multibody structure and motion segmentation by branch and bound model selection an efficient and robust framework is proposed for two view multiple structure and motion segmentation of unknown number of rigid objects the segmentation problem has three unknowns namely the object memberships the corresponding fundamental matrices and the number of objects to handle this otherwise recursive problem hypotheses for fundamental matrices are generated through local sampling once the hypotheses are available a combinatorial selection problem is formulated to optimize a model selection cost which takes into account the hypotheses likelihoods and the model complexity an explicit model for outliers is also added for robust segmentation the model selection cost is minimized through the branch and bound technique of combinatorial optimization the proposed branch and bound approach efficiently searches the solution space and guaranties optimality over the current set of hypotheses the efficiency and the guarantee of optimality of the method is due to its ability to reject solutions without explicitly evaluating them the proposed approach was validated with synthetic data and segmentation results are presented for real images

a more efficient branch and bound algorithm for feature selection abstract an algorithm is presented to be able to select the globally optimal subset of d features from a larger d feature set this is a fundamental problem in statistical pattern recognition and combinatorial optimization exhaustive enumeration is computationally unfeasible in most applications this algorithm dynamically searches for the globally optimal solution on a minimum solution tree which is a subtree of the solution tree used in the traditional branch and bound algorithm the new algorithm is compared theoretically with the branch and bound algorithm the analysis and the experimental results show that it is more efficient than the traditional algorithm

segmentation of range images as the search for geometric parametric models segmentation of range images has long been considered in computer vision as an important but extremely difficult problem in this paper we present a new paradigm for the segmentation of range images into piecewise continuous surfaces data aggregation is performed via model recovery in terms of variable order bi variate polynomials using iterative regression model recovery is initiated independently in regularly placed seed regions in the image all the recovered models are potential candidates for the final description of the data selection of the models is defined as a quadratic boolean problem and the solution is sought by the wta winner takes all technique which turns out to be a good compromise between the speed of computation and the accuracy of the solution the overall efficiency of the method is achieved by combining model recovery and model selection in an iterative way partial recovery of the models is followed by the selection optimization procedure and only the best models are allowed to develop further

a tool for the analysis of quasi newton methods with application to unconstrained minimization the bfgs update formula is shown to have an important property that is inde pendent of the algorithmic context of the update and that is relevant to both constrained and unconstrained optimization the bfgs method for unconstrained optimization using a variety of line searches including backtracking is shown to be globally and superlinearly convergent on uniformly convex problems the analysis is particularly simple due to the use of some new tools introduced in this paper

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

noncommutative instantons and twistor transform recently n nekrasov and a schwarz proposed a modification of the adhm construction of instantons which produces instantons on a noncommutative deformation of 4 in this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces we exhibit one to one correspondences between three classes of objects framed bundles on a noncommutative 2 certain complexes of sheaves on a noncommutative 3 and the modified adhm data the modified adhm construction itself is interpreted in terms of a noncommutative version of the twistor transform we also prove that the moduli space of framed bundles on the noncommutative 2 has a natural hyperkahler metric and is isomorphic as a hyperkahler manifold to the moduli space of framed torsion free sheaves on the commutative 2 the natural complex structures on the two moduli spaces do not coincide but are related by an so 3 rotation finally we propose a construction of instantons on a more general noncommutative 4 than the one considered by nekrasov and schwarz a q deformed 4

region oriented compression of color images using fuzzy inference and fast merging a new region based lossy compression scheme for color images is proposed the segmentation method belongs to the split and merge category splitting is carried out using the watershed transform in the merging stage a fuzzy color preserving rule based system and a novel one dimensional graph structure are introduced to provide accurate results with reduced computational complexity the compression part is based on the shape adaptive dct with dc correction method the quantization matrices used have been designed according to the properties of the employed transform promising perceptual results for the low bit rate range compared to previously reported compression methods have also been reported

