closed form solution of local shape from shading at critical points in the theory of shape from shading behaviours of the local solution around a critical point of the image play an important role this paper shows that the second derivatives of the object surface can be locally determined at these image critical points closed form expressions of the surface second derivatives in terms of the second derivatives of the image brightness and of the reflectance map are shown they are derived as follows by differentiating the image irradiance equation twice at an image critical point a set of polynomial equations is obtained that contains the second derivatives of the surface of the image brightness and of the reflectance map regarding these equations as simultaneous equations for unknown surface second derivatives they are algebraically solved and their explicit expressions are derived such a derivation is possible only at image critical points and is impossible at any other image point the applicability of the derived expressions to noisy images is tested using synthetic images

higher cohomology of divisors on a projective variety if l is ample or merely nef then of course hi x ox ml o md for i 0 in general the converse is false for instance it can happen that h i x ox ml 0 for m 0 and all i even if l is not nef or for that matter pseudoeffective however our main result shows that if one considers also small perturbations of the divisor in question then in fact the maximal growth of higher cohomology characterizes non ample divisors

a simple augmented constraint method for multi objective mathematical integer programming problems abstract a simple augmented constraint saugmecon method is put forward to generate all non dominated solutions of multi objective integer programming moip problems the saugmecon method is a variant of the augmented constraint augmecon method proposed in 2009 and improved in 2013 by mavrotas et al however with the saugmecon method all non dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration these innovative acceleration mechanisms include 1 an extension to the acceleration algorithm with early exit and 2 an addition of an acceleration algorithm with bouncing steps the same numerical example in lokman and koksalan 2012 is used to illustrate workings of the method then comparisons of computational performance among the method proposed by ozlen and azizog lu 2009 ozlen et al 2013 the method developed by lokman and koksalan 2012 and the saugmecon method are made by solving randomly generated general moip problem instances as well as special moip problem instances such as the mokp and mosp problem instances presented in table 4 in lokman and koksalan 2012 the experimental results show that the saugmecon method performs the best among these methods more importantly the advantage of the saugmecon method over the method proposed by lokman and koksalan 2012 turns out to be increasingly more prominent as the number of objectives increases

fixed points of endomorphisms on two dimensional complex tori abstract in this paper we investigate fixed point numbers of endomorphisms on complex tori specifically motivated by the asymptotic perspective that has turned out in recent years to be so fruitful in algebraic geometry we study how the number of fixed points behaves when the endomorphism is iterated our first result shows that the fixed points function of an endomorphism on a two dimensional complex torus can have only three different kinds of behaviours and we characterize these behaviours in terms of the analytic eigenvalues our second result focuses on simple abelian surfaces and provides criteria for the fixed points behaviour in terms of the possible types of endomorphism algebras

multiple objectives satisficing under uncertainty we propose a class of functions called multiple objective satisficing mos criteria for evaluating the level of compliance of a set of objectives in meeting their targets collectively under uncertainty the mos criteria include the joint targets achievement probability joint success probability criterion as a special case and also extend to situations when the probability distributions are not fully characterized we focus on a class of mos criteria that favors diversification which has the potential to mitigate severe shortfalls in scenarios when any objective fails to achieve its target naturally this class excludes joint success probability we further propose the shortfall aware mos criterion s mos which is inspired by the probability measure and is diversification favoring we also show how to build tractable approximations of the s mos criterion because the s mos criterion maximization is not a convex optimization problem we propose improvement algorithms via solving sequences of convex optimization problems we report encouraging computational results on a blending problem in meeting specification targets even in the absence of full probability distribution description

the eikonal equation some results applicable to computer vision in this paper we investigate certain first order partial differential equations which formulate the relationship between the light reflected from a surface and its shape particular emphasis is given to eikonal equations two results are presented first we prove that a special type of eikonal equation has only one convex and positive c2 solution in some neighborhood of a singular point using this result we show that a restricted form of this equation has exactly two solutions these results have application in scanning electron microscopy

