-d\?@|Œ G+;<.-?@B@G+.D0@;A._=1#E25BFk‹(+#:[59<J&?@0U;A25#+|K(+[W%q7iPlBUXZ„N?U%8(^2M0U%8;>=H%80UG:.D#:JI2c=12c.DJEBFB;|.‚{V;>B‰?@.1G:0U*M.1.u#^;AJE#+=L;<;A.X)*l;>,/JE;An1.L;A._?T#+|KJŠ[Wd‚.1=L.1e30U#I;ƒG:?U?U.1;AG+BS0U;<.2N=L0U#R[5;ƒ0U?U;>25.1BK(+0U?@;<7I2N2W#p*M=HG+.1.D*M2)%52N#:7+B@B1G:.‚dˆ%N%Me3BF;AG:JEn1._;A;ABOX)BO;AJ+JEG+;|;A;A{V#+[5.1[WG 0U.1BU[N#:=L0@25=12N0U.(+.‚7i;ABO?@G:G+0@%825.1?kk
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,^.S?@G:.|].D;<[NGN?U.DJ&BF(+* 284t[50U25(+7&Xq%50@;>%8#^=L.DBDCc?@G:%8?;ABDC)?@G+. zo¹ ¬ I)¹ a³ G ±8°U¯Z²_¸ Z¶Z°z¹M ¶8O-³/«H,^©1.&d `?@G:.1.?
M O-,^.&?@G+.&XZ%80U;A%5#:=L.W4b2N0-?UG+.I[50U25(+7 |;<?@GXq%59<(:.DB'9<._B@B-?@G:%5#€2N0-.D„c(:%59Q?U2 -%5#:J
XZ|%8;<0U?@;AGs%5#:XZ=L%8.O9A(+4b.D25B!0]9A?@.DG+BU.‚BS[5?@0UG:25%5(+#s7W25|0;<?@.DG&„c(:Xq%5%59\9<(:?@.D2 B]![50U%8.D#:%ZJ ?U.10o?UM G:O!%8# ,/.Mzd?@`G+.L.M?7+ 0U25M ,^Oˆ%8,+,^;A.‚9<;<?T?@PiG+.S4b2N7+0!0U25?@,:G+%5.W,+[N;A9<0@;<2N?TP-(+7x4b2N|0Q;<?U?@G+Gs.‰XZ[N%80@9A2N(+(+.D7 B
[5[50U0U.D25%8(:?@7`.Ddo0ˆe3?@G^G+%8.1# #Iz?@d G:a..L|? ;ƒ?UG+;<M #+krO][N,^0@2N.‚(+?@7RG+.!XZ%8*M0U;>.D%8%5#:#h=1. 4b2N0]?UG+.‚;>BO†:JE0U.1BF†:?3#+[5._0UJ&25(+,)7IP %8#:J M OQ?UG+.‚*M._%8#h4b2N0K?@G+.B@.D=L2N#:J
M O M O M OT M O M O
M ¼+bd Z1#O
|G+.D0@.
<
MO 4
MO
MO
4
4
4
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M O
MO ¼+d
M O
M bZ O
M O M O
M O M O
¼+d ¾
M bZ O
,XH 1
½,(:½
NR
M
O
M O
- s?
4
- s?
4
M O 3 M O 1M O
M O 3 ¼+d
M O M O
M bZ %O
7/=1%52N#RBUBFe3,/;A,+G+.!9A.u.S0@._,/XZJE.D%5(:BF9<?S(+=L._._?@BKJWG+0U28?U.D42MB@QG+%l25?@2MB@9>J.D9A%82)O0H=D=H=1%ZGh%5?U#p.‰,/.L?U?@?TG+G+|K.!.D.1#x?@.DG+#R,/0U.'.D?UB@G+JEG+.S.12N?@?T9A.D|]J 0@2l*Mˆ*M?@;A#+G^2).D%ZJ+Ji?.D*M,)BDdPp;<#+‰%R;A*M2ZB@|];<;<*MnD.D.DX57+B .D9A0D.'CcB@;AJ+.DM „c.1#c(+OL?@do.D;<#c†^"$#&?@=1;>%8%8*W?@96;A%525B@#c.D#&%5Ph280U=HB@4a;<GI?@?U(:G+?U%8.!G+?@0@*M;A2N25(+2)#:[5J+BKG .D?UBKG+%5;A;A9<BB 9
0U.D%89A9APh.D„c(+;AXZ%89A.1#c?3?@2l?@G+.;>JE.D#N?U;ƒ†/=1%Z?U;<2N#p284tB@.17^%80H%Z?@;A#+[lXZ%89A(+.DB,/.L?T|K.1.D#R?UG+.*M2EJE.DBDd
S?@e3G^G+%Z.D?‰0@JE.!2);>.DBB3%M#:0@28.D?‰9A%8JE?@.D;A257^#:.DB@#:G+JI;A7&25#I,/.L?@?TG+|K.!.1?U.DG+#R0U.D?UG+B@G+.25|9>JŠ;ƒ?UdoG+e3;A#EG+kr.![N0@?@2N25(+?U%57I9ŠXqXq%5%50@0@;>;>%8%8#^#^=L=L. .S;ABOJ+M .L†:O3#+%8._#:JIJ&,c?UP G+.!?@25?U%89ŠXZ%50@;>%8#:=1.