multistage branch and bound merging for planar surface segmentation in disparity space an iterative split and merge framework for the segmentation of planar surfaces in the disparity space is presented disparity of a scene is modeled by approximating various surfaces in the scene to be planar in the split phase the number of planar surfaces along with the underlying plane parameters is assumed to be known from the initialization or from the previous merge phase based on these parameters planar surfaces in the disparity image are labeled to minimize the residuals between the actual disparity and the modeled disparity the labeled planar surfaces are separated into spatially continuous regions which are treated as candidates for the merging that follows the regions are merged together under a maximum variance constraint while maximizing the merged area a multistage branch and bound algorithm is proposed to carry out this optimization efficiently each stage of the branch and bound algorithm separates a planar surface from the set of spatially continuous regions the multistage merging estimates the number of planar surfaces and their labeling the splitting and the multistage merging is repeated till convergence is reached or satisfactory results are achieved experimental results are presented for variety of stereo image data

motion competition a variational approach to piecewise parametric motion segmentation we present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence our model is based on a conditional probability for the spatio temporal image gradient given a particular velocity model and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length exploiting the bayesian framework we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions the resulting functional can be interpreted as an extension of the mumford shah functional from intensity segmentation to motion segmentation in contrast to most alternative approaches the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set we propose two different representations of this motion boundary an explicit spline based implementation which can be applied to the motion based tracking of a single moving object and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects numerical results both for simulated ground truth experiments and for real world sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion

mdl based segmentation and motion modeling in a long image sequence of scene with multiple independently moving objects this paper presents a method for spatiotemporal segmentation of long image sequences of scenes which include multiple independently moving objects based on the minimum description length mdl principle first a family of motion models is constructed each of which corresponds to a physically meaningful motion such as translation with constant velocity or a combination of translation and rotation then the motion description length is formulated when an object changes the type of the motion or a new part of an object appears the corresponding temporal or spatial segmentation is carried out ambiguous segmentation of two consecutive images can be resolved by minimizing the motion description length in a long sequence of images experiments on several real image sequences show the validity of our method

mdpe a very robust estimator for model fitting and range image segmentation in this paper we propose a novel and highly robust estimator called mdpe1 maximum density power estimator this estimator applies nonparametric density estimation and density gradient estimation techniques in parametric estimation model fitting mdpe optimizes an objective function that measures more than just the size of the residuals both the density distribution of data points in residual space and the size of the residual corresponding to the local maximum of the density distribution are considered as important characteristics in our objective function mdpe can tolerate more than 85 outliers compared with several other recently proposed similar estimators mdpe has a higher robustness to outliers and less error variance we also present a new range image segmentation algorithm based on a modified version of the mdpe quick mdpe and its performance is compared to several other segmentation methods segmentation requires more than a simple minded application of an estimator no matter how good that estimator is our segmentation algorithm overcomes several difficulties faced with applying a statistical estimator to this task

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

an analysis of reduced hessian methods for constrained optimization we study the convergence properties of reduced hessian successive quadratic programming for equality constrained optimization the method uses a backtracking line search and updates an approximation to the reduced hessian of the lagrangian by means of the bfgs formula two merit functions are considered for the line search thel1 function and the fletcher exact penalty function we give conditions under which local and superlinear convergence is obtained and also prove a global convergence result the analysis allows the initial reduced hessian approximation to be any positive definite matrix and does not assume that the iterates converge or that the matrices are bounded the effects of a second order correction step a watchdog procedure and of the choice of null space basis are considered this work can be seen as an extension to reduced hessian methods of the well known results of powell 1976 for unconstrained optimization

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

a discrete particle swarm optimization method for feature selection in binary classification problems abstract this paper investigates the feature subset selection problem for the binary classification problem using logistic regression model we developed a modified discrete particle swarm optimization pso algorithm for the feature subset selection problem this approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset we compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets the results show that the proposed discrete pso algorithm is competitive in terms of both classification accuracy and computational performance

projective reconstruction and invariants from multiple images this correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views and the computation of projective invariants of these configurations from their images a basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs it is proven that once the epipolar geometry is known the configurations of many geometric structures for instance sets of points or lines are determined up to a collineation of projective 3 space spl pscrsup 3 by their projection in two independent images this theorem is the key to a method for the computation of invariants of the geometry invariants of six points in spl pscrsup 3 and of four lines in spl pscrsup 3 are defined and discussed an example with real images shows that they are effective in distinguishing different geometrical configurations since the fundamental matrix is a basic tool in the computation of these invariants new methods of computing the fundamental matrix from seven point correspondences in two images or six point correspondences in three images are given

