Approximating rank-width and clique-width quickly Abstract. Rank-width was defined by Oum and Seymour [2006] to investigate clique-width. They constructed an algorithm that either outputs a rank-decomposition of width at most f (k) for some function f or confirms that rank-width is larger than k in time O(|V | 9 log |V |) for an input graph G = (V, E) and a fixed k. We develop three separate algorithms of this kind with faster running time. We construct an O(|V | 4 )-time algorithm with f (k) = 3k + 1 by constructing a subroutine for the previous algorithm; we avoid generic algorithms minimizing submodular functions used by Oum and Seymour. Another one is an O(|V | 3 )-time algorithm with f (k) = 24k, achieved by giving a reduction from graphs to binary matroids; then we use an approximation algorithm for matroid branch-width by Hliněný [2005]. Finally we construct an O(|V | 3 )-time algorithm with f (k) = 3k − 1 by combining the ideas of the two previously cited papers. Graph complexity measures such as tree-width and branch-width are important for algorithmic purposes and for understanding the structure of families of graphs. One An earlier article on the first two algorithms appeared in Proceedings of the 31st International Workshop on Graph-Theoretic Concepts in Computer Science, 2005, Lecture Notes in Computer Science, vol. 3787, Springer, pp. 49-58, and is also contained in the author's Ph.D. thesis: "Graphs of Bounded Rank-width," Princeton University, 2005. This research was partially supported by NSF grant 0354742 while the author was at Georgia Institute of Technology as was also partially supported by the SRC Program of Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MOST) (No. R11-2007-035-01002-0). Author's address: S.-I. Oum, Department of Mathematical Sciences, KAIST, Daejeon, Republic of Korea, e-mail: sangil@kaist.edu. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. Instead, Oum and Seymour [2006] found an "approximation" algorithm that either outputs a (2 3k+2 − 1)-expression or confirms that the clique-width of G is larger than k. This can be combined with algorithms requiring a k-expression and therefore these algorithms no longer have to require a k-expression as an input to be polynomial-time algorithms. To obtain this approximation algorithm, they defined another graph-width parameter called the rank-width, and showed that rank-width is at most clique-width and clique-width is at most 2 1+rank-width −1. In addition, they showed a polynomial-time algorithm to find a rank-decomposition of width 3k + 1 or to confirm that the rank-width is larger than k. (Rank-width is defined as the minimum possible width of all rank-decompositions. We will discuss its definition in the next section.)In this article we improve their results; we present three separate algorithms with faster running time that, for fixed k, output a rank-decomposition of width at most f (k) for some function f or confirm that the rank-width is larger than k. We summarize them in Table I .The following is one of the consequences. Courcelle and Oum [2007] showed that, for each k, there is a formula of modulo-2 counting monadic second-order logic (C 2 MS logic) expressing that the rank-width is at most k. C 2 MS logic is an extension of first-order logic, which allows set variables denoting sets of objects (in our case, sets of vertices) and the set predicate Approximating Rank-Width and Clique-WidthEven(X ) expressing that the set denoted by the set variable X is finite and has even cardinality. In fact, every graph problem expressible in C 2 MS logic can also be solved in linear time if an input graph is given with a k-expression [Courcelle 1997] (or see Courcelle and Oum [2007] We remark that if k is not fixed and is given with an input, then testing whether the clique-width is at most k is NP-complete, shown by Fellows et al. [2006]. It is also NP-complete to test whether the rank-width is at most k if k is given with an input. This can be deduced from the NP-hardness of finding branch-width of graphs [Seymour and Thomas 1994] by relating the rank-width of bipartite graphs and the branch-width of binary matroids [Oum 2005b ] and using the theorem [Hicks and McMurray 2007; Mazoit and Thomassé 2005] stating that the branch-width of the cycle matroid of a graph with at least one cycle is equal to the branch-width of the graph.In this article, all graphs are simple, undirected, and finite.For a graph G and two disjoint subsets X, Y ⊆ V (G), we define, where rk is the matrix rank function; and we define the cut-rank A subcubic tree is a tree with at least two vertices such that every vertex is incident with at most three edges. A leaf of a tree is a vertex incident with exactly one edge. A rank-decomposition of a graph G = (V, E) is a pair (T, L) of a subcubic tree T and a bijective function L : V → {t : t is a leaf of T }. (If |V | ≤ 1, then G admits no rank-decomposition.)For an edge e of T , the connected components of T \e induce a partition (X, Y ) of the set of leaves of T . The width of an edge e of a rank-decomposition We need the following definitions and operations on k-graphs.(1) For i ∈ {1, . . . , k}, let · i denote a k-graph with a single vertex labeled by i.(2) For distinct i, j ∈ {1, 2, . . . , k}, we define a unary operator η i, j such thatThis adds edges between vertices labeled by i and vertices labeled by j. (3) We let ρ i→ j be the unary operator such that ρ i→ j (G, lab) = (G, lab ), where lab(v) otherwise. This mapping relabels every vertex labeled by i into j. (4) Finally, ⊕ is a binary operation that makes the disjoint union. Note that G ⊕G = G.The k-graph produced by performing these operations in order, therefore, has vertex set the set of occurrences of the constant symbols in t; and this k-graph (and any k-graph isomorphic to it) is called the value val(t) of t. If a k-expression t has value (G, lab), we say that t is a k-expression of G. The clique-width of a graph G, denoted by cw(G), is the minimum k such that there is a k-expression of G. For instance, K 4 (the complete graph with four vertices) can be constructed byTherefore, K 4 has a 2-expression, and cw(K 4 ) ≤ 2. It is easy to see that cw(K 4 ) > 1, and therefore cw(K 4 ) = 2. We remark that an n-vertex graph of clique-width at most k can have arbitrary long k-expressions, but such long k-expressions can be shortened to k-expressions of length O(n) by removing useless operations. Oum and Seymour [2006] showed that having small clique-width is equivalent to having small rank-width, as follows.PROPOSITION 2.2 [OUM AND SEYMOUR 2006]. For every graph G,k+1 − 1)-expression of the input graph G.Definition 2.3. Let G = (V, E) be a graph and v ∈ V . The graph obtained by applying local complementation at v to G is Approximating Rank-Width and Clique-WidthThe graph obtained by pivoting an edge uv is defined by G ∧ uv = G * u * v * u. We say that H is locally equivalent to G if H can be obtained by applying a sequence of local complementations to G.A pivoting is well defined because G * u * v * u = G * v * u * v if u and v are adjacent [Oum 2005b ]. Both local complementation and