A. Rosenfeld, R.A. Hummel and S.W. Zucker, Scene Labelling by Relaxation Operations, IEEE Transactions on Systems, Man and Cybernetics, 6, 420--433, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....may only have one peak because of the vast range of intensities for each object and an overlap between these. Bhanu and Faugeras[17] propose a gradient relaxation algorithm for solving the above problem and compare it to non linear probabilistic relaxation algorithm proposed by Rosenfeld[183]. The process is based on assigning each pixel an initial probability of occurrence and then using 26 gradient relaxation based on compatibility function that taken into account the relationship between a pixel and its eight neighbours. The relaxation process is iterative where pixel values are ....

A. Rosenfeld, Scene labelling by relaxation operations, IEEE Transactions on Systems, Man and Cybernetics, vol. 6, no. 6, pp. 420-433, 1976.

....with a tuple, which specifies whether it belongs to a given region or if it is a boundary pixel. This tentative segmentation was then refined by relaxation labelling that ensures local consistency of pixel labelling during segmentation by minimising the entropy of local neighbourhoods (see [84,103] for details on relaxation labelling for 2D and 3D images) If a pixel does not belong to the boundary, then it is assigned to one of the regions. This classification is entirely uni dimensional in the co occurrence direction and contains no explicit local consistency. The consistency for regions ....

A.R.R. Hummel and S. Zucker, Scene labelling by relaxation operations, IEEE Transactions on Systems, Man and Cybernetics, vol. 6, pp. 420-433, 1976.

....for CSPs, constraints can never be violated. This is, however, Preprint submitted to Elsevier Science 1 August 2002 sometimes inflexible. Thus, various efforts are made for equipping conventional CSP with soft constraints which can partially be violated. The extended frameworks include fuzzy CSPs [64,83,58,18 20,65,11,20,22,25,37], probabilistic CSPs [27,2,60,61,73] and more general valued CSPs [69,16,42,70] as well as semiring based CSPs [8 10] Among these extended frameworks, fuzzy CSPs are the most popular. Generally speaking, a crisp constraint can be viewed as a set of tuples, and thus using the concept of fuzzy ....

A. Rosenfeld, R. Hummel, and S. Zucker. Scene labelling by relaxation operations. IEEE Transaction on Systems, Man and Cybernetics, 6(6), 1976.

....for CSPs, constraints can never be violated. This is, however, Preprint submitted to Elsevier Science 1 August 2002 sometimes in exible. Thus, various e orts are made for equipping conventional CSP with soft constraints which can partially be violated. The extended frameworks include fuzzy CSPs [64,83,58,18 20,65,11,20,22,25,37], probabilistic CSPs [27,2,60,61,73] and more general valued CSPs [69,16,42,70] as well as semiring based CSPs [8 10] Among these extended frameworks, fuzzy CSPs are the most popular. Generally speaking, a crisp constraint can be viewed as a set of tuples, and thus using the concept of fuzzy ....

A. Rosenfeld, R. Hummel, and S. Zucker. Scene labelling by relaxation operations. IEEE Transaction on Systems, Man and Cybernetics, 6(6), 1976.

....approaches [6] Structural approaches such as autocorrelation consider a textured image as composed of repeating or periodical texture elements like tile wall. Statistical approaches such as co occurrence matrices, auto regression, maximum entropy power spectrum estimation and Relaxation Labelling [11] consider the texture as a set of statistics extracted from local image measurements. Generally, they are good for textures with random spatial arrangements. 1.2 Segmentation based on positional information This class of approaches involves the detection of luminance discontinuities such as ....

A. Rosenfeld, R. A. Hummel, and S. W. Zucker. Scene Labelling by Relaxation Operations. 6:420--433, 1976.

....Computer Science, Washington University, Campus Box 1045, One Brookings Drive, St. Louis, MO 63130. email: zhang cs.wustl.edu 1 1 Introduction and Overview One of the most important recent advances in the studies of constraint satisfaction problems (CSPs) is the introduction of soft constraints [1, 5, 12, 14] to capture many important aspects of real world constraint problems. In traditional CSPs, all constraints are treated equally, and must all be satis ed to solve the problem. Such CSPs are not always e ective at modeling real world constraint problems. Soft constraint is a categorical term that ....

....algorithm can bene t from # encoding of a particular CSP, the same bene ts should be attainable with greater eciency by modifying the search to simulate # encoding. 18 5 Related Work and Discussions Soft constraints were initially proposed and studied under the notions of fuzzy constraints [12], uncertain constraints [5] soft constraints [1, 2] and valued constraints [13, 14] In these studies, special structures have been imposed onto the values of constraints. For instance, in the soft constraint framework [1, 2] semiring structures were considered, and in the valued constraint ....