a reference direction approach to multiple objective integer linear programming abstract we propose the use of a reference direction reference point approach to solving multiple objective integer linear programming problems the reference direction reference point is determined by the aspiration levels for the criteria that the decision maker wants to improve within this framework two methods are developed viz a pure integer method that operates entirely with integer solutions and a continuous integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function obviously the pure integer method is time consuming we therefore propose a decision support system that combines the two methods this way the adbantages of each method can be used to their fullest extent we illustrate the proposed decision support system with a numerical example

solving multiobjective multiconstraint knapsack problems using mathematical programming and evolutionary algorithms abstract in this paper we solve instances of the multiobjective multiconstraint or multidimensional knapsack problem momckp from the literature with three objective functions and three constraints we use exact as well as approximate algorithms the exact algorithm is a properly modified version of the multicriteria branch and bound mcbb algorithm which is further customized by suitable heuristics three branching heuristics and a more general purpose composite branching and construction heuristic are devised comparison is made to the published results from another exact algorithm the adaptive e constraint method laumanns m thiele l zitzler e 2006 an efficient adaptive parameter variation scheme for metaheuristics based on the epsilon constraint method european journal of operational research 169 932 942 using the same data sets furthermore the same problems are solved using standard multiobjective evolutionary algorithms moea namely the spea2 and the nsgaii the results from the exact case show that the branching heuristics greatly improve the performance of the mcbb algorithm which becomes faster than the adaptive e constraint regarding the performance of the moea algorithms in the specific problems spea2 outperforms nsgaii in the degree of approximation of the pareto front as measured by the coverage metric especially for the largest instance

an interactive reference point approach for multiobjective mixed integer programming using branch and bound abstract we propose an interactive reference point approach for multiple objective mixed integer linear programming problems that exploits the use of branch and bound techniques for solving the scalarizing programs at each dialogue phase the decision maker must specify a criterion reference point or just choose an objective function he she wants to improve in respect to the previous efficient nondominated solution in the latter case a directional search is performed adjusting automatically the reference point used at each stage tchebycheff mixed integer scalarizing programs are successively solved by branch and bound postoptimality techniques have been developed enabling the algorithm to profit from previous computations to solve the next scalarizing programs the previous branch and bound tree is used as a starting point and operations of simplification and branching are then performed to obtain a new efficient solution computational results have shown that this approach is effective for carrying out directional or local searches for efficient solutions

an improved version of the augmented e constraint method augmecon2 for finding the exact pareto set in multi objective integer programming problems generation or a posteriori methods in multi objective mathematical programming momp is the most computationally demanding category among the momp approaches due to the dramatic increase in computational speed and the improvement of mathematical programming algorithms the generation methods become all the more attractive among today s decision makers in the current paper we present the generation method augmecon2 which is an improvement of our development augmecon although augmecon2 is a general purpose method we will demonstrate that augmecon2 is especially suitable for multi objective integer programming moip problems specifically augmecon2 is capable of producing the exact pareto set in moip problems by appropriately tuning its running parameters in this context we compare the previous and the new version in a series of new and old benchmarks found in the literature we also compare augmecon2 s performance in the generation of the exact pareto sets with established methods and algorithms based on specific moip problems knapsack set packing and on published results except from other mathematical programming methods augmecon2 is found to be competitive also with multi objective meta heuristics momh in producing adequate approximations of the pareto set in multi objective combinatorial optimization moco problems

on nef subvarieties abstract in this paper we first study generalizations of fujita vanishing theorems for q ample divisors we then apply them to study positivity of subvarieties with nef normal bundle in the sense of intersection theory after ottem s work on ample subschemes we introduce the notion of a nef subscheme which generalizes the notion of a subvariety with nef normal bundle we show that restriction of a pseudoeffective resp big divisor to a nef subvariety is pseudoeffective resp big we also show that ampleness and nefness are transitive properties we define the weakly movable cone as the cone generated by the pushforward of cycle classes of nef subvarieties via proper surjective maps this cone contains the movable cone and shares similar intersection theoretic properties with it thanks to the aforementioned properties of nef subvarieties on the other hand we prove that if y x is an ample subscheme of codimension r and d y is q ample then d is q r ample this is analogous to a result proved by demailly peternell schneider and kuronya