soft fuzzy rough sets for robust feature evaluation and selection the fuzzy dependency function proposed in the fuzzy rough set model is widely employed in feature evaluation and attribute reduction it is shown that this function is not robust to noisy information in this paper as datasets in real world applications are usually contaminated by noise robustness of data analysis models is very important in practice in this work we develop a new model of fuzzy rough sets called soft fuzzy rough sets which can reduce the influence of noise we discuss the properties of the model and construct a new dependence function from the model then we use the function to evaluate and select features the presented experimental results show the effectiveness of the new model

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

interacting geometric priors for robust multimodel fitting recent works on multimodel fitting are often formulated as an energy minimization task where the energy function includes fitting error and regularization terms such as low level spatial smoothness and model complexity in this paper we introduce a novel energy with high level geometric priors that consider interactions between geometric models such that certain preferred model configurations may be induced we argue that in many applications such prior geometric properties are available and should be fruitfully exploited for example in surface fitting to point clouds the building walls are usually either orthogonal or parallel to each other our proposed energy function is useful in dealing with unknown distributions of data errors and outliers which are often the factors leading to biased estimation furthermore the energy can be efficiently minimized using the expansion move method we evaluate the performance on several vision applications using real data sets experimental results show that our method outperforms the state of the art methods without significant increase in computation

energy based geometric multi model fitting geometric model fitting is a typical chicken egg problem data points should be clustered based on geometric proximity to models whose unknown parameters must be estimated at the same time most existing methods including generalizations of ransac greedily search for models with most inliers within a threshold ignoring overall classification of points we formulate geometric multi model fitting as an optimal labeling problem with a global energy function balancing geometric errors and regularity of inlier clusters regularization based on spatial coherence on some near neighbor graph and or label costs is np hard standard combinatorial algorithms with guaranteed approximation bounds e g expansion can minimize such regularization energies over a finite set of labels but they are not directly applicable to a continuum of labels e g mathcal r 2 in line fitting our proposed approach pearl combines model sampling from data points as in ransac with iterative re estimation of inliers and models parameters based on a global regularization functional this technique efficiently explores the continuum of labels in the context of energy minimization in practice pearl converges to a good quality local minimum of the energy automatically selecting a small number of models that best explain the whole data set our tests demonstrate that our energy based approach significantly improves the current state of the art in geometric model fitting currently dominated by various greedy generalizations of ransac

the residue complex of a noncommutative graded algebra where x rx x is the set of points of dimension q the q skeleton q qy1 and k x is an injective hull of the residue field k x the coboundary a operator d k x a k y is nonzero precisely when y is an immediate a a w x specialization of x for a discussion of the commutative theory see rd w x and ye2 in this paper we propose a definition of the residue complex r of a noncommutative noetherian graded k algebra a s k a a 1 2 we begin in section 1 with the generalized auslander gorenstein a g condition this condition can be checked whenever a has a dualizing complex if a is gorenstein i e has finite injective dimension it reduces

geometric information criterion for model selection in building a 3 d model of the environment from image and sensor data one must fit to the data an appropriate class of models which can be regarded as a parametrized manifold or geometric model defined in the data space in this paper we present a statistical framework for detecting degeneracies of a geometric model by evaluating its predictive capability in terms of the expected residual and derive the geometric aic we show that it allows us to detect singularities in a structure from motion analysis without introducing any empirically adjustable thresholds we illustrate our approach by simulation examples we also discuss the application potential of this theory for a wide range of computer vision and robotics problems

fast branch bound algorithms for optimal feature selection a novel search principle for optimal feature subset selection using the branch bound method is introduced thanks to a simple mechanism for predicting criterion values a considerable amount of time can be saved by avoiding many slow criterion evaluations we propose two implementations of the proposed prediction mechanism that are suitable for use with nonrecursive and recursive criterion forms respectively both algorithms find the optimum usually several times faster than any other known branch bound algorithm as the algorithm computational efficiency is crucial due to the exponential nature of the search problem we also investigate other factors that affect the search performance of all branch bound algorithms using a set of synthetic criteria we show that the speed of the branch bound algorithms strongly depends on the diversity among features feature stability with respect to different subsets and criterion function dependence on feature set size we identify the scenarios where the search is accelerated the most dramatically finish in linear time as well as the worst conditions we verify our conclusions experimentally on three real data sets using traditional probabilistic distance criteria