pivoting have appeared in several papers, notably in Bouchet's [1994, 1990, 1989, 1988].It is easy to show the following proposition.The following lemma will be used in Section 3.We show that, for fixed k, there is an O(n 4 )-time algorithm that, with a n-vertex graph, outputs a rank-decomposition of width at most 3k + 1 or confirms that the input graph has rank-width larger than k. Oum and Seymour [2006] used generic algorithms minimizing submodular functions [Iwata et al. 2001 ] to find a set Z minimizing the cut-rank functionIf this can be done in time γ then we obtain an O(n(n 2 + γ ))-time algorithm to output a rank-decomposition of width at most 3k + 1 or confirm that the input graph has rank-width larger than k. In Oum and Seymour [2006], γ is O(n 8 log n), and therefore the O(n 9 log n)-time algorithm is obtained.To obtain an O(n 4 )-time algorithm, we construct a direct combinatorial algorithm that minimizes the cut-rank function. We first define blocking sequences, introduced by Geelen [1995]. Let G be a graph and A, B be two disjoint subsets ofThe following proposition appears frequently in applications of blocking sequences. Since there is no blocking sequence for (A, B) in G, there is no directed path from A• to B • in D. Let J be the set of ends of directed paths in D from A • with at least one edge. We claim that ρ G (A ∪ J ) = k.To prove this, we would like to show that ρ *We proceed by induction on |X | + |Y |. If |X | ≤ 1 and |Y | ≤ 1, then we haveThe proof of Proposition 3.1 is algorithmic. We summarize the algorithm as follows.Input. A graph G = (V, E) and two disjoint subsets A and B of V . Output. One of the following: PROOF. Let k = ρ * G (A, B) .We prove one short lemma to be used.and the lemma is proved. Now let us prove the proposition by using the lemma.(Let us first check the axiom (i) of blocking sequences. By applying Lemma 2.5 forTo check (ii), we apply the same inequality and obtain that Proposition 3.3 is now used to find a cut with minimum cut-rank while separating A and B, as follows. PROPOSITION 3.5. Algorithm 3.4 is correct and its running time is O(|VIf there is a blocking sequence with m vertices in G i,0 , then we apply m pivotings. By Proposition 3.3, we reduce the length of the blocking sequence by each pivoting, and after all m pivotings, we have Since m ≤ |V |, we need apply at most |V | pivotings to get G i+1,0 from G i,0 in (M2) and this can be done in time O(|V | 4 ). Notice that we also need time to find w in B and |B| ≤ |V |.Since Approximating Rank-Width and Clique-WidthProposition 3.5 is enough to be used for our purposes, but if we limit the size of |A| and |B|, then we can achieve a better running time as follows. PROOF. We assume that the graph G is stored in the adjacency matrix by preprocessing the adjacency list in time O(|V | 2 ). Since the rank of (l + 1) × (l + 1) or (l + 1) × l matrices can be evaluated in time In order to get G i+1,0 from G i,0 , we need at most |V | pivotings because m ≤ |V |. Therefore it can be done in time O(|V | 3 ); notice that since |B| ≤ l, it takes a constant time to find w. As we discussed in the beginning of this section, we obtain the following theorem. THEOREM 3.7. For fixed k, there is an algorithm, for the input graph G = (V, E), that either concludes that rw(G) > k or outputs a rank-decomposition of G of width at most 3k + 1; and its running time is O(|VIn the second algorithm, we will transform our problem into a matroid problem and then use Hliněný's algorithm [2005] on matroid branch-width. It turns out that the rank-width of bipartite graphs is essentially equivalent to the branch-width of binary matroids [Oum 2005b ]. We will discuss this after showing that we can transform our problem into a problem on bipartite graphs. a graph transformation B from graphs to bipartite graphs, described as follows. For a graph G = (V, E) , B(G) is defined as a bipartite graph on the vertex set V × {1, 2, 3, 4} such that:A theorem by combined with Proposition 2.2 implies that there exist two functions f 1 and f 2 such that f 1 (rw(G)) ≤ rw(B(G)) ≤ f 2 (rw(G)), but it does not give explicit constructions of f 1 and f 2 . We will prove this inequality when f 1 (k) = k/4 and f 2 (k) = max(2k, 1). This result will be used in the next section.PROPOSITION 4.1. For every graph G, we have rw(B(G)) ≤ max(2 rw(G), 1).PROOF. If the rank-width of G is zero, then G has no edges at all and it is easy to see that the rank-width of B(G) is 1. Now we assume that the rank-width of G is nonzero. We claim that rw(B(G)) ≤ 2 rw(G). Let k be the rank-width of G. Then there is a rank-decomposition (T, L) of G of width k. Let N be the set of leaves of T .We aim to construct a rank-decomposition (T , L ) of B(G) so that its width is at most 2k. Let T be a tree such that V (T ) = (V (T )×{0})∪(N ×{1, 2, 3, 4, 12, 34}) and let the following hold.(ii) for all v ∈ N , (v, 12) is adjacent to both (v, 1) and (v, 2) in T ; (iii) for all v ∈ N , (v, 34) is adjacent to both (v, 3) and (v, 4) in T ; and (iv) for all v ∈ N , (v, 0) is adjacent to both (v, 12) and (v, 34) Informally speaking, we obtain T from T by replacing each leaf with a rooted binary tree having four leaves. For each vertex (v, i) We claim that the width of (T , L ) is at most 2k. For each edge e = vw ∈ E(T ), let (X, Y ) be a partition of N induced by the connected components of T \e. Then, the edge (v, 0)(w, 0) ofIt is straightforward to see thatWe now consider the remaining edges of T . Each of them induces a partition (X, Y ) of leaves of T such that |X | ≤ 2 or |Y | ≤ 2. So, ρ B(G) (L −1 (X )) ≤ 2. Therefore we obtain that the width of (T , L ) is at most 2k. In particular this implies that rw(G) ≤ 4 rw(B(G)).PROOF. Let e be an edge of T . Since T is a subtree of T , e is also an edge of T . Let (X, Y ) be a partition of leaves of T induced by connected components of T \e.For subsets A 1 , A 2 , A 3 , A 4 of V , we denote the set (We now claim that for each i ∈ {1, 2, 3},To see this, we look at the matrix defining the cut-rank functions.By symmetry, we also obtain that ρ *. By adding these inequalities for i ∈ {1, 2, 3}, we obtain that |A 1 A 4 | ≤ 3k.Let M be the adjacency matrix of G. We observe that rk(M[A 4 ,Then we have the following bound of ρ G (A 1 ).Therefore the width of (T, L) is at most 4k. For general matroid theory, we refer to Oxley's book [1992]. We call M = (E, I) a matroid if E is a finite set and I is a collection of subsets of E, satisfying the following.(i) ∅ ∈ I.