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4
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T
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%M O 3 M OT - M O ?
MO3
3 %M O
M OxT - M O ?
3 M O
M O M OT M O M O
T %M O - 1M O ? 3 T M O - M O ?
+¼ d
XZXZe3%8%8G+0U0U.;A;A%5%5†^#:#:0U=L=LBF._. ?QBo,+280H4`%5dt._=H"‹%5YN?Q=H.LGW?@;>BV._25JuyT4Š(:?UBF?@.1?ˆG+0U.‰?@*~G+?T.‚|];>B\BF2u?U(+G+[N*0@.‰2N28|(+4/7:;<?@?@BDG+G:d6;A.O#Ee3|]k‹G+[5.D0U.S;<25[NBF(+Gc._7M?@=L.D2NXZJl#:%8JMBU0U„N;>%8,+(^#:0H%8%5=10U=H. .DY5JM.1?@JE._;>Jld\BT?H"‹?@%8?Q.1#:0U;>=1BŠ*.DyTB\(:;ABK,/BF?ˆ.L=1?T%5?@|KG:9<9A.1.‚.D.1JMB@#M(+?U*~?UG+G+.‰.O25,/4V*M.L?@?T.DG+|K%5.O.1#:|K.DBo#E.125k‹;A4/[5[50U._Gc25%5?U(+.D=HGJ7
?@[5G^0U25%Z(:?7f?@G:%5.#:[5Jf0H%8?@#:G+.RJR[5*l0H._%8%8#:# Jj*M=D.D%8%8#p#adI,/.e3|G+.W0@;<?F,/?U.L.1?T#p|K%5.1B.D#Ek‹[50U25(+7fXZ%80U;A%5#:=L.W=1%5# ,^.M4b(:0F?UG+.10lBF;A*M7+9<;<†:._JŠdI‰28?U.
M O 1M OsT M O M O
M ¼+bd Z O
|K‰B.S@;A#+2N,E[ ?U]Q%5;<„/# dcM ¼+dbZ OŠ?U2‚.D9<;A*M;<#^%Z?@. ;<#M ]QO„/TdcM ¼:dM ZOF$O-<z_½ CN?BF(+,^BTM?U;ƒ?UO 3#(E-?@;A#+[MM O½X?? M M OaO 4b3 250 M OF08%8#:JlB@;<*M7+9A;ƒ4bP);A#+[:C
*W^ ;A#:%ZmE=L.I;A*l?U;AG+n1.p;A#+[l?@25?@?UG:%8.9XZ,^%5.10@?T;>|]%8.D#:.1=1#p. [50Up25(+JE7&2)._XZBM%80U#+;A%528#:?h=LJE. .D7^.D#:M J OLC 25# zCQ?UG+. -*M;<#:;<*M;An1;A#+[ M Ol|;<9A9,/.p?@G+.
M O %M O -<j
½ ? 1M O 3c- M O ? M O 3
M ¼+d %¼ (NO
e6%89A2-9VG:JE%q.LX5?U.1.‚0U?@*M2l;<#+,/.O.!?@J+G+.L.‚?@.D*M0@*M%8mE;A#+;<*M.DJ`;An1d ;A#+O[ 2Zt|K4b.125X50 .D0DCN?@G:M ;AOHB30N#+?@G:.D.D.‚J&„c(:#+28%8?3#c?U,/;ƒ?U.!;<._J+BQ25JE#+.1.!?@.1;A#:0U*MJE.1;<7/#:.1.D#^JMJE,).1P #c?@]]9APW„)B14bd2N0KM ¼+._bd %5Z =HG Ot?@z`2 dˆe3M ¼+G+bd Z .1%O0U.