a general branch and bound formulation for understanding and synthesizing and or tree search procedures citing the confusing statements in the ai literature concerning the relationship between branch and bound b b and heuristic search procedures were present a simple and general formulation of b b which should help dispel much of the confusion we illustrate the utility of the formulation by showing that through it some apparently very different algorithms for searching and or trees reveal the specific nature of their similarities and differences in addition to giving new insights into the relationships among some ai search algorithms the general formulation also provides suggestions on how existing search procedures may be varied to obtain new algorithms

joint segmentation of collectively moving objects using a bag of words model and level set evolution in scenes with collectively moving objects to disregard the individual objects and take the entire group into consideration for motion characterization is a promising approach with wide application prospects in contrast to studies on the segmentation of independently moving objects our purpose is to construct a segmentation of these objects to characterize their motions at a macroscopic level in general the collectively moving objects in a group have very similar motion behavior with their neighbors and appear as a kind of global collective motion this paper presents a joint segmentation approach for these collectively moving objects in our model we extract these macroscopic movement patterns based on optical flow field sequences specifically a group of collectively moving objects correspond to a region where the optical flow field has high magnitude and high local direction coherence as a result our problem can be addressed by identifying these coherent optical flow field regions the segmentation is performed through the minimization of a variational energy functional derived from the bayes classification rule specifically we use a bag of words model to generate a codebook as a collection of prototypical optical flow patterns and the class conditional probability density functions for different regions are determined based on these patterns finally the minimization of our proposed energy functional results in the gradient descent evolution of segmentation boundaries which are implicitly represented through level sets the application of our proposed approach is to segment and track multiple groups of collectively moving objects in a large variety of real world scenes

motion estimation with quadtree splines this paper presents a motion estimation algorithm based on a new multiresolution representation the quadtree spline this representation describes the motion field as a collection of smoothly connected patches of varying size where the patch size is automatically adapted to the complexity of the underlying motion the topology of the patches is determined by a quadtree data structure and both split and merge techniques are developed for estimating this spatial subdivision the quadtree spline is implemented using another novel representation the adaptive hierarchical basis spline and combines the advantages of adaptively sized correlation windows with the speedups obtained with hierarchical basis preconditioners results are presented on some standard motion sequences

invariant optimal feature selection a distance discriminant and feature ranking based solution the goal of feature selection is to find the optimal subset consisting of m features chosen from the total n features one critical problem for many feature selection methods is that an exhaustive search strategy has to be applied to seek the best subset among all the possible nm feature subsets which usually results in a considerably high computational complexity the alternative suboptimal feature selection methods provide more practical solutions in terms of computational complexity but they cannot promise that the finally selected feature subset is globally optimal we propose a new feature selection algorithm based on a distance discriminant fsdd which not only solves the problem of the high computational costs but also overcomes the drawbacks of the suboptimal methods the proposed method is able to find the optimal feature subset without exhaustive search or branch and bound algorithm the most difficult problem for optimal feature selection the search problem is converted into a feature ranking problem following rigorous theoretical proof such that the computational complexity can be greatly reduced the proposed method is invariant to the linear transformation of data when a diagonal transformation matrix is applied fsdd was compared with relieff and mrmrmid based on mutual information on 8 data sets the experiment results show that fsdd outperforms the other two methods and is highly efficient

motion based object segmentation and estimation using the mdl principle there are increasing demands for ultralow bit rate video image transmission we present a new formulation of moving object segmentation and motion estimation to quantify the potential gain in using object oriented motion compensation in image sequence coding motivated by real valued parameter estimation required in object oriented motion compensated video source coding a framework motivated by rissanen s 1983 minimum description length mdl principle is proposed to more tightly couple motion estimation and object segmentation algorithms to the overall objective of minimizing source bit rate a new objective function is constructed and a suboptimal procedure to segment and estimate moving objects in a scene is proposed each object is represented by chain coded block boundaries affine motion parameters and motion compensated prediction error a number of experimental comparisons between block and object oriented coding schemes suggests a significant potential coding gain using object oriented motion compensated coding