A. Rosenfeld, R. A. Hummel, and S. W. Zucker. Scene labelling by relaxation operations. IEEE Trans. on Systems, Man, and Cybernetics, 6(6):420-433, 1976.

....methods for CSP s is to work on each propagation constraint independently, and deterministically to extract information about locally consistent assignments. This has lead to various consistency algorithms for networks of constraints, the most widely applicable of these being arc consistency [RHZ75, Mon74] Consistency can be applied as a preliminary to the search steps or interleaved with them [HE80] The application of these techniques in logic programming was accomplished through two complementary extensions [VD86, Van89] ffl explicit finite domains of values to allow the expression of ....

A. Rosenfeld, A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. Technical Report TR-379, Computer Science Department, University of Maryland, 1975.

....the language: the SFD system and our implementation of clp(FD,S) We also give some performance results on various examples. 1 Introduction In [1, 2] a general framework for finite domains constraint satisfaction and optimization has been defined, where classical CSPs [15, 13, 14] fuzzy CSPs [16, 9, 17], partial CSPs [10] and others can be easily cast. This framework is based on a semiring structure. Moreover, the authors show that local consistency algorithms can be used, provided that certain conditions on the semiring operations are satisfied. Restricting to that case and integrating ....

A. Rosenfeld, R.A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. IEEE Transactions on Systems, Man, and Cybernetics, 6(6), 1976.

....situations which can arise when input is corrupted or incomplete. Furthermore, neither search nor arc consistency use evidence derived from the input, relying merely on pre defined constraint relations. To overcome these problems, Rosenfeld, Hummel and Zucker formulated probabilistic relaxation in (Rosenfeld et al. 1976). However the convergence properties of their algorithm are not easily characterised (Kittler and Illingworth 1985) In (Hummel and Zucker 1983) Hummel and Zucker adopted a more information theoretic approach in their reformulation of relaxation as an optimisation problem. Faugeras and Berthod ....

A. Rosenfeld, R. A. Hummel, and S. W. Zucker (1976). Scene labelling by relaxation operations. IEEE Transactions on Systems, Man and Cybernetics 6, 420--433.

....nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to variables is allowed or not is not enough or sometimes not even possible. For this reason, many extensions of the classical CSP framework have been proposed in the literature. For example, fuzzy [DFP93, RHZ76, Rut94, Sch92], partial [FW92] probabilistic [FL93] hierarchical [BMMW89] More recently, all these extensions have been unified in a general framework [BMR95, BMR97] called SCSP, which uses a semiring (that is, a domain plus two operations satisfying certain properties) to associate with each tuple of ....

....combination and projection reduce indeed in this case to the usual operations for the satisfiability of a set of constraints and for the elimination of some variables, respectively. Other interesting semirings can be thought. For example, the paradigm of fuzzy constraint problems (FCSPs) [DFP93, RHZ76, Rut94, Sch92], where tuples get as Learning Solution Preferences in CSPs 14 signed values between 0 and 1 (to be interpreted as their level of preference) and the goal is to maximize the minimum level of preference, can be described by using the c semiring where A = fx j x in [0; 1]g, max, Theta = ....

A. Rosenfeld, R.A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. IEEE Transactions on Systems, Man, and Cybernetics, 6(6), 1976.

....Relaxation operations have been long used in engineering fields to solve systems of equations [Southwell 40] but it got its biggest success when the extension to symbolic domain Relaxation labelling was applied to constraint propagation field, specially in low level vision problems. Waltz 75, Rosenfeld et al. 76] Relaxation labelling is a generic name for a family of iterative algorithms which perform function optimization, based on local information. This relates them closely to neural nets and gradient step. Let V = fv 1 ; v 2 ; v n g be a set of variables Let t i = ft i 1 ; t i 2 ; ....

....meet a certain convergence criterion, at least under appropriate conditions 1 [Zucker et al. 78, Zucker et al. 81, Hummel Zucker 83] This is called the updating function and it is used to compute and normalize the new weight values for each possible tag. Several formulas have been proposed [Rosenfeld et al. 76] and some of them have been proven to be approximations of a gradient step algorithm. The updating formulas must increase the weight associated with values with a higher support, and decrease those of values with lower support. This is achieved by multiplying the current weight of a value by a ....