a generic and provably convergent shape from shading method for orthographic and pinhole cameras we describe a mathematical and algorithmic study of the lambertian shape from shading problem for orthographic and pinhole cameras our approach is based upon the notion of viscosity solutions of hamilton jacobi equations this approach provides a mathematical framework in which we can show that the problem is well posed we prove the existence of a solution and we characterize all the solutions our contribution is threefold first we model the camera both as orthographic and as perspective pinhole whereas most authors assume an orthographic projection see horn and brooks 1989 for a survey of the sfs problem up to 1989 and zhang et al 1999 kozera 1998 durou et al 2004 for more recent ones thus we extend the applicability of shape from shading methods to more realistic acquisition models in particular it extends the work of prados et al 2002a and rouy and tourin 1992 we provide some novel mathematical formulations of this problem yielding new partial differential equations results about the existence and uniqueness of their solutions are also obtained second by introducing a generic hamiltonian we define a general framework allowing to deal with both models orthographic and perspective thereby simplifying the formalization of the problem thanks to this unification each algorithm we propose can compute numerical solutions corresponding to all the modeling third our work allows us to come up with two new generic algorithms for computing numerical approximations of the continuous solution of the shape from shading problem as well as a proof of their convergence toward that solution moreover our two generic algorithms are able to deal with discontinuous images as well as images containing black shadows

existence and uniqueness in photometric stereo we analyze the problem of recovering the shape of a smooth lambertian surface from two images obtained by consecutive illumination of the surface by distant point light sources from two different directions we discuss the issues of existence and uniqueness for the corresponding system of two first order nonlinear partial differential equations we show that generically this system has up to a constant a unique solution we also examine exceptional cases for which there is no such uniqueness

an interactive procedure for multiple objective integer linear programming problems abstract there are many practical problems where the objective functions and the constraints can be represented by linear functions but the decision variables are restricted to only integer values our objective is to present an interactive procedure for the multiple objective integer linear programming problem that is fast does not place too many demands on the decision maker and can be implemented without requiring any special software we illustrate the proposed procedure with a numerical example and report some computational experience

a multiresolution approach for shape from shading coupling deterministic and stochastic optimization shape from shading is an ill posed inverse problem for which there is no completely satisfactory solution in the existing literature in this paper we address shape from shading as an energy minimization problem we first show that the deterministic approach provides efficient algorithms in terms of cpu time but reaches its limits since the energy associated with shape from shading can contain multiple deep local minima we derive an alternative stochastic approach using simulated annealing the obtained results strongly outperform the results of the deterministic approach the shortcoming is an extreme slowness of the optimization therefore we propose a hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework

a method for finding the set of non dominated vectors for multiple objective integer linear programs abstract an algorithm for enumerating all non dominated vectors of multiple objective integer linear programs is presented using a straightforward theoretical approach the problem is solved using a sequence of progressively more constrained integer linear programs generating a new solution at each step the algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large real life problems

an algorithm for the multiple objective integer linear programming problem abstract a technique is presented for solving the multiple objective integer linear programming problem the technique can be used to identify some or all efficient solutions while the technique is applicable with any integer programming algorithm it is well suited for implementation using integer postoptimality techniques such an implementation based on balas additive algorithm is described for problems with zero one variables

uniqueness in shape from shading for general images of smooth objects wholly contained in the field of view and for illumination symmetric around the viewing direction it is proven that shape is uniquely determined by shading thus shape from shading is a well posed problem under these illumination conditions and regularization is unnecessary for surface reconstruction and should be avoided generic properties of surfaces and images are established questions of existence are also discussed under the conditions above it is argued that most images are effectively impossible with no corresponding physically reasonable surface and that any image can be rendered effectively impossible by a small perturbation of its intensities this is explicitly illustrated for a synthetic image the proofs are based on ideas of dynamical systems theory and global analysis