rings with auslander dualizing complexes abstract a ring with an auslander dualizing complex is a generalization of an auslander gorenstein ring we show that many results which hold for auslander gorenstein rings also hold in the more general setting on the other hand we give criteria for existence of auslander dualizing complexes which show these occur quite frequently the most powerful tool we use is the local duality theorem for connected graded algebras over a field filtrations allow the transfer of results to nongraded algebras we also prove some results of a categorical nature most notably the functoriality of rigid dualizing complexes

an improvement on floating search algorithms for feature subset selection a new improved forward floating selection iffs algorithm for selecting a subset of features is presented our proposed algorithm improves the state of the art sequential forward floating selection algorithm the improvement is to add an additional search step called replacing the weak feature to check whether removing any feature in the currently selected feature subset and adding a new one at each sequential step can improve the current feature subset our method provides the optimal or quasi optimal close to optimal solutions for many selected subsets and requires significantly less computational load than optimal feature selection algorithms our experimental results for four different databases demonstrate that our algorithm consistently selects better subsets than other suboptimal feature selection algorithms do especially when the original number of features of the database is large

socp relaxation bounds for the optimal subset selection problem applied to robust linear regression abstract this paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion with an special emphasis on applications to computing the least trimmed squares estimator ltse for robust regression the computation of the ltse is a challenging subset selection problem involving a nonlinear program with continuous and binary variables linked in a highly nonlinear fashion the selection of a globally optimal subset using the branch and bound bb algorithm is limited to problems in very low dimension typically d 5 as the complexity of the problem increases exponentially with d we introduce a bold pruning strategy in the bb algorithm that results in a significant reduction in computing time at the price of a negligeable accuracy lost the novelty of our algorithm is that the bounds at nodes of the bb tree come from pseudo convexifications derived using a linearization technique with approximate bounds for the nonlinear terms the approximate bounds are computed solving an auxiliary semidefinite optimization problem we show through a computational study that our algorithm performs well in a wide set of the most difficult instances of the ltse problem

a comparative study of suboptimal branch and bound algorithms abstract the branch and bound algorithm is widely known as an efficient approach for selecting optimal feature subsets if the optimality of the solution is allowed to be compromised it is possible to further improve the search speed of the branch and bound algorithm this paper studies the look ahead search strategy which can eliminate many solutions deemed to be suboptimal early in the branch and bound search we propose ways to incorporate the look ahead search scheme into four major branch and bound algorithms namely the basic branch and bound algorithm the ordered branch and bound algorithm the fast branch and bound algorithm and the adaptive branch and bound algorithm a comparative study of the look ahead scheme in terms of the computational cost and the solution quality on these suboptimal branch and bound algorithms is carried out on real data sets furthermore we test the feasible use of suboptimal branch and bound algorithms on a high dimensional data set and compare its performance with other well known suboptimal feature selection algorithms

weak proregularity weak stability and the noncommutative mgm equivalence abstract let a be a commutative ring and let a be a finitely generated ideal in it it is known that a necessary and sufficient condition for the derived a torsion and a adic completion functors to be nicely behaved is the weak proregularity of a in particular the mgm equivalence holds because weak proregularity is defined in terms of elements of the ring it involves limits of koszul complexes it is not suitable for noncommutative ring theory in this paper we introduce a new condition on a torsion class t in a module category weak stability our first main theorem says that in the commutative case the ideal a is weakly proregular if and only if the corresponding torsion class t is weakly stable we then study weak stability of torsion classes in module categories over noncommutative rings there are three main theorems in this context for a torsion class t that is weakly stable quasi compact and finite dimensional the right derived torsion functor is isomorphic to a left derived tensor functor the noncommutative mgm equivalence that holds under the same assumptions on t a theorem about symmetric derived torsion for complexes of bimodules this last theorem is a generalization of a result of van den bergh from 1997 and corrects an error in a paper of yekutieli zhang from 2003

existence theorems for dualizing complexes over non commutative graded and filtered rings abstract in this note we prove existence theorems for dualizing complexes over graded and filtered rings thereby generalizing some results by zhang yekutieli and jorgensen