;>[fBK.%'G:0U.1%q9>X5%Z.!?@;AJE25;A#^0@BF._G+=z;A?@7h9APh,/4b.L0U?T25|K* .1.D]Q#h„/?@xd G:M .S¼:XZd Z %59<(+OQ.!?@G+=L.2N*M0U.D7+=1(E(+?@0H._BFJW;AX5.S4b2N0@0 .D]9A%8%8?@#:;A25Jh#:B@?@G+G:;A%87 ?=125*M7+(E?U.DJh4b250K?@G+.S#+.1mc? S& aT½5d
M T J½ O M OT M T J½ O
M ¼+d ¼+½ O
|;<?@Gp;<#:;ƒ?U;A%59`XZ%89A(+. %MTJ½ O MT½ Ozd
w+0U25* ]Q„/xd M ¼:d Z ¾ O]|].!2N,E?U%5;<#&?@G+.0U.D=1(+0HBF;AX5.S0@.D9A%8?@;A25#
%M xT J½ O 1M O M OT M xT ½ O M T J½ O
M ¼+d $¼ Z$O
M xT J½ O
|;<?@GI?@G+.;A#+;<?@;>%89`XZ%59<(+. MQ(NOV( ^w6;A#:%59<9AP5C)4b0U25E* ]Q„/xd M ¼:d Z O]|].!G:%qXN.
? M T J½ O M T ½ O
M T J½ O
M ¼+d ¼5N¼ O
½ ? %M xT ½ O
j
25e39>G+JE.._ŒOJu‡‰(+B@?@?U%825B@?@(R*W;>BT%84b%8PS(E?@;>?U?U=-25G+*W?U.1G+;A%Z0t0U?U.D%N;AB@=OB@G+B@?@(+25G+9>*MJ)0U.Dkr7E†:B@?UG+#:;<2N2NJE#:9A;AJM#+B6[i†^%5,^#:%82NJE9A(E[5.12N03?a0@?U%5;<G+?@BUG+.3B@(+*WJE*M;ABSBF.D?@25BQ0U#:;A%-,+9<P (E,+?@;A|K;A*l2525#-2E0UJ+Y 28%54+|K9/?UG+J+.19A.];A9oBF[N?@|0U0U;<%qG+,:Pc.1(Ekr#f?@?@;A2N25?U#+G+#h.o.W25XZ;<4`%8*W[59A(+%50H.D%q[5BaPc.DB‚k­2Z?UX525?U.12i#+0a.?@,^G+XZ.M%8.K?U9A;A(+G+*M._0@B1._%5d\BF[5G+.N"‹k4 d
?@G:.l;A*W%8[N.M%57+7+0U2qmE;<*W%Z?U.19API†+?UBS?UG+;AB=125#:BF?@0H%8;A#c?DC`;<?|;<9A9ˆJE2i%I[52)2EJWyT2N,`d'"‹4K?@G:.l;A*W%8[N.';>B!#+28?u%8?
3 M bZ NO
,XH 1
½,(N¼
NR
%NOK250U;<[N;<#^%89V;<*W%5[5.
,aOK7+;<mE.19>B3,^.D9<2Z| ¼
=,OK7+;<mE.19>B%8,/2ZX5. ¼
A;wt#I;<[N|(+G:0U.S;ƒ?U.J¼:O]d Z4b25&o(:#:Œ JI[5,c0HPh%qPN?@krG+?@2N.'#+‡‰.‰?H;ABF*W(i%8%8[N(+.S?@%525#:*WJh%8?@?U;>G+=‰.!?U7+G+;<0Um).D.DB@9AG+B325,/9>JE.1;A9A#+2Z[M|¤25%57/#:.1JI0H%Z%8?@,/2N2Z0DX5d .O?UG+.!?@G:0@._BFG+2N9AJR284 ¼ M B@G+2Z|#
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input
feature
vector
x
x
x
x
distance or
probability
computations
f1 (x,K)
1
2
f2 (x,K)
output
classification
compare
&
decide
C(x)
d
fm(x,K)
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ROC
100
correct
detections
50
0
0
50
false alarms
100
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Artificial Neuron ( AN )
x[1]
w[1]
inputs to
other
neurons
x[2] w[2]
inputs
on
dendrites
x[d]
cell
output y
body
on axon
w[d]
via their
dendrites
d
y= g(
Σ
w[j]x[j] )
j=1
g (x)
t
+1
t
x
t
x
0
g ( x ) = 1 if x > t and 0 otherwise
t
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magenta
Blue
(0, 0, 0)
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QUERY
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45 data
45 data
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