learning shape from shading by a multilayer network the multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input output data in this paper we present a novel use of the network in which the example data are not explicitly given we consider the problem of shape from shading in computer vision where the input image coordinates and the output surface depth satisfy only a known differential equation we use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights the stochastic gradient and conjugate gradient methods are used for the minimization boundary conditions for either surface depth or surface normal or both can be imposed by adjusting the same network at different levels it is further shown that the light source direction can be estimated based on an initial guess by integrating the source estimation with the surface estimation extensions of the method to a wider class of problems are discussed the efficiency of the method is verified by examples of both synthetic and real images

impossible and ambiguous shading patterns a smooth object depicted in a monochrome image will often exhibit brightness variation or shading a problem much studied in computer vision has been that of how object shape may be recovered from image shading when the imaging conditions are such that an overhead point source illuminates a smooth lambertian surface the problem may be formulated as that of finding a solution to an eikonal equation this article will focus on the existence and uniqueness of such solutions reporting recent results obtained with regard to existence shading patterns are exhibited for which there is no corresponding object shape specifically a necessary and sufficient condition is presented for a circularly symmetric eikonal equation to admit exclusively unbounded solutions additionally a sufficient condition is given for an eikonal equation to have no solution whatsoever in connection with uniqueness we consider eikonal equations defined over a disc such that the euclidean norm of the gradient of any solution is circularly symmetric vanishes exactly at the disc center and diverges to infinity as the circumference of the disc is approached contrary to earlier influential work a class of such eikonal equations is shown to possess simultaneously circularly symmetric and noncircularly symmetric bounded smooth solutions

a parallel fast sweeping method for the eikonal equation we present an algorithm for solving in parallel the eikonal equation the efficiency of our approach is rooted in the ordering and distribution of the grid points on the available processors we utilize a cuthill mckee ordering the advantages of our approach is that 1 the efficiency does not plateau for a large number of threads we compare our approach to the current state of the art parallel implementation of zhao 2007 14 and 2 the total number of iterations needed for convergence is the same as that of a sequential implementation i e our parallel implementation does not increase the complexity of the underlying sequential algorithm numerical examples are used to illustrate the efficiency of our approach

cone contraction and reference point methods for multi criteria mixed integer optimization abstract interactive approaches employing cone contraction for multi criteria mixed integer optimization are introduced in each iteration the decision maker dm is asked to give a reference point new aspiration levels the subsequent pareto optimal point is the reference point projected on the set of admissible objective vectors using a suitable scalarizing function thereby the procedures solve a sequence of optimization problems with integer variables in such a process the dm provides additional preference information via pair wise comparisons of pareto optimal points identified using such preference information and assuming a quasiconcave and non decreasing value function of the dm we restrict the set of admissible objective vectors by excluding subsets which cannot improve over the solutions already found the procedures terminate if all pareto optimal solutions have been either generated or excluded in this case the best pareto point found is an optimal solution such convergence is expected in the special case of pure integer optimization indeed numerical simulation tests with multi criteria facility location models and knapsack problems indicate reasonably fast convergence in particular under a linear value function we also propose a procedure to test whether or not a solution is a supported pareto point optimal under some linear value function

an interactive multiple objective linear programming method for a class of underlying nonlinear utility functions this paper develops a method for interactive multiple objective linear programming assuming an unknown pseudo concave utility function satisfying certain general properties the method is an extension of our earlier method published in this journal zionts s wallenius j 1976 an interactive programming method for solving the multiple criteria problem management sci 22 6 652 663 various technical problems present in predecessor versions have been resolved in addition to presenting the supporting theory and algorithm we discuss certain options in implementation and summarize our practical experience with several versions of the method

a combined tchebycheff aspiration criterion vector interactive multiobjective programming procedure in this paper we combine the tchebycheff method of steuer and choo with wierzbicki s aspiration criterion vector method in order to form an improved procedure for interactive multiple objective programming the combined procedure is sensible because the tchebycheff and aspiration criterion vector methods possess complementary distinguishing characteristics solve similar optimization problems to probe the nondominated set and share a similar computer user interface in the early iterations tchebycheff probes of the nondominated set might be conducted to locate promising neighborhoods of search in later iterations aspiration criterion vector probes might be used to pinpoint a final solution computational experience is reported showing the improved effectiveness of the combined procedure when employed in this fashion when compared against the tchebycheff and aspiration criterion vector methods run separately

