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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA
Justin Solomon* Andy Nguyen* Adrian Butscher Mirela Ben-Chen Leonidas Guibas
Stanford University
M1 M2
Á :M1 !M2
M1 M2
M1 M2
Á :M1 !M2
Global Ambiguity
Local Ambiguity
M1 M2
Represent maps probabilistically
Represent maps probabilistically
M1
M2
Likelihood of a matched pair
M1 M2
P12 2 Prob(M1 £M2)
Likelihood of a matched pair
p1
p0
p01
p1
S1
S1
(p0; p0)
(p1; p01)
(p1; p1)
M1
M2U
V
P12(U £V ) 2 [0;1]
Likelihood of a matched pair
M1
M2U
Conditional probability distribution
PU2(B) 2 [0;1]
M1
M2
V
P1V (A) 2 [0;1]
Conditional probability distribution
M1 = U1 [ ¢ ¢ ¢ [UN1M2 = V1 [ ¢ ¢ ¢ [VN2
Voronoi cells
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Descriptor matching
Continuity
Sharpness
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Descriptor matching http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6130444
EÁ(A) =X
ij
aijÁij
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Continuity
Earth Mover’s Distance
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Sharpness
Es(A) =X
ij
a2ij = kAk2Fro
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Descriptor matching
Continuity
Sharpness
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Descriptor matching
Continuity
Sharpness
Linear program!
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Sharp transition
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)
Sharp transition
Want this point
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)min
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)min
=
such that
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)min
=
such that
Primal
Emap(A) =EÁ(A) +¸Econt(A) +¯Es(A)min
=
such that
EÁ(A¤)
Primal
Emap(A)=EÁ(A)+¸Econt(A)+¯Es(A)
min
=
suchthat
EÁ(A¤)
Dual
Dual
=
max
such that
EÁ(A¤)
¸
Dual
=
max
such that
EÁ(A¤)
¸¸
Dual
=
min
such that
EÁ(A¤)
¸¸
¸
New primal
=
min
suchthat
EÁ(A¤)
¸
¸
¸
New primal
=
min
suchthat
EÁ(A¤)
¸
¸
¸
Continuous soft maps
Basis for probability measures
Basis for probability measures
Validation improves
Sharpness decreases
Computing denser maps
Applications to graphics and other fields
Map collections and composition
TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAA TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAA
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