(ii) If A ∈ I and B ⊆ A then B ∈ I. (iii) For every Z ⊆ E, the maximal subsets of Z in I have the same size r (Z ). We call r (Z ) the rank of Z .An element of I is called independent in M. We let E(M) = E. A matroid M = (E, I) is binary if there exists a matrix N over GF (2) such that E is a set of column vectors of N and I = {X ⊆ E : X is linearly independent}. The A branch-decomposition of a matroid M is a pair (T, L) of a subcubic tree T and a bijective function L :For an edge e of T , the connected components of T \e induce a partition (X, Y ) of the set of leaves of T . The width of an edge e of a branch-decompositionThe width of (T, L) is the maximum width of all edges of T . The branch-width bw(M) of M is the minimum of the width of all branchdecompositions of M. (If |E(M)| ≤ 1, we define bw(M) = 1.) Branch-width has been defined by Robertson and Seymour [1991] .The following proposition links branch-width of binary matroids with rank-width of bipartite graphs. (G, A, B) . Then the branch-width of M is one more than the rank-width of G.We will now show another algorithm that approximates rank-width as in Section 3, but in time O(n 3 ) with a worse approximation ratio. We take a different approach based on Propositions 4.1 and 4.2. We use the following algorithm for binary matroids developed by Hliněný [2005]. PROOF. Let G = (V, E) be the input graph. We may assume that E(G) = ∅. If it confirms that the branch-width of M is larger than 2k +1, then the rank-width of B(G) is larger than 2k, and therefore the rank-width of G is larger than k.If it outputs a branch-decomposition of M of width at most 6k +1, then the output is a rank-decomposition of B(G) of width at most 6k. This can be transformed into a rank-decomposition of G of width at most 24k in linear time by Proposition 4.2.In this section we aim to combine the idea of Oum and Seymour [2006] with that of Hliněný [2005]. The main bottleneck of the algorithm by Oum and Seymour was the subroutine minimizing the cut-rank functions. In the first algorithm, we improve the running time by constructing such an algorithm faster than generic algorithms minimizing submodular functions. Here we use monadic second-order logic to achieve a better running time. Given a monadic second-order formula with free variables representing sets of vertices, in order to produce a satisfying assignment to the free variables, we need a k-expression of the input graph. We will construct a k-expression from subgraphs iteratively. Hliněný [2005] used a similar idea on matroids of bounded branch-width and formulas of an appropriate version of monadic second-order logic. Since we are able to find such assignments in linear time in this case, we can use a lemma that is refined from the paper by Oum and Seymour [2006] to reduce 3k + 1 to 3k − 1 in the approximation algorithm.5.1. MONADIC SECOND-ORDER LOGIC. We consider a graph G without parallel edges as a relational structure V (G), edg , where edg(x, y) is true if and only if two vertices x and y are adjacent in G. Monadic second-order logic is the extension of first-order logic allowing variables denoting subsets of the domains of the considered relational structure. On graphs, the domain is the set of vertices. Thus, monadic second-order formulas on graphs are logic formulas which can use ∃, ∀, ∨, ∧, ¬, ∈, true, and edg with first-order variables, each representing a vertex and set variables, each representing a set of vertices. This logic is often called monadic second-order logic of the first kind (MS 1 logic), to distinguish from that of the second kind (MS 2 logic). Monadic second-order logic of the second kind is more general; it allows set variables, each representing a set of edges or a set of vertices. 5.2. REFINING THE GREEDY ALGORITHM FOR RANK-WIDTH. There is a notion called a tangle that is strongly related to branch-width and rank-width. Here we define it for rank-width. For a graph G = (V, E) , a ρ G -tangle of order k + 1 is a set T of subsets of V satisfying the following three axioms.(T1) If ρ G (X ) ≤ k then either X ∈ T or V \X ∈ T . (T2) For all X 1 , X 2 , X 3 ∈ T , we have X 1 ∪ X 2 ∪ X 3 = V . (T3) V \{v} / ∈ T for all v ∈ V .Robertson and Seymour [1991] showed that the minimum order of a ρ G -tangle is equal to the rank-width. Their theorem (3.1) in Robertson and Seymour [1991] is for arbitrary symmetric submodular functions and in this article we state its corollary for rank-width. We will now show (T2). Suppose that X 1 , X 2 , X 3 ∈ T such that X 1 ∪ X 2 ∪ X 3 = V . Thus we know that for each i = 1, 2, 3, we have either (A, B) = 3k − 1, we may assume that X 1 , X 2 ⊆ A. Since X 1 ∪ X 2 ∪ X 3 = V , we deduce that X 3 ⊆ A and therefore ρ * G (X 3 ∩ A, B) ≤ k − 1. Since V \X 3 ⊆ A, we have ρ * G (A\X 3 , B) ≤ ρ G (V \X 3 ) ≤ k and therefore ρ(A) = 3k − 1 ≤ ρ * G (A\X 3 , B) + ρ * G (X 3 ∩ A, B) ≤ 2k − 1, a contradiction. We just showed that T satisfies (T2). We conclude that T is a ρ G -tangle of order k + 1, contradictory to Theorem 5.1.An important consequence of Lemma 5.2 is the following lemma, which will allow us to use a greedy algorithm to find a rank-decomposition. Therefore we may assume that ρ G (B) = 3k − 1. By Lemma 5.2, there exists a partition (S, T ) of V such that ρ G (S) ≤ k, ρ * Graph complexity measures such as tree-width and branch-width are important for algorithmic purposes and for understanding the structure of families of graphs. One 10:2 S.-I. OUM of them is the clique-width, defined by Courcelle and Olariu [2000] . We discuss its definition in the next section. Many NP-hard graph problems are solvable in polynomial time if a tree-like decomposition corresponding to clique-width, called a k-expression, is given as an input in addition to the adjacency list of the input graph. (In fact, the clique-width is the minimum k so that there is a k-expression of G.) In general, every graph problem expressible in monadic second-order logic with quantifications over vertices and vertex sets (MS 1 -logic) can be solved in linear time if the input graph is given with a k-expression . However, problems such as deciding whether the graph is Hamiltonian [Wanke 1994 ] and finding the chromatic number [Kobler and Rotics 2003] are not expressible in monadic second-order logic, but have nevertheless polynomial-time algorithms on graphs of bounded clique-width if the input graph is given with a k-expression. Therefore we hope to have, for each fixed k, a polynomial-time algorithm to find a k-expression of an input graph if the input graph has clique-width at most k. This problem is still open when k > 3. Corneil et al. [2000] solved this problem when k = 3.. Instead, Oum and Seymour [2006] found an "approximation" algorithm that either outputs a (2 3k+2 − 1)-expression or confirms that the clique-width of G is larger than k. This can be combined with algorithms requiring a k-expression and therefore these algorithms no longer have to require a k-expression as an input to be polynomial-time algorithms. To obtain this approximation algorithm, they defined another graph-width parameter called the rank-width, and showed that rank-width is at most clique-width and clique-width is at most 2 1+rank-width −1. In addition, they showed a polynomial-time algorithm to find a rank-decomposition of width 3k + 1 or to confirm that the rank-width is larger than k. (Rank-width is defined as the minimum possible width of all rank-decompositions. We will discuss its definition in the next section.). In this article we improve their results; we present three separate algorithms with faster running time that, for fixed k, output a rank-decomposition of width at most f (k) for some function f or confirm that the rank-width is larger than k. We summarize them in Table I .. The following is one of the consequences.