on complete integrals and uniqueness in shape from shading in this paper we analyze the problem of representing solutions of a first order partial differential equation in terms of complete integrals we show that some of the existing results referring to the representability problem are incomplete additionally we analyze in the context of complete integrals the uniqueness problem for the shape recovery of a smooth lambertian surface from an image obtained by illuminating this surface by an overhead distant point light source specifically we revisit the uniqueness results already existing in the shape from shading literature that concern eikonal equations corresponding to the images of a lambertian hemisphere and a lambertian plane we show that the latter results are incomplete and indicate how to fill the gaps in the corresponding proofs

zero one programming with multiple criteria abstract the study of multiple criteria problems is not new but during the last seventeen years more and more study has been done in this area the study of 0 1 multiple criteria problems started much later than the study of continuous multiple criteria problems some of the earliest works on 0 1 problems with multiple criteria was first presented in 1973 quite a few solution methods have been developed since then especially during the last seven years in this paper most of these methods and some applications will be treated

a branch and bound algorithm for mixed zero one multiple objective linear programming abstract in this paper a branch and bound algorithm for the generation of the efficient set in mixed zero one multiple objective linear programming problems is presented the algorithm is developed as to take account of the multiple objectives in the node fathoming procedure in order to extend the algorithm s applicability to large sized problems from real life an interactive procedure is introduced which systematically reduces the number of efficient points and thus saves considerable computational effort without losing essential information the algorithm is tested in randomly generated problems along with a case study conceming the power generation sector

an interactive branch and bound algorithm for multiple criteria optimization we present a new interactive algorithm for multiple criteria optimization the algorithm is of the branch and bound type and differs from previous interactive algorithms in several ways first the field of application is wider because it applies to two important classes of multiple criteria decision problems those for which the feasible set is convex and those for which the feasible set is discrete secondly the algorithm does not require a great deal from the decision maker he is merely required to indicate his preference between two vectors whenever the algorithm so demands

k stability of cubic threefolds we prove that the k moduli space of cubic threefolds is identical to their geometric invariant theory git moduli more precisely the k semistability k polystability and k stability of cubic threefolds coincide with the corresponding git stabilities which could be explicitly calculated in particular this implies that all smooth cubic threefolds admit kahler einstein ke metrics and provides a precise list of singular ke ones to achieve this our main new contribution is an estimate in dimension 3 of the volumes of kawamata log terminal singularities introduced by chi li this is obtained via a detailed study of the classification of 3 dimensional canonical and terminal singularities which was established during the study of the explicit 3 dimensional minimal model program

shape from shading level set propagation and viscosity solutions we present a new implementation of an algorithm aimed at recovering a 3d shape from its 2d gray level picture in order to reconstruct the shape of the object an almost arbitrarily initialized 3d function is propagated on a rectangular grid so that a level set of this function tracks the height contours of the shape the method imports techniques from differential geometry fluid dynamics and numerical analysis and provides an accurate shape from shading algorithm the method solves some topological problems and gracefully handles cases of non smooth surfaces that give rise to shocks in the propagating contours real and synthetic images of 3d profiles were submitted to the algorithm and the reconstructed surfaces are presented demonstrating the effectiveness of the proposed method

a multiple objective interactive lagrangean relaxation approach abstract this paper extends the lagrangean relaxation ideas for integer scalar optimisation problems to integer vector optimisation problems and incorporates an interactive branch and bound routine

symmetric shape from shading using self ratio image in this paper we present a symmetric shape from shading sfs approach to recover both shape and albedo for symmetric objects lambertian surfaces with unknown varying albedo and orthographic projections are assumed in our formulation of symmetric sfs we have two image irradiance equations one is the standard equation used in sfs and the other is a self ratio image irradiance equation this new image irradiance equation relates the self ratio image which is defined as the ratio of two halves of the input image to light source and surface shape the introduction of the self ratio image facilitates the direct use of symmetry cue based on the self ratio image a new model based symmetric source from shading algorithm is also presented we then propose symmetric sfs algorithms to recover both shape and albedo from a single image and present experimental results the new symmetric sfs scheme has one important property the existence of a unique global solution which consists of unique local solutions at each point simultaneously obtained using the intensity information at that point and the surrounding local region and the assumption of a cal c 2 surface proofs for the existence of a unique solution in the cases of unknown constant and non constant albedos are provided