Rosenfeld, R.; Hummel, R.; Zucker, S.; Scene labelling by relaxation operations. IEEE Transactions on Systems, Man and Cybernetics. vol SMC 6, p420, 1976

....matching configuration with the largest probability. The principle advantage of this approach is that the processes which lead to matching errors can be modelled objectively by probability distributions. It was (Hummel and Zucker, 1983) who first showed that the probabilistic relaxation scheme of (Rosenfeld et al. 1976) could be interpreted as the minimisation of an energy function based on label probabilities and a set of heuristically defined support functions. Following on from this, Faugeras and Berthod, 1981) and (Bhanu and Faugeras, 1984) developed similar energy based criteria which maximised consistency ....

....which is optimised with a neural network. Ranganath and Chipman (Ranganath and Chipman, 1992) similarly use inter object measurements in the definition of a support function for probabilistic relaxation, albeit in an ad hoc fashion. Symbolic approaches include the original relaxation scheme of (Rosenfeld et al. 1976); their definition of a support function and relaxation scheme is such that measurements were used in the initialisation of probabilities, but as the scheme progresses this information is overridden by labelling constraints. This has been seen as a weakness of the classic PR technique. Recent work ....

[Article contains additional citation context not shown here]

Rosenfeld, A., Hummel, R. A., and Zucker, S. W. (1976). Scene labelling by relaxation operations. IEEE Transactions on Systems, Man and Cybernetics, 6:420--433.

.... operations had been long used in engineering fields to solve systems of equations (Southwell, 1940) but they got their biggest success when the extension to symbolic domain relaxation labelling was applied to constraint propagation field, specially in low level vision problems (Waltz, 1975; Rosenfeld et al. 1976). The possibility of applying it to NLP tasks was pointed out by (Pelillo Refice, 1994) who use a toy POS tagging problem to evaluate their constraint compatibility estimating method. It has been applied more massively to NLP disambiguation tasks in (Padr o, 1998) The presented tagger has the ....

Rosenfeld, R.; Hummel, R. & Zucker, S. (1976). Scene labelling by relaxation operations. In IEEE Transactions on Systems, Man and Cybernetics, Vol.6, n.6.

....available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to variables is allowed or not is not enough or sometimes not even possible. For these reasons, it is natural to try to extend the CSP formalism in this direction. For example, in [RHZ76, DFP93, Rut94] CSPs have been extended with the ability to associate with each tuple, or to each constraint, a level of preference, and with the possibility of combining constraints using min max operations. This extended formalism has been called Fuzzy CSPs (FCSPs) Other extensions concern the ....

....relaxation algorithm proposed in [MR91] It is possible to check that an alternative way to represent CSPs in the SCSP framework is by using the following c semiring: h(fag) S ; T ; fagi, where (S) is the powerset of a set S, and a is any value. 6. 2 Fuzzy CSPs Fuzzy CSPs (FCSPs) RHZ76, DFP93, Rut94] extend the notion of classical CSPs by allowing non crisp constraints, that is, constraints which associate a preference level with each tuple of values. Such level is always between 0 and 1, where 1 represents the best value (that is, the tuple is allowed) and 0 the worst one ....

A. Rosenfeld, R.A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. IEEE Transactions on Systems, Man, and Cybernetics, 6(6), 1976.

....nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to variables is allowed or not is not enough or sometimes not even possible. For this reason, many extensions of the classical CSP framework have been proposed in the literature. For example, fuzzy [DFP93, RHZ76, Rut94, Sch92], partial [FW92] probabilistic [FL93] hierarchical [BMMW89] More recently, all these extensions have been unified in a general framework [BMR95] called SCSP, which uses a semiring (that is, a domain plus two operations satisfying certain properties) to associate with each tuple of values for ....

A. Rosenfeld, R.A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. IEEE Transactions on Systems, Man, and Cybernetics, 6(6), 1976.

....completely available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to variables is allowed or not is not enough or sometimes not even possible. For these reasons, it is natural to try to extend the CSP formalism in this direction. For example, in [8, 31, 32, 33] CSPs have been extended with the ability to associate with each tuple, or with each constraint, a level of preference, and with the possibility of combining constraints using min max operations. This extended formalism has been called Fuzzy CSPs (FCSPs) Other extensions concern the ability to ....

....ordering S here reduces to 0 S 1. As predictable, all the properties related to k consistency hold. In fact, is idempotent. Thus the results of Theorems 2 and 4 apply. Also, since the domain of the semiring is finite, the result of Theorem 3 applies as well. 2.4.2. Fuzzy CSPs. Fuzzy CSPs (FCSPs) [8, 31, 32, 33] extend the notion of classical CSPs by allowing non crisp constraints, that is, constraints which associate a preference level with each tuple of values. Such level is always between 0 and 1, where 1 represents the best value (that is, the tuple is allowed) and 0 the worst one (that is, the tuple ....