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O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Automatic role recognition based on conversational and prosodic behaviour This paper proposes an approach for the automatic recognition of roles in settings like news and talk-shows, where roles correspond to specific functions like Anchorman, Guest or Interview Participant. The approach is based on purely nonverbal vocal behavioral cues, including who talks when and how much (turn-taking behavior), and statistical properties of pitch, formants, energy and speaking rate (prosodic behavior). The experiments have been performed over a corpus of around 50 hours of broadcast material and the accuracy, percentage of time correctly labeled in terms of role, is up to 89%. Both turn-taking and prosodic behavior lead to satisfactory results. Furthermore, on one database, their combination leads to a statistically significant improvement. One of the most common phenomena psychologists observe in social interactions is that people play roles, i.e. they display predictable behavioral patterns perceived by others as addressing needs or fulfilling functions in a given interaction setting [10] . Thus, it is not surprising that the computing community has paid significant attention to the automatic recognition of roles, in particular with approaches based on analysis and understanding of nonverbal behavior [14] . This paper proposes an approach for the recognition of roles in formal settings (news and talk-shows) based on turntaking and prosodic behavior. Turn-taking accounts for who talks when and how much and provides a description of how each person participates in a conversation. Prosodic behavior accounts for the way people talk, i.e. their pitch, loudness and speaking rate. The approach includes three main steps (see Figure 1 ). The first is the segmentation of the data into turns, time intervals during which only one person is talking. The second is the extraction of turn-taking and prosodic features from each turn. The third is the mapping of the feature vectors extracted from each turn into a sequence of roles with Conditional Random Fields.. The main novelty of this work with respect to the stateof-the-art is that, to the best of our knowledge, this is the first attempt where prosodic features are applied to role recognition. The performances achieved seem to confirm that people playing different roles display different prosodic behaviors, that is they exhibit specific ways of speaking. Furthermore, this is the first work, to the best of our knowledge, where prosodic and turn-taking behavior are combined to provide a full description of nonverbal vocal behavior in conversations. With respect to previous work of the authors in the same domain [12] , the main novelty is not only the use of prosodic behavior, but also that the role assignment is performed for each turn rather than for each person. This is a major improvement because it ensures that the same person can play different roles in the same interaction and that role assignment can be performed even if only part of the interaction is actually available.. The results show that both prosodic and turn-taking behavior, when used individually, achieve satisfactory performances (up to 89% accuracy). Moreover, the combination of the two leads to a statistically significant improvement with respect to the best individual performance on one of the databases.. Role recognition is interesting not only from a social interaction analysis point of view [14] , but also in an application perspective. Roles can enrich the description of multiparty recordings for indexing and retrieval purposes, can be used in summarization systems to detect interventions more likely to contain important information, or can support browsing systems by allowing a user to quickly identify turns associated to a role of interest.. The rest of the paper is organized as follows: Section 2 proposes a survey of related works, Section 3 describes the proposed approach, Section 4 describes experiments and results, and Section 5 draws some conclusions. This paper has proposed an approach for automatic role recognition based on turn-taking and prosodic behavior. To the best of our knowledge, this is the first work showing that roles, at least in the settings considered, are associated to specific ways of speaking corresponding to different regions of the prosodic features space. Furthermore, the experiments show that, in some cases, the combination of turn-taking and prosodic features improves to a statistically significant extent the performance. The recognition step is performed with linear chain CRFs where the feature functions allow one to capture relationships between roles and observation values or between roles following one another in the turn sequences.. The main source of error in the automatic case is the speaker clustering. The delay between the actual and detected speaker changes results into an accuracy loss of more than 10% that can be eliminated only by obtaining a better speaker segmentation. This means that further progress on role modeling can be obtained only working on other, possibly more spontaneous data, and roles that are less constrained than those considered in this work and possibly relevant to more general human-human interaction scenarii, like, e.g., those described in general theories of social interaction [10] . This might help to identify better directions for the improvement of the models such as the use of kernels exploiting the correlations between features. Two main approaches have been used for the recognition of roles, the analysis of turn-taking, and the modeling of lexical choices. In a few cases, the two approaches have been combined and some works propose movement based features (fidgeting) as well, resulting into multimodal approaches based on both audio and video analysis. Turn-taking has been used in [12, 13] , where temporal proximity of speakers is used to build social networks and extract features fed to Bayesian classifiers based on discrete distributions. Temporal proximity, and duration of interventions, are used in [3, 6, 7, 11] as well, where they are combined with the distribution of words in speech transcriptions. Role recognition is based on BoosTexter (a text categorization approach) in [3] , on the combination of Bayesian classifiers (working on turntaking) and Support Vector Machines (working on term distributions) in [7] , and on probabilistic sequential approaches (Hidden Markov Models and Maximum Entropy Classifiers) in [6, 11] . An approach based on C4.5 decision trees and empirical features (number of speaker changes, number of speakers talking in a given time interval, number of overlapping speech intervals, etc.) is proposed in [2] . A similar approach is proposed in [9] , where the features are the probability of starting speaking when everybody is silent or when someone else is speaking, and role recognition is performed with a Bayesian classifier based on Gaussian distributions. The only multimodal approaches are proposed in [5, 15] , where features accounting for speaking activity and fidgeting are recognized using Support Vector Machines first [15] , replaced then with influence models to exploit dependencies across roles [5] . Even if they use fidgeting features, these two works still suggest that audio-based features are the most effective for the recognition of roles.