restricted volumes and divisorial zariski decompositions we give a relation between the existence of a zariski decomposition and the behavior of the restricted volume of a big divisor on a smooth complex projective variety moreover we give an analytic description of the restricted volume in the line of boucksom s work it enables us to define the restricted volume of a transcendental class on a compact k ahler manifold in a natural way the relation can be extended to a transcendental class

numerical shape from shading for discontinuous photographic images the height u x y of a continuous lambertian surface of known albedo i e grayness is related to u x y information recoverable from a black and white flash photograph of the surface by the partial differential equation sqrt u 2 x u 2 y n 0 we review the notion of a unique viscosity solution for this equation when n is continuous and a recent unique extension of the viscosity solution when n is discontinuous we prove convergence to this extension for a wide class of the numerical algorithms that converge when n is continuous after discussing the properties of the extension and the order of error in the algorithms simulating the extension we point out warning signs which when observed in the numerical solution usually indicate that the surface is not continuous or that the viscosity solution or its extension does not correspond to the actual surface finally we discuss a method that in some of these cases allows us to correct the simulation and recover the actual surface again

biobjective robust optimization over the efficient set for pareto set reduction abstract this paper presents a biobjective robust optimization formulation for identifying robust solutions from a given pareto set the objectives consider both solution and model robustness when the exact values of the selected solution are affected by uncertainty the problem is formulated equivalently as a model with uncertainty on the constraint parameters and objective function coefficients structural properties and a solution algorithm are developed for the case of multiobjective linear programs the algorithm is based on facial decomposition each subproblem is a biobjective linear program and is related to an efficient face of the multiobjective program the resulting pareto set reduction methodology allows the handling of continuous and discrete pareto sets and can be generalized to consider criteria other than robustness the use of secondary criteria to further break ties among the many efficient solutions provides opportunities for additional trade off analysis in the space of the secondary criteria examples illustrate the algorithm and characteristics of solutions obtained

meaning and validity of interactive procedures as tools for decision making this papers examines procedures based on answers to questions an entity q asks an actor d in accordance with a protocol p the aim is either to select an alternative a considered by d to be the optimal choice among a set of alternatives a or to formulate a utility function u considered relevant by d for comparing alternatives in a what gives meaning to the final result of this type of interactive procedure on which criteria can its validity be assessed in analysing three questions of a parlor game we can produce evidence that the answers to such questions do not depend on p alone but that the way in which d produces his answers plays just a central role threee different hypotheses concerning this points led us to a new approach to this type of question an approach which point out the illusive nature of certain types of answers

multicriteria integer programming a hybrid dynamic programming recursive approach dynamic programming recursive equations are used to develop a procedure to obtain the set of efficient solutions to the multicriteria integer linear programming problem an alternate method is produced by combining this procedure with branch and bound rules computational results are reported

an algorithm for multiobjective zero one linear programming a branch and bound algorithm is presented which is based on the extension of implicit enumeration techniques to multiobjective zero one linear programming and which appears to be computationally quite efficient domination tests aiming at identifying paths of the enumeration tree that lead to dominated solutions as high up the tree as possible are developed some computational results are also given

height and gradient from shading the method described here for recovering the shape of a surface from a shaded image can deal with complex wrinkled surfaces integrability can be enforced easily because both surface height and gradient are represented the robustness of the method stems in part from linearization of the reflectance map about the current estimate of the surface orientation at each picture cell the new scheme can find an exact solution of a given shape from shading problem even though a regularizing term is included this is a reflection of the fact that shape from shading problems are it not ill posed when boundary conditions are available or when the image contains singular points

