g, for each pixel x in the image domain Ω ⊆ R d , a label ℓ(x) ∈ {1, . . . , l} which assigns one of l class labels to x so that the labeling function ℓ a for each pixel x in the image domain Ω ⊆ R
dheres to some data fidelity as well as spatial coherency constraints.
http://projecteuclid.org/download/pdf_1/euclid.jdg/1214429996
Introduction to Optimization and Semidifferential Calculus
https://books.google.com/books?isbn=1611972140
Michel C. Delfour - 2012 - Mathematics
The set of all minimizing points of f in U is denoted argmin f(U)* 'a e U : f(a) = inf f(Fundamentals of Functional Analysis - Page 45 - Google Books Result
https://books.google.com/books?isbn=9401587558
Semën Samsonovich Kutateladze - 2013 - Mathematics
Here, as usual, lim inf f(y):= lim f(y):= sup inf f(U) y-r y-r Uer(x) is the lower limit of f at x (with respect to T(z)). < =>: If x 2 dom f then (x, t) # epi f for all t e R. Hence, ...Transactions of the Ninth Prague Conference: On ...
https://books.google.com/books?isbn=9027715009
J. Kozesnik - 1983 - Technology & Engineering
л xeA x If u is a continuity point of Рд, then F (u) = inf F (u) . xeA x Proof. Let A C (Convex Analysis - Page 299 - Google Books Result
https://books.google.com/books?isbn=1400873177
Ralph Tyrell Rockafellar - 2015 - Mathematics
... + co, we have dom (inf F) = dom F. By definition, u" is a Kuhn–Tucker vector for (P) if and only if inf F is finite at 0 and (inf F)(u) > (inf F)(0) + (—u", u), Vu.
RIEMANNIAN STRUCTURES OF PRESCRIBED GAUSSIAN
CURVATURE FOR COMPACT 2-MANIFOLDS
MELVYN S. BERGER
Let (M,g) denote a smooth (say C3
) compact two-dimensional manifold,
equipped with some Riemannian metric g. Then, as is well-known, M admits
a metric gc
of constant Gaussian curvature c in fact the metrics g and gc
can
be chosen to be conformally equivalent. Here, we determine sufficient conditions
for a given non-simply connected manifold M to admit a Riemannian structure
g (conformally equivalent to g) with arbitrarily prescribed (Holder continuous)
Gaussian curvature K(x). If the Euler-Poincare characteristic χ(M) of M is
negative, the sufficient condition we obtain is that K(x) < 0 over M. Note
that this condition is independent of g, and this result is obtained by solving
an isoperimetric variational problem for g. If K(x) is of variable sign for
χ(M) < 0, or if χ(M) > 0, then the desired critical point may not be an
absolute minimum and our methods do not succeed. If χ(M) = 0, our methods
apply when K(x) satisfies an integral condition with respect to the given metric
g (see § 3) this result is perhaps not unreasonable since, for χ(M) < 0,
distinct Riemannian structures on M need not be conformally equivalent.
1. Preliminaries
By passing (if necessary) to the orientable two-sheeted covering space of M,
we may suppose M is orientable and admits a Riemannian structure with
metric tensor g, Gaussian curvature k(x), and volume element dV. If K(x) is
a given (Holder continuous) function defined on M, we shall attempt to
determine a metric tensor g, conformal with g, whose Gaussian curvature
k(x) = K(x) at each point of M, i.e., we shall seek a smooth function a defined
on M such that g = e
2σg and k(x) = K(x). To find the equation which will
determine σ in terms of the given data K(x), k(x) and g, we recall that in
terms of isothermal parameters (u, v) on M an element of arc length can be
written ds2
= γ{du2
+ dv2
}, and the Gaussian curvature can be written
(1) k= -irψogγ)uu
+ (log r
),,}
Setting γ' = γ exp 2σ, in place of γ in (1), we obtain the desired equation
Communicated by I. M. Singer, May 2, 1970 and, in revised form, August 11, 1970.
[PDF]Convex Optimization for Multi-Class Image Labeling with a ...
ipa.iwr.uni-heidelberg.de/ipabib/Papers/Lellmann-et-al-09b.pdf
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that the labeling function ℓ adheres to some data fidelity as well as spatial coherency ... In terms of Markov Random Fields, the data and regularization terms can ...
You visited this page on 3/27/16.
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hci.iwr.uni-heidelberg.de/.../lellmann08multiclasst...
Heidelberg University
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École Polytechnique Fédérale de Lausanne
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