O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Structure-aware hair capture (a) An image of (b) Point cloud with (c) Failure of (d) Color-coded (e) Synthesized (f) A frame from captured hairstyle 3D orientation field previous method reconstructed wisps hair strands hair simulationFigure 1: Our system takes a collection of images as input (a) and reconstructs a point cloud with a 3D orientation field (b). In contrast to previous methods (e.g. [Paris et al. 2008] ) that straightforwardly grow hair strands from the scalp following the orientation field and hence cannot reconstruct complex hairstyles with convoluted curl structures (c), we reconstruct complete, coherent and plausible wisps (d) aware of the underlying hair structures. The wisps can be used to synthesize hair strands (e) that are plausible for animation or simulation (f).Existing hair capture systems fail to produce strands that reflect the structures of real-world hairstyles. We introduce a system that reconstructs coherent and plausible wisps aware of the underlying hair structures from a set of still images without any special lighting. Our system first discovers locally coherent wisp structures in the reconstructed point cloud and the 3D orientation field, and then uses a novel graph data structure to reason about both the connectivity and directions of the local wisp structures in a global optimization. The wisps are then completed and used to synthesize hair strands which are robust against occlusion and missing data and plausible for animation and simulation. We show reconstruction results for a variety of complex hairstyles including curly, wispy, and messy hair. Shared between culture, nature, and sculpture, the hairstyle is a medium that creates a unique expression of self. A person's hairstyle is a vital component of his or her identity, and can provide strong cues about age, background, and even personality. The same is true of virtual characters, and the modeling and animation of hair occupy a large portion of the efforts of digital artists. Driven by increased expectations for the quality of lead and secondary characters, as well as digital doubles, this effort has only been increasing.. Acquiring complex hairstyles from the real world holds the promise of achieving higher quality with lower effort, much as 3D scanning has revolutionized the modeling of faces and other objects of high geometric complexity. This is especially true for digital doubles, which require high fidelity, and secondary animated characters, which may appear by the dozens and must receive less personalized attention from 3D modeling artists. However, even for lead characters that are modeled largely by hand, it is frequently easier to start with scanned data than to begin modeling from a blank canvas. This allows the digital hair to exploit the full talents of real-world stylists, who express their creativity through cutting, shearing, perming, combing, and waxing.. Despite the potential benefits of capturing real-world hairstyles, there is a large gap between the data produced by existing acquisition techniques and the form in which a hairstyle must end up to be incorporated into a production pipeline. Hair animation, whether done by hand or via physical simulation, typically operates on a collection of guide strands. Each of these is a curve through space, starting from a point on the scalp and going to the tip of the hair. The guide hairs must not intersect, and the entire collection must not be overly tangled. The hair model consists of tens of thousands of strands, whose motion is interpolated from the guide strands.. How close are existing hair capture systems to this representation? The raw output of 3D acquisition devices is typically an unstruc- Figure 2 : Overview of our method. We start with a collection of input images, reconstruct a point cloud with 3D orientation field, and cover the point cloud with ribbons that reveals the locally coherent wisp structures. A connection and direction analysis is then performed on the ribbons to determine their directions and connect them up into long wisps. Finally the wisps are used to synthesize the strands.. tured point cloud or a partial surface. Prior research on hair capture has typically augmented this geometry with a 3D orientation field, computed from orientations observed in a number of images. Given these two types of data, it is possible to grow a set of strands from the scalp whose position is constrained to the reconstructed geometry and whose direction follows the orientation field.. There are two major difficulties with this approach. First, the geometry will always suffer from missing regions and noise because of the complex occlusion patterns of hair. Second, the orientation field is necessarily extrapolated from what was observed on the outermost layer of hair. As a result, the grown hair strands exhibit a variety of undesirable artifacts: they may suddenly reverse direction and form implausible U-shapes, diverge wildly from their neighbors, exhibit variations in density, or simply fail to reach all parts of the visible hair volume (see, for example, Figure 1c ). Moreover, these independently-grown strands have no natural and coherent grouping structure that allows them to be controlled by guide hairs. As a result, it is impossible to incorporate these systems, based on naive strand-growing, into animation pipelines.. We describe a system that reconstructs structured hair models plausible for hair animation and simulation ( Figure 1 ) by performing a higher-level analysis of the hair's structure. The system incorporates four key insights. First, it grows groups or wisps of hair coherently. This not only matches the structure of real hairstyles, which frequently contain strands that run nearly parallel to many of their neighbors, but also allows each wisp to be associated with a guide strand for animation. Second, it builds up a connection graph, allowing strands to span regions of missing geometric data. As long as two curvature-compatible portions of hair have been acquired, our system is able to connect across the gap between them. Third, it explicitly resolves the 180-degree ambiguity of orientation fields by performing a global Markov Random Field (MRF) optimization on the directions associated with nodes in the graph. This keeps strands from performing sudden U-turns. Finally, it ensures that each portion of visible surface is connected back to the scalp along some path. This allows our system to work for arbitrarily complex hairstyles, even if a naive strand-growing method would have difficulty reaching the end of, e.g., a complicated curl, by strictly following the orientation field.. Our algorithm begins with a point cloud and orientation field obtained from a collection of still images (Sec. 4) and extracts a set of local strand segments. These are clustered into "ribbons" that cover sets of parallel strands (Sec. 5), and connected across gaps in the point cloud (Sec. 6.1). Following a global direction analysis (Sec. 6.2), we connect up the ribbons to each other, and to the scalp (Sec. 7.1), to obtain complete wisps with plausible topology. These not only drive the final strand synthesis (Sec. 7.3), but also can be used as guide strands for hair simulation (Sec. 8). Our method is shown in Figure 2 . Its input is a set of images captured from multiple views for a real hairstyle (or, for some of our examples, a wig). We key the images to separate foreground and background, and use the Patch-based Multi-View Stereo (PMVS) [Furukawa and Ponce 2010] algorithm to reconstruct a raw point cloud with normals. We perform Moving Least Squares (MLS) fitting to filter the points and normals and compute the 3D orientation field on the points according to the 2D orientation maps (Sec. 4).. We then identify locally coherent wisp structures and group them into ribbons that cover the input point cloud. To achieve this goal, we first grow strand segments on the point cloud, following the 3D orientation field and stopping at discontinuities in orientation.. (Sec. 5.1). Then we cover the grown strand segments with ribbons to expand the local regions into coherent wisp structures (Sec. 5.2).. Because of occlusion and missing data, the ribbons are disconnected from each other and do not form complete wisps. We discover missing connections between adjacent ribbons by trying to fit circular arcs to the covered strand segments of the ribbons (Sec. 6.1). Good fits indicate plausible connections between ribbons, which we encode in a connection graph. We also associate a growth direction with each ribbon by globally optimizing for compatible connections and local hints of ribbon direction using a Markov Random Field (MRF) formulation (Sec. 6.2). Following the connections and optimized directions, the ribbons can be connected up to form complete wisps (Sec. 6.3).. We attach the wisps to the scalp of a manually fit head model (Sec. 7.1), then generate interior wisps to fill in the empty regions inside the hair volume, which had been occluded in the input (Sec. 7.2). Finally we synthesize strands using the complete attached wisps and the interior wisps (Sec. 7.3). We present results of our pipeline on five datasets. Three of these are of wigs, and were captured using a single digital SLR camera mounted on a motorized spherical gantry and moved to 50 positions (Figure 12 left) . These results are shown in Figure 1 and the first two rows of Figure 13 . Two other results ( Figure 13 , last two rows) are of real hair, and were captured using a rig containing 30 cameras (Figure 12 right).. As shown in Figure 1 , our system is capable of reconstructing challenging hair styles. Our connection graph is able to establish correct correspondences among the partially-visible portions of curls, and hence our reconstructed wisps are, in most cases, able to follow the curls all the way from the scalp to the tips. Figure 14 compares the reconstruction details to the input hairstyle and shows that our reconstructed hair model can faithfully reveal the intricate hair structures in the input hairstyle. Figure 13 , first row, contains many crossing wisps that present a challenge to competing algorithms, while the second row illustrates a complicated and disordered hairstyle. Though we are not able to reconstruct each curl perfectly, many specific curls are captured, and the general impression of the hairstyle makes our reconstructed data suitable for virtual characters.. 