[Article contains additional citation context not shown here]

A. Rosenfeld, R. Hummel, S. Zucker. Scene Labelling by Relaxation Operations. IEEE Trans. on Sys., Man, and Cyb., vol. 6. n.6, 1976.

....in such a way that it can be proven to meet a certain convergence criterion, at least under appropriate conditions 1 [ZKH78, ZLM81, HZ83] This is called the updating function and it is used to compute and normalize the new weights for each possible label. Several formulas have been proposed [RHZ76] and some of them have been proven to be approximations of a gradient step algorithm. The updating formulas must increase the weight associated with labels with a higher support, and decrease those of labels with lower support. This is achieved by multiplying the current weight of a label by a ....

R. Rosenfeld, R. Hummel, and S. Zucker. Scene labelling by relaxation operations. IEEE Transactions on Systems, Man and Cybernetics, 6(6):420-- 433, 1976.

....available nor crisp. In fact, in such situations, the ability of stating whether an instantiation of values to variables is allowed or not is not enough or sometimes not even possible. For these reasons, it is natural to try to extend the CSP formalism in this direction. For example, in [ Rosenfeld et al. 1976; Dubois et al. 1993; Ruttkay, 1994 ] CSPs have been extended with the ability to associate to each tuple, or to each constraint, a level of preference, and with the possibility of combining constraints using min max operations. This extended formalism has been called Fuzzy CSPs (FCSPs) Other ....

....S here reduces to 1 S 0. As predictable, all the properties related to k consistency hold. In fact, is idempotent. Thus the results of Theorems 11 and 13 apply. Also, since the domain of the semiring is finite, the result of Theorem 12 applies as well. 5. 2 Fuzzy CSPs Fuzzy CSPs (FCSPs) Rosenfeld et al. 1976; Dubois et al. 1993; Ruttkay, 1994; Schiex, 1992 ] extend the notion of classical CSPs by allowing non crisp constraints, that is, constraints which associate a preference level to each tuple of values. Such level is always between 0 and 1, where 1 represents the best value (that is, the tuple ....

A. Rosenfeld, R.A. Hummel, S.W. Zucker. Scene Labelling by Relaxation Operations. IEEE Trans. on Sys., Man, and Cyb., vol. 6. n.6, 1976.

.... (Larrosa Meseguer 1995b) Although relaxation operations had long been used in engineering fields to solve systems of equations (Southwell 1940) they did not achieve their breakthrough success until relaxation labelling their extension to the symbolic domain was applied by (Waltz 1975, Rosenfeld et al. 1976) to constraint propagation field, especially in low level vision problems. Relaxation labelling is a technique that can be used to solve consistent labelling problems (clps) see (Larrosa Meseguer 1995a) A consistent labelling prob A MACHINE LEARNING APPROACH TO POS TAGGING 19 lem ....

Rosenfeld, R., Hummel, R., Zucker, S. (1976). Scene labelling by relaxation operations. IEEE Transactions on Systems, Man and Cybernetics. Vol.6, n.6.

....methods for CSP s is to work on each propagation constraint independently, and deterministically to extract information about locally consistent assignments. This has lead to various consistency algorithms for networks of constraints, the most widely applicable of these being arc consistency [RHZ75, Mon74] Consistency can be applied as a preliminary to the search steps or interleaved with them [HE80] The application of these techniques in logic programming can be related back to the enforcement of link consistency in connections graphs [Kow79] Finite domain propagation in logic ....

A. Rosenfeld, A. Hummel, and S.W. Zucker. Scene labelling by relaxation operations. Technical Report TR-379, Computer Science Department, University of Maryland, 1975.

No context found.

A. Rosenfeld, R.A. Hummel and S.W. Zucker, Scene Labelling by Relaxation Operations, IEEE Transactions on Systems, Man and Cybernetics, 6, 420--433, 1976.

No context found.

A. Rosenfeld, R. A. Hummel, and S. W. Zucker. Scene labelling by relaxation operations. IEEE Trans. on Systems, Man, and Cybernetics, 6(6):420-433, 1976.

No context found.

A.Rosenfeld, R.A.Hummel and S.W.Zucker. Scene Labelling by Relaxation Operations. IEEE Transactions on Systems, Man and Cybernetics 6, 420--433, 1976.

No context found.

A. Rosenfeld, R. Hummel, and S. Zucker (1976). Scene labelling by relaxation operations. IEEE Trans. on Sys., Man, and Cyb. 6(6).

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Hummel, R. A.; Rosenfeld, A.; and Zucker, S.W. 1976. Scene Labelling by Relaxation Operations. IEEE Transactions on Systems, Man and Cybernetics, 6(6):420-433.

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