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We prove that the topographic map structure of upper semicontinuous functions, defined in terms of classical connected components of its level sets, and of functions of bounded variation (or a generalization, the WBV functions), defined in terms of M-connected components of its level sets, coincides when the function is a continuous function in WBV. Both function spaces are frequently used as models for images. Thus, if the domain Ω' of the image is Jordan domain, a rectangle, for instance, and...
Let X and Y be two compact spaces endowed with
respective measures μ and ν satisfying the condition µ(X) = v(Y). Let c be a continuous function on the product space X x Y. The mass transfer problem consists in determining a measure ξ on
X x Y whose marginals coincide with μ and ν, and such that
the total cost ∫ ∫ c(x,y)dξ(x,y) be minimized. We first
show that if the cost function c is decomposable, i.e., can be
represented as the sum of two continuous functions defined on X and
Y, respectively,...
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