76:8 • L. Luo et al. Hair capture. Most existing hair capture methods generate a strand set model by growing hair strands independently, constrained by the captured hair orientations and geometry. Paris et al. [2004] proposed a method to estimate 3D hair orientations from highlights under a moving light source with known trajectory. They grow strands along the estimated orientations, starting at the scalp. Wei et al. [2005] introduced a technique to create a strand model from the visual hull constructed from many views. The strands are grown constrained by the orientation consistency across the views. Paris et al. [2008] introduced an active acquisition system capable of accurately capturing the positions of the exterior hair strands. A strand model is generated by growing the strands within the diffused orientation field from the scalp to the captured exterior hair layer. Jakob et al. [2009] proposed a system to capture fiber-byfiber hair assemblies by growing hairs through the intersecting ribbons created by back-projecting the 2D strands with shallow depthof-fields. Chai et al. [2012] showed how to create an approximate strand model from a single image using the inter-strand occlusion relationships and the head model fit to match the face in the image. Beeler et al. [2012] introduces a system to capture facial hairs using multi-view stereo matching. Their method employs a refinement method to improve the connections between the captured strand segments and remove outlier hairs. Luo et al. [2012] proposed a method to grow a strand model in the orientation field constrained by the geometry constructed from hair orientation fields. Herrera et al. [2012] applied thermal imaging to generate a strand model by growing strands on the boundary of the captured hairstyle. Their method joins the loose ends of nearby segments with smooth curvature and connects the strands to a user-defined ellipsoid as the scalp.. Geometry-based hair modeling. Structured models are commonly used in geometry-based hair modeling. A more complete survey on hair modeling techniques can be found in [Ward et al. 2006 ], here we only enumerate a few recent work relevant to ours. Ward et al. [2003] used a high level skeleton representation to control various low level representations for level-of-detail hair modeling. Kim and Neumann [2002] employed a hierarchy of generalized cylinders to model and edit hair in multi-resolution. Yuksel et al. [2009] introduced "Hair Meshes" to model hair using polygonal meshes with various topological operations. Wang et al. [2009] introduced a method to synthesize new hair styles from guide strands based on texture synthesis techniques.. Model-based reconstruction. Model fitting methods have been applied to the reconstruction of a variety of objects, e.g., architecture, furniture and trees. Livny et al. [2010] uses a tree skeletal model to reconstruct tree structures from point cloud input. Nan et al. [2010] introduced "SmartBoxes" to interactively reconstruct urban architectures with regular box-like structures. Li et al. [2010] uses "Arterial Snakes" to reconstruct delicate interleaving manmade structures.. Comparison to our method. We build upon many of the ideas pioneered by the papers above, including matching hair strands to a reconstructed orientation field, exploiting a constant-curvature prior to hypothesize connections between partial strands, and connecting reconstructed strands to the scalp. However, we achieve a more plausible reconstruction that better matches the structures of real hair by focusing on wisp reconstruction, performing a global direction analysis, and using a connection graph data structure to find long connected paths between visible hair strands and points on the scalp. As a result, we are able to reconstruct complex hairstyles including curly and messy hair, and produce hair models that are plausible for animation and simulation.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Exploiting Multiple Cues in Motion Segmentation based on Background Subtraction This paper presents a novel algorithm for mobile-object segmentation from static background scenes, which is both robust and accurate under most of the common problems found in motion segmentation. In our first contribution, a case analysis of motion segmentation errors is presented taking into account the inaccuracies associated with different cues, namely colour, edge and intensity. Our second contribution is an hybrid architecture which copes with the main issues observed in the case analysis by fusing the knowledge from the aforementioned three cues and a temporal difference algorithm. On one hand, we enhance the colour and edge models to solve not only global and local illumination changes (i.e. shadows and highlights) but also the camouflage in intensity. In addition, local information is also exploited to solve the camouflage in chroma. On the other hand, the intensity cue is applied when colour and edge cues are not available because their values are beyond the dynamic range. Additionally, temporal difference scheme is included to segment motion where those three cues can not be reliably computed, for example in those background regions not visible during the training period. Lastly, our approach is extended for handling ghost detection. The proposed method obtains very accurate and robust motion segmentation results in multiple indoor and outdoor scenarios, while outperforming the most-referred stateof-art approaches. During the last decades, important research efforts in Computer Vision have been focused on developing theories, methods and systems for modelling and understanding motion perception. Motion information is the basis for a wide range of applications such as smart surveillance systems, control applications, advanced user interfaces, and motion basis diagnosis, among others [1] . A particular domain-of-interest can be found in the semantic evaluation of people behaviour in image sequences, in which different tasks are required, such as acquisition, detection, tracking, action recognition and behaviour reasoning [2] , but still the basis for this high-level interpretation relies on when and where motion has been detected in an image.. Detecting moving agents is a fundamental and difficult problem because an accurate segmentation enhances the performance of the subsequent steps of human behaviour understanding [3] . But reliable (and fast) motion segmentation is hard due to the intrinsic nature of typical scenarios, where global and local illumination changes (i.e. shadows and highlights), camouflage and repetitive moving regions (like waving flags or tree leaves) should be commonly addressed, as well as other physical changes such as bootstrapping and ghosts [4] . Most used techniques for handling these issues are background subtraction, frame differencing, a combination of both, or optical flow [1, 5, 6, 7] . Even though many algorithms have been proposed in the literature, the detection of moving objects in complex environments is still far from being completely solved.. In this paper, a novel approach which outperforms most-known techniques used for motion segmentation is proposed. The main contributions of this paper are: (i) a novel, deep theoretical case analysis is presented for the cues most used in the literature for motion segmentation; we analyse when and why inaccuracies and errors appear due to these cues. (ii) A new hybrid architecture is presented based on such an analysis; we exploit the benefits of fusing colour, edge, and intensity cues together with temporal difference [8, 9] . (iii) New colour and edge models are proposed; in particular a novel chromatic-invariant cone model for colour segmentation, and an invariant gradient model which fuses magnitude and orientation for edge segmentation (thus avoiding false edges due to intense global illumination changes).. Regarding with the performance of our method, it can handle (i) nonphysical changes (such as global or local illumination changes and camouflages), (ii) physical changes (such as bootstrapping and ghosts), and (iii) sensor dynamic range problems. In particular, Ghost cases are successfully detected on-the-fly without increasing the computational cost. Furthermore, our approach can detect dark camouflage