a two level generative model for cloth representation and shape from shading in this paper we present a two level generative model for representing the images and surface depth maps of drapery and clothes the upper level consists of a number of folds which will generate the high contrast ridge areas with a dictionary of shading primitives for 2d images and fold primitives for 3d depth maps these primitives are represented in parametric forms and are learned in a supervised learning phase using 3d surfaces of clothes acquired through photometric stereo the lower level consists of the remaining flat areas which fill between the folds with a smoothness prior markov random field we show that the classical ill posed problem shape from shading sfs can be much improved by this two level model for its reduced dimensionality and incorporation of middle level visual knowledge i e the dictionary of primitives given an input image we first infer the folds and compute a sketch graph using a sketch pursuit algorithm as in the primal sketch guo et al 2003 the 3d folds are estimated by parameter fitting using the fold dictionary and they form the skeleton of the drapery cloth surfaces then the lower level is computed by conventional sfs method using the fold areas as boundary conditions the two levels interact at the final stage by optimizing a joint bayesian posterior probability on the depth map we show a number of experiments which demonstrate more robust results in comparison with state of the art work in a broader scope our representation can be viewed as a two level inhomogeneous mrf model which is applicable to general shape from x problems our study is an attempt to revisit marr s idea marr and freeman 1982 of computing the 2frac12d sketch from primal sketch in a companion paper barbu and zhu 2005 we study shape from stereo based on a similar two level generative sketch representation

asymptotic cohomological functions on projective varieties we consider certain cohomological invariants called asymptotic cohomological functions which are associated to irreducible projective varieties asymptotic cohomological functions are generalizations of the concept of the volume of a line bundle the asymptotic growth of the number of global sections to higher cohomology we establish that they give a notion invariant under the numerical equivalence of divisors and extend uniquely to continuous functions on the real neron severi space to illustrate the theory we work out these invariants for abelian varieties smooth surfaces and certain homogeneous spaces

an interactive algorithm for solving multiple objective integer linear programming problems abstract we propose a reference direction based interactive algorithm to solve multiple objective integer linear programming moilp problems at each iteration of the solution procedure the algorithm finds weak nondominated solutions to the relaxed moilp problem only at certain iterations if the dm so desires an additional mixed integer programming problem is solved to find an integer weak nondominated solution which is close to the current continuous weak nondominated solution to the relaxed moilp problem in the proposed algorithm dm has to provide only the reference point at each iteration no special software is required to implement the proposed algorithm the algorithm is illustrated with an example

a review of interactive methods for multiobjective integer and mixed integer programming this paper makes a review of interactive methods devoted to multiobjective integer and mixed integer programming moip momip problems the basic concepts concerning the characterization of the non dominated solution set are first introduced followed by a remark about non interactive methods vs interactive methods then we focus on interactive moip momip methods including their characterization according to the type of preference information required from the decision maker the computing process used to determine non dominated solutions and the interactive protocol used to communicate with the decision maker we try to draw out some contrasts and similarities of the different types of methods

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

asymptotic cohomological functions of toric divisors we study functions on the class group of a toric variety measuring the rates of growth of the cohomology groups of multiples of divisors we show that these functions are piecewise polynomial with respect to finite polyhedral chamber decompositions as applications we express the self intersection number of a t cartier divisor as a linear combination of the volumes of the bounded regions in the corresponding hyperplane arrangement and prove an asymptotic converse to serre vanishing

using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems we propose an interactive approach for multiple objective integer linear programming moilp problems that combines the use of the tchebycheff metric with cutting plane techniques at each interaction the method computes the nondominated solution for the moilp problem that is closest to a reference point according to the tchebycheff metric the information provided by the decision maker in each dialogue phase is used to adjust the next reference point through a sensitivity analysis stage cutting plane techniques enable the method to take advantage of computations performed at previous iterations to solve the next scalarizing integer program we address both theoretical issues and the computational implementation