feature subset selection using separability index matrix effective feature subset selection fss is an important step when designing engineering systems that classify complex data in real time the electromyographic emg signal based walking assistance system is a typical system that requires an efficient computational architecture for classification the performance of such a system depends largely on a criterion function that assesses the quality of selected feature subsets however many well known conventional criterion functions use less relevant features for classification or they have a high computational cost here we propose a new criterion function that provides more effective fss the proposed criterion function known as a separability index matrix sim provides features pertinent to the classification task and a very low computational cost this new function produces to a simple feature selection algorithm when combined with the forward search paradigm we performed extensive experimental comparisons in terms of classification accuracy and computational costs to confirm that the proposed algorithm outperformed other filter type feature selection methods that are based on various distance measures including inter intra euclidean mahalanobis and bhattacharyya distances we then applied the proposed method to a gait phase recognition problem in our emg signal based walking assistance system we demonstrated that the proposed method performed competitively when compared with other wrapper type feature selection methods in terms of class separability and recognition rate

rigid complexes via dg algebras let a be a commutative ring b a commutative a algebra and m a complex of b modules we begin by constructing the square sq b a m which is also a complex of b modules the squaring operation is a quadratic functor and its construction requires differential graded dg algebras if there exists an isomorphism p m sq b a m then the pair m p is called a rigid complex over b relative to a there are some finiteness conditions there is an obvious notion of rigid morphism between rigid complexes we establish several properties of rigid complexes including their uniqueness existence under some extra hypothesis and formation of pullbacks f b m p resp f m p along a finite resp essentially smooth ring homomorphism f b c in the subsequent paper rigid dualizing complexes over commutative rings we consider rigid dualizing complexes over commutative rings building on the results of the present paper the project culminates in our paper rigid dualizing complexes and perverse sheaves on schemes where we give a comprehensive version of grothendieck duality for schemes the idea of rigid complexes originates in noncommutative algebraic geometry and is due to van den bergh 1997

affine noetherian pi rings have enough clans abstract a noetherian pi ring which is affine over the centre can be localized at every finite or infinite link connectivity component p in the sense that the multiplicative set b p satisfies the ore condition and determines p

homological integral of hopf algebras the left and right homological integrals are introduced for a large class of infinite dimensional hopf algebras using the homological integrals we prove a version of maschke s theorem for infinite dimensional hopf algebras the generalization of maschke s theorem and homological integrals are the keys to studying noetherian regular hopf algebras of gelfand kirillov dimension one

efficient algorithms for robust feature matching abstract one of the basic building blocks in any point based registration scheme involves matching feature points that are extracted from a sensed image to their counterparts in a reference image this leads to the fundamental problem of point matching given two sets of points find the affine transformation that transforms one point set so that its distance from the other point set is minimized because of measurement errors and the presence of outlying data points it is important that the distance measure between the two point sets be robust to these effects we measure distances using the partial hausdorff distance point matching can be a computationally intensive task and a number of theoretical and applied approaches have been proposed for solving this problem in this paper we present two algorithmic approaches to the point matching problem in an attempt to reduce its computational complexity while still providing a guarantee of the quality of the final match our first method is an approximation algorithm which is loosely based on a branch and bound approach due to huttenlocher and rucklidge technical report 1321 dept of computer science cornell university ithaca 1992 proc ieee conf on computer vision and pattern recognition new york 1993 pp 705 706 we show that by varying the approximation error bounds it is possible to achieve a tradeoff between the quality of the match and the running time of the algorithm our second method involves a monte carlo method for accelerating the search process used in the first algorithm this algorithm operates within the framework of a branch and bound procedure but employs point to point alignments to accelerate the search we show that this combination retains many of the strengths of branch and bound search but provides significantly faster search times by exploiting alignments with high probability this method succeeds in finding an approximately optimal match we demonstrate the algorithms performances on both synthetically generated data points and actual satellite images

dualizing complexes over noncommutative graded algebras the motivation for the work presented in this paper was two questions posed by m artin let a be a d dimensional regular graded algebra over the field k with augmentation ideal m see def 4 13 denote by hi a resp hi a the dth left resp right local cohomology of a at the ideal m i e hi a lim extd a m a and similarly for hi a as left modules and as right modules hi a and h a are both isomorphic to a hom a k up to a twist in degrees all operations are taking place in the graded category