cases which can be distinguished from shadows and changes of global illumination. Interestingly, real-time performance can be fulfilled because the method is highly parallelizable, mainly due to the pixel-wise nature of the proposed components.. This paper is organized as follows: next section presents a comprehensive literature review in motion segmentation and compares the main contributions of our approach w.r.t. the state of the art. Section 3 presents an analysis of the cues typically applied in motion segmentation, emphasizing those cases in which such cues can not be reliably applied. This theoretical evaluation leads to our segmentation approach which is explained in section 4: we explain how intensity, colour, edge cues and temporal difference are used together for addressing most of the identified anomaly cases. The experimental results described in section 5 demonstrates that the performance of the resulting method applied to both indoor and outdoor sequences of several, most popular databases outperforms most well-known segmentation approaches. Lastly, section 6 presents the main lines of future research based on the results obtained. The approach described in this paper combines colour, intensity and edge cues, and a temporal differencing technique in a collaborative architecture, in which each module is devoted to a specific task. The proposed framework is built upon a case analysis of motion segmentation problems associated with the use of different cues. Consequently, this theoretical study has allowed us to define when each cue can be used to address different segmentation failures.. The background models built for each cue have been improved with respect to the current state of the art. A novel chromatic invariant cone model is proposed. Also, combining invariant gradient orientation with its magnitude allows our system to detect false edges due to intense global illumination changes.. The proposed hybrid approach can cope with different colour problems as dark and light foreground. Furthermore, we solve problems with the dynamic range (in cases of saturation and lack of colour) using intensity cues. Our approach also tackles camouflage in intensity and chroma, together with global and local (shadows and highlights) illumination changes. In addition, problems like bootstrapping and ghosts are handled.. Experiments on complex indoor and outdoor scenarios have yielded robust and accurate results, thereby demonstrating the ability of the system to deal with unconstrained and dynamic scenes.. For future work, a proper updating process should be included in the approach to incorporate motionless objects to the background model. Furthermore, the use of a pixel-updating process can help to reduce false positives obtained by using the intensity mask due to drastic illumination changes. Furthermore, colour invariant normalisation or colour constancy techniques can be used to improve the colour model. The edge model can be enhanced by avoiding false edges due to local intense illumination changes. Further, edge linking or B-spline techniques can be used to avoid the partial loss of foreground borders due to camouflage, thereby improving the edge mask. A statistical-based decision approach that combines the use of multiples cues could be useful to reduce some of the parameters described in this article. Lastly, the discrimination between the agents and the local environments can be enhanced by using new cues (such as texture) or tracking.

O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Improved Two-Point Codes on Hermitian Curves One-point codes on the Hermitian curve produce long codes with excellent parameters. Feng and Rao introduced a modified construction that improves the parameters while still using one-point divisors. A separate improvement of the parameters was introduced by Matthews considering the classical construction but with two-point divisors. Those two approaches are combined to describe an elementary construction of two-point improved codes. Upon analysis of their minimum distance and redundancy, it is observed that they improve on the previous constructions for a large range of designed distances. H ERMITIAN curves are defined with the equation over the finite field with elements. The number of points is maximal given the genus of the curve and Hermitian codes constructed with Goppa's method have excellent parameters [1] - [7] . The curve has as important advantages that the codes are easy to describe and to encode and decode. The most studied Hermitian codes are the one-point codes. They are obtained by evaluation of functions in the linear span of for a fixed . To a function corresponds the codeword , where the , for are distinct rational points on the affine curve. Together the codewords generate a code . Different methods have been presented that give codes with better parameters. An idea due to Feng and Rao [8] is to enlarge the code without reducing its distance by carefully selecting extra codewords. We illustrate their idea for a particular case. For , the codes and are of type and , respectively. It appears that to increase the dimension of the code we have to accept a smaller distance. However, it can be shown that words in have weight at least six. By adding two independent words from to we obtain a code. The parameters of improved one-point Hermitian codes are given in closed form in [9] .. A second idea, first applied by Matthews [5] , is to consider vector spaces of functions that correspond to two-point divisors instead of one-point divisors. Recently the complete description of the actual minimum distance for all two-point Hermitian codes [7] , [15] , [20] . From their description we obtain that the best Hermitian two-point codes are very similar to one-point codes. They can be defined as subcodes of the codes by removing the functions and in the generating set and omitting the point in the evaluation, which reduces the code length by one. This claim is a consequence of the results in [7] , [15] , [20] (see Section IV). The codes and have subcodes and of type and , respectively. For the two-point codes thus obtained, we still have the possibility to improve them further using the Feng and Rao idea. In this paper, we give bounds for the parameters of Feng-Rao improved two-point codes of special form. Fig. 1 summarizes the constructions of Hermitian codes, with arrows pointing in the direction of better codes.

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New Algorithms for Mining the Reputation of Participants of Online Auctions The assessment of credibility and reputation of contractors in online auctions is the key issue in providing reliable environment for customer-to-customer e-commerce. Confident reputation rating system is an important factor in managing risk and building customer satisfaction. Unfortunately, most online auction sites employ a very simple reputation rating scheme that utilizes user feedbacks and comments issued after committed auctions. Such schemes are easy to deceive and do not provide satisfactory protection against several types of fraud. In this paper we propose two novel measures of trustworthiness, namely, credibility and density. We draw inspiration from social network analysis and present two algorithms for reputation rating estimation. Our first algorithm computes the credibility of participants by an iterative search of inter-participant connections. Our second algorithm discovers clusters of participants who are densely connected through committed auctions. We test both measures on real-world data and we experimentally compare them with existing solutions. In this paper we have presented two novel measures for reputation rating in the online auction environment. Our measures, credibility and density, evaluate the reputation of auction participants by mining the topology of the network of seller-buyer relationships to retrieve useful knowledge. We believe that the patterns that we discover in the network provide additional insight into user characteristics and can be used as a predictor of user reliability. The experiments prove the practical usability and applicability of the presented solution. Our work extends previous proposals in the number of ways, namely, it considers the structure of inter-participant relationships and computes the reputation ratings iteratively by simulating the flow of credibility between auction participants. The results of conducted experiments encourage us to follow the research in the area. For the moment, we compute the reputation of a buyer and a seller disjointly, even if they are the same physical person. The next step is to combine the information about these reputation ratings for every distinct individual. An interesting, yet often disregarded, feature of online bidding is the timing of the bid. We believe that the timing carries valuable knowledge about the nature of the bid and can be successfully used to discover fraud. Finally, our experiments were conducted on a fairly small subset of the original data. Due to the immense popularity of online auctions, the volume of data to be analyzed poses a significant challenge. We plan to scale the algorithms to allow for almost real-time analysis of huge amounts of raw data. Reputation systems [11] are commonly used to build trust on the Internet, where millions of individuals perform