Computing Visual Correspondence with Occlusions via Graph Cuts

will use the following formula for correspondence between binary vectors and
configurations:
∀a ∈A 0
∀a ∈A α
f(a) = 1− x(a)
f(a) = x(a)
∀a /∈ Ã f(a) = 0
Let us denote a configuration defined by a vector x as f x .Thus,wehavethe
energy of binary variables:
where
˜E(x) = ˜ Edata(x)+ ˜ Eocc(x)+ ˜ Esmooth(x)+ ˜ Eunique(x)
˜Edata(x) =Edata(f x ),
˜Eocc(x) =Eocc(f x ),
˜Esmooth(x) =Esmooth(f x ),
˜Eunique(x) =Eunique(f x ).
(Eunique(f) encodes the uniqueness constraint: it is zero if f is unique, and
infinity otherwise). Let’s consider each term separately, and show that each
satisfies condition (6).
1. Data term.
˜Edata(x) =
a∈A(f x )
D(a) =
f x (a) · D(a)
AsingletermE a (x) = f x (a) · D(a) depends only on one variable x(a).
Therefore, condition (6) is not violated.
16
a∈ Ã
(7)