practical update criteria for reduced hessian sqp global analysis in this paper a new update criterion is proposed to improve the nocedal overton update criterion for reduced hessian successive quadratic programming sqp global and r linear convergence is proved for the new criterion and the nocedal overton criterion using nonorthogonal basis matrices which allow efficient implementations of the reduced hessian sqp for solving large scale equality constrained problems

calibration and empirical bayes variable selection for the problem of variable selection for the normal linear model selection criteria such as aic c p bic and ric have fixed dimensionality penalties such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical bayes formulation based on this calibration we propose empirical bayes selection criteria that use hyperparameter estimates instead of fixed choices for obtaining these estimates both marginal and conditional maximum likelihood methods are considered as opposed to traditional fixed penalty criteria these empirical bayes criteria have dimensionality penalties that depend on the data their performance is seen to approximate adaptively the performance of the best fixed penalty criterion across a variety of orthogonal and nonorthogonal set ups including wavelet regression empirical bayes shrinkage estimators of the selected coefficients are also proposed

multiple motion segmentation with level sets segmentation of motion in an image sequence is one of the most challenging problems in image processing while at the same time one that finds numerous applications to date a wealth of approaches to motion segmentation have been proposed many of them suffer from the local nature of the models used global models such as those based on markov random fields perform in general better in this paper we propose a new approach to motion segmentation that is based on a global model the novelty of the approach is twofold first inspired by recent work of other researchers we formulate the problem as that of region competition but we solve it using the level set methodology the key features of a level set representation as compared to active contours often used in this context are its ability to handle variations in the topology of the segmentation and its numerical stability the second novelty of the paper is the formulation in which unlike in many other motion segmentation algorithms we do not use intensity boundaries as an accessory the segmentation is purely based on motion this permits accurate estimation of motion boundaries of an object even when its intensity boundaries are hardly visible since occasionally intensity boundaries may prove beneficial we extend the formulation to account for the coincidence of motion and intensity boundaries in addition we generalize the approach to multiple motions we discuss possible discretizations of the evolution pde equations and we give details of an initialization scheme so that the results could be duplicated we show numerous experimental results for various formulations on natural images with either synthetic or natural motion

two view motion segmentation with model selection and outlier removal by ransac enhanced dirichlet process mixture models we propose a novel motion segmentation algorithm based on mixture of dirichlet process mdp models in contrast to previous approaches we consider motion segmentation and its model selection regarding to the number of motion models as an inseparable problem our algorithm can simultaneously infer the number of motion models estimate the cluster memberships of correspondences and identify the outliers the main idea is to use mdp models to fully exploit the geometric consistencies before making premature decisions about the number of motion models to handle outliers we incorporate ransac into the inference process of mdp models in the experiments we compare the proposed algorithm with naive ransac gpca and schindler s method on both synthetic data and real image data the experimental results show that we can handle more motions and have satisfactory performance in the presence of various levels of noise and outlier

residue complex for sklyanin algebras of dimension three we describe the residue complex for three dimensional sklyanin algebras which are the interesting special cases of quantum polynomial rings in three variables in particular we show that the multiplicities of the point modules in the residue complex are all one just as in the classical case of commutative polynomial rings in three variables we explain why the residue complex in the quantum case has the same multiplicities of point modules as that in the commutative case even if there are fewer point modules in the quantum case by pointing out two quantum anomalies

development and evaluation of fast branch and bound algorithm for feature matching based on line segments by extending the previously proposed geometric branch and bound algorithm with bounded alignment for point pattern matching the paper presents the development and evaluation of a new and fast algorithm for image registration based on line segments using synthetically generated data sets with randomly distributed line segments and hard test cases with highly symmetric line patterns as well as real remote sensing images the developed algorithm is shown to be computationally fast highly robust capable of handling severely corrupted data sets with considerable line segment position errors as well as significant fragmented and spurious line segments in the images to be matched