commercial transactions without knowing each other. Web-based auction sites typically rely on trust models in which credibility of participants is assessed by counting positive and negative feedbacks received from their trading partners after each auction [6] . A critical analysis of this simple model can be found in [8] . The author points to the subjective nature of feedbacks, the lack of feedback context, the need to perform feedback aging. Of particular importance is the fact that positive and negative feedbacks are highly asymmetric. Users provide positive feedbacks willingly, but they refrain from providing a negative feedback in the fear of retaliation. Indeed, a negative feedback is usually issued when the quality of service becomes totally unacceptable. Otherwise, users choose not to provide a feedback at all. Thus, traditional feedback-based reputation systems grossly overestimate the reputation of users (particularly of sellers) by not considering these missing feedbacks.. Several solutions have been recently proposed to address some limitations of current feedback-based models. In [1] the authors introduced a complaint-only trust management method. A method presented in [4] evaluates the quality of feedbacks assuming that a feedback is credible if it is consistent with the majority of feedbacks for a given user. The authors of [2] proposed to introduce a trusted third party that could be used to authorize, identify, and establish the reputation of auction participants. A comparison of fraud mechanisms in online auctions and pay-per-call industry in the early 1990s can be found in [13] . The author states that the existing efforts of the online auction industry self-regulation are not adequate and would not solve the problem, hence legal action must be undertaken by the government to provide consumers with protection. In [14] a trust model called PeerTrust for peer-to-peer e-commerce communities was proposed. The presented model includes several trust parameters, such as the feedback in terms of satisfaction, number of transactions, credibility of feedback, transaction context, and community context. An interesting idea of trust and distrust propagation was formulated in [5] . The authors present a method to compute trust between any two individuals based on a small amount of explicit trust and distrust statements per individual.. In our approach, rather than trying to solve all the problems with reputation assessment in Web-based auctions, we focus on just one issue that we believe is the most important, i.e. the credibility of the feedback. We go a step further than [14] with the goal of discovering networks of artificial auction participants created by cheating sellers and providing reciprocal positive comments. We mine the network of auction participants to derive knowledge on seller's credibility that would be independent of other users' feedbacks.. The problem of evaluating the importance of Web pages by Web search engines can be regarded as similar to the problem of reputation assessment in online auctions. In terms of implementation details our method for credibility assessment in online auctions is similar to an algorithm proposed to evaluate the quality of Web pages, called HITS (hyperlink-induced topic search) presented in [7] . HITS divides pages into authorities (covering a certain topic) and hubs (directory-like pages linking to authorities devoted to a certain topic). In our method, we apply a similar distinction, dividing auction participants into those that are mainly sellers and those that are mainly buyers. Our second method, i.e. the assessment of seller density, is similar to density-based clustering schemes.

O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Energy efficiency in multiaccess fading channels under QoS constraints 1 In this paper, transmission over multiaccess fading channels under QoS constraints is studied in the low power regime. QoS constraints are imposed as limitations on the buffer violation probability. The effective capacity, which characterizes the maximum constant arrival rates in the presence of such statistical QoS constraints, is employed as the performance metric. The minimum received bit energy levels and wideband slope regions are characterized for different transmission and reception strategies, namely time-division multiple-access (TDMA), superposition coding with fixed decoding order, and superposition coding with variable decoding order. It is shown that the minimum received bit energies achieved by these different strategies are the same and independent of the QoS constraints. When wideband slope regions are considered, the suboptimality of TDMA with respect to superposition schemes is shown. For the case of superposition coding, it is proven that varying the decoding order at the receiver with the fading realizations does not enlarge the wideband slope region. Energy efficiency is an important consideration in wireless systems and has been rigorously analyzed from an informationtheoretic perspective. In [1] , Verdú has extensively studied the spectral efficiency-bit energy tradeoff in the wideband regime, considering the Shannon capacity as the performance metric. For the Gaussian multiaccess channel, Caire et al. [2] have shown that time division multiple-access (TDMA) is in general a suboptimal transmission scheme in the low-power regime unless one considers the asymptotic scenario in which the power vanishes. It is also shown that fading makes the superposition strategy more favorable. In this analysis, Shannon capacity formulation is again adopted as the main performance metric. However, Shannon capacity does not quantify the performance in the presence of quality-of-service (QoS) limitations in the form of constraints on queueing delays or queue lengths.. At the same time, providing QoS guarantees is one of the key requirements in the development of next generation wireless communication networks. In real time services, such as voice over IP (VoIP) and interactive-video (e.g,. videoconferencing), latency is a key QoS metric. Additionally, for fading channels with random variations and volatile conditions, providing deterministic delay guarantees either is not possible or, when it is possible, requires the system to operate pessimistically and 1 This work was supported by the National Science Foundation under Grants CNS -0834753, and CCF -0917265.. achieve low performance underutilizing the resources. Therefore, wireless systems are better suited to support statistical QoS guarantees.. In [3] , the effective capacity is defined as the maximum constant arrival rate that a given time-varying service process can support while providing statistical QoS guarantees. The analysis and application of effective capacity in various settings have attracted much interest recently (see e.g. [4] - [9] and references therein). For instance, related to this study, we in [7] and [8] addressed the energy efficiency in a single-user setting when the wireless systems operate under buffer constraints and employ either adaptive or fixed transmission schemes for pointto-point links. In [9] , we characterized the effective capacity regions of fading multiaccess channels with different scheduling policies. In that work, it has been found that TDMA and superposition coding with variable decoding with respect to channel states can outperform superposition strategy with fixed decoding.. In this paper, we consider the performance of TDMA and superposition strategies in the presence of statistical QoS constraints but concentrate on the low-power regime. More specifically, we employ the tools provided in [1] and [2] to investigate the minimum bit energy levels and wideband slope regions under QoS constraints. The main results of this paper are the following: The same minimum bit energy is achieved by different transmission and reception schemes and this minimum bit energy level is the same as that attained in the absence of QoS limitations. When a finer analysis is conducted through the study of wideband slope regions, it is noted that TDMA is in general suboptimal with respect to superposition coding, and when superposition schemes are employed for transmission, varying the decoding order at the receiver does not improve the performance in terms of the wideband slope regions. In this paper, we have considered different transmission strategies over multiaccess fading channels under QoS constraints in the low-power regime. We have found that the minimum received bit energies for different users are the same for different transmission and reception techniques. Moreover, minimum bit energy levels do not get affected by the presence of QoS limitations. However, these hold in the asymptotic regime in which SNR vanishes. At low but nonzero SNR levels, performance is investigated through the wideband slope regions which are in general shown to depend on the transmission and reception strategies and QoS exponents. We have noted that stringent QoS constraints lead to smaller wideband slopes. We have shown that superposition strategy with fixed decoding order performs as well as that with variable decoding order in the low-power regime. We have proven that TDMA is suboptimal. For superposition coding with variable decoding order, the decoding order does not affect the slope region.

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