an interactive fuzzy satisficing method for large scale multiobjective 0 1 programming problems with fuzzy parameters through genetic algorithms abstract in this paper by considering the experts imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective block angular 0 1 programming problems involving fuzzy numbers are formulated using the level sets of fuzzy numbers the corresponding nonfuzzy multiobjective 0 1 programming problem is introduced and an extended pareto optimality concept is defined for the multiobjective 0 1 programming problem the fuzzy goal of the decision maker for each objective function quantified by eliciting the corresponding membership function is considered since the decision maker must select a compromise or satisficing solution from the extended pareto optimal solution set including an infinite number of elements in general an interactive fuzzy satisficing method through genetic algorithms for deriving a satisficing solution for the decision maker from an extended pareto optimal solution set is presented then for fixed and reference membership levels the corresponding extended pareto optimal solution can be obtained by solving a minimax problem with block angular structure in order to solve the minimax problem efficiently we adopt a genetic algorithm with decomposition procedures finally both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments

seshadri constants diophantine approximation and roth s theorem for arbitrary varieties in this paper we associate an invariant alpha x l to an algebraic point x on an algebraic variety x with an ample line bundle l the invariant alpha measures how well x can be approximated by rational points on x with respect to the height function associated to l we show that this invariant is closely related to the seshadri constant epsilon x l measuring local positivity of l at x and in particular that roth s theorem on mathbb p 1 generalizes as an inequality between these two invariants valid for arbitrary projective varieties

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

solving zero one multiple objective programs through implicit enumeration abstract research on algorithms designed to solve zero one multiple objective linear programs has been rather limited this paper presents a solution procedure for these problems based on the concept of implicit enumeration computational experience is reported and analyzed advantages disadvantages and extensions of the algorithm are discussed

an algorithm for the bi criterion integer programming problem abstract we specify a variation of the weighting method for multi criterion optimization which determines nondominated solutions to the bi criterion integer programming problem the technique makes use of imposed constraints based on nondominated points for the bi criterion case we develop an algorithm which finds all nondominated points by solving a sequence of single criterion integer programming problems we present computational results for the linear 0 1 case and discuss the extension of our algorithm to the general multi criterion integer programming problem

a nadel vanishing theorem via injectivity theorems the purpose of this paper is to establish nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we generalize kollar s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics by making use of the theory of harmonic integrals moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles

an overview of techniques for solving multiobjective mathematical programs multiobjective mathematical programming has been one of the fastest growing areas of or ms during the last 15 years this paper presents some reasons for the rapidly growing increase in interest in multiobjective mathematical programming a discussion of the advantages and disadvantages of the three general approaches articulation of the decision maker s preference structure over the multiple objectives prior to during or after the optimization towards multiobjective mathematical programming a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming and a discussion of important areas for further research the overview concentrates on those techniques which require an articulation of the decision maker s preference structure either during or after the optimization since these are the areas where most of the recent research has been conducted it differs from previous overviews in that in addition to the timing of the elicited preference informa

an algorithm for optimizing a linear function over an integer efficient set optimizing a linear function over the efficient set of a multiobjective integer linear programming moilp problem is a topic of unquestionable practical as well as mathematical interest within the field of multiple criteria decision making as known those problems are particularly difficult to deal with due to the discrete nature of the efficient set which is not explicitly known nor a suitable implicit description is available in this work an exact algorithm is presented to optimize a linear function over the efficient set of a moilp the approach here proposed defines a sequence of progressively more constrained single objective integer problems that successively eliminates undesirable points from further consideration the algorithm has been coded in c sharp using cplex solver and computational experiments have been undertaken in order to analyze performance properties of the algorithm over different problem instances randomly generated

a class of practical interactive branch and bound algorithms for multicriteria integer programming abstract a practical interactive solution approach to multicriteria integer programming problems is developed the problem is solved by a branch and bound method that employs the zionts and wallenius procedure 23 for solving the multicriteria linear programming problem the development of algorithms for multicriteria decision problems itself is a multicriteria problem which involves the simultaneous minimization of the number of questions asked of the decision maker and the solution time two branch and bound algorithms that follow different search strategies to meet different levels of these criteria have been developed further two families of hybrid algorithms that incorporate a combination of the strategies of the two algorithms have also been developed strategies for the exploration of the decision maker s preference structure are discussed computational experience with the algorithms is presented the class of algorithms represents a collection of viable solution strategies applicable to a variety of decision making styles