Graph-based methods have become well-established tools for image segmentation. Viewing the image as a weighted graph, these methods seek to extract a graph cut that best matches the image content. Many of these methods are interactive, in that they allow a human operator to guide the segmentation process by specifying a set of hard constraints that the cut must satisfy. Typically, these constra...

The support of a set A is the crisp subset of A with nonzero membership grades. Similarly, the core of a set A is the crisp subset of A with membership grade equal to one. So, supp(A) = {x|μA(x) > 0} and core(A) = {x|μA(x) = 1}. (1.1.4) The α-cut Aα of a set A is the crisp subset of A with membership grades of at least α. So, Aα = α-cut(A) = {x|μA(x) ≥ α}. (1.1.5) Note that core(A) = 1-cut(A). ...

Contents 1. Introduction. 2. Heirs. 3. The invariance group of a cut. 4. Review of T-convex valuation rings. 5. The invariance valuation ring of a cut. 6. A method for producing cuts with prescribed signature. 7. Existentially closed extensions. 1. Introduction. Let M be a totally ordered set. A (Dedekind) cut p of M is a couple (p L , p R) of subsets p L , p R of M such that p L ∪ p R = M and ...

The aim of this paper is robust identification of smart foam, as an electroacoustic transducer, considering unmodeled dynamics due to nonlinearities in behaviour at low frequencies and measurement noise at high frequencies as existent uncertainties. Set membership estimation combined with model error modelling technique is used where the approach is based on worst case scenario with unknown but...

In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm...

The simple max-cut problem is as follows: given a graph, find a partition of its vertex set into two disjoint sets, such that the number of edges having one endpoint in each set is as large as possible. A split graph is a graph whose vertex set admits a partition into a stable set and a clique. The simple max-cut decision problem is known to be NP-complete for split graphs. An indifference grap...

We investigate various notions of sobriety for topological spaces that are equivalent in ZF set theory with the Axiom of Choice but may differ in the absence of choice principles. The Ultrafilter Principle UP (alias Prime Ideal Theorem) suffices for the desired conclusions. We derive from UP three topological postulates and prove their equivalence in ZF without choice: the Well-Filtration Princ...

We show how to associate an R-tree to the set of cut points of a continuum. If X is a continuum without cut points we show how to associate an R-tree to the set of cut pairs of X . AMS Classification 54F15,54F05,20F65,20E08

Figure 2.1: Embedding the (black) data points in an appropriate higher-dimensional space using makes them " look " like a linear subspace. The distance D(x) of a point x to the data is then its (weighted) distance to Figure 2.3: Reconstructing the " hand " curve from a 2D data set of 162 points: (a) The input point set. (b) The color-coded MaD where blue and red colors indicate lower and higher...