category level object segmentation by combining bag of words models with dirichlet processes and random fields this paper addresses the problem of accurately segmenting instances of object classes in images without any human interaction our model combines a bag of words recognition component with spatial regularization based on a random field and a dirichlet process mixture bag of words models successfully predict the presence of an object within an image however they can not accurately locate object boundaries random fields take into account the spatial layout of images and provide local spatial regularization yet as they use local coupling between image labels they fail to capture larger scale structures needed for object recognition these components are combined with a dirichlet process mixture it models images as a composition of regions each representing a single object instance gibbs sampling is used for parameter estimations and object segmentation our model successfully segments object category instances despite cluttered backgrounds and large variations in appearance and viewpoints the strengths and limitations of our model are shown through extensive experimental evaluations first we evaluate the result of two methods to build visual vocabularies second we show how to combine strong labeling segmented images with weak labeling images annotated with bounding boxes in order to limit the labeling effort needed to learn the model third we study the effect of different initializations we present results on four image databases including the challenging pascal voc 2007 data set on which we obtain state of the art results

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

automatic image segmentation by dynamic region merging this paper addresses the automatic image segmentation problem in a region merging style with an initially oversegmented image in which many regions or superpixels with homogeneous color are detected an image segmentation is performed by iteratively merging the regions according to a statistical test there are two essential issues in a region merging algorithm order of merging and the stopping criterion in the proposed algorithm these two issues are solved by a novel predicate which is defined by the sequential probability ratio test and the minimal cost criterion starting from an oversegmented image neighboring regions are progressively merged if there is an evidence for merging according to this predicate we show that the merging order follows the principle of dynamic programming this formulates the image segmentation as an inference problem where the final segmentation is established based on the observed image we also prove that the produced segmentation satisfies certain global properties in addition a faster algorithm is developed to accelerate the region merging process which maintains a nearest neighbor graph in each iteration experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm

simultaneous two view epipolar geometry estimation and motion segmentation by 4d tensor voting we address the problem of simultaneous two view epipolar geometry estimation and motion segmentation from nonstatic scenes given a set of noisy image pairs containing matches of n objects we propose an unconventional efficient and robust method 4d tensor voting for estimating the unknown n epipolar geometries and segmenting the static and motion matching pairs into n independent motions by considering the 4d isotropic and orthogonal joint image space only two tensor voting passes are needed and a very high noise to signal ratio up to five can be tolerated epipolar geometries corresponding to multiple rigid motions are extracted in succession only two uncalibrated frames are needed and no simplifying assumption such as affine camera model or homographic model between images other than the pin hole camera model is made our novel approach consists of propagating a local geometric smoothness constraint in the 4d joint image space followed by global consistency enforcement for extracting the fundamental matrices corresponding to independent motions we have performed extensive experiments to compare our method with some representative algorithms to show that better performance on nonstatic scenes are achieved results on challenging data sets are presented

a fitting model for feature selection with fuzzy rough sets a fuzzy rough set is an important rough set model used for feature selection it uses the fuzzy rough dependency as a criterion for feature selection however this model can merely maintain a maximal dependency function it does not fit a given dataset well and cannot ideally describe the differences in sample classification therefore in this study we introduce a new model for handling this problem first we define the fuzzy decision of a sample using the concept of fuzzy neighborhood then a parameterized fuzzy relation is introduced to characterize the fuzzy information granules using which the fuzzy lower and upper approximations of a decision are reconstructed and a new fuzzy rough set model is introduced this can guarantee that the membership degree of a sample to its own category reaches the maximal value furthermore this approach can fit a given dataset and effectively prevents samples from being misclassified finally we define the significance measure of a candidate attribute and design a greedy forward algorithm for feature selection twelve datasets selected from public data sources are used to compare the proposed algorithm with certain existing algorithms and the experimental results show that the proposed reduction algorithm is more effective than classical fuzzy rough sets especially for those datasets for which different categories exhibit a large degree of overlap

bayesian model estimation and selection for epipolar geometry and generic manifold fitting computer vision often involves estimating models from visual input sometimes it is possible to fit several different models or hypotheses to a set of data and a decision must be made as to which is most appropriate this paper explores ways of automating the model selection process with specific emphasis on the least squares problem of fitting manifolds in particular algebraic varieties e g lines algebraic curves planes etc to data points illustrated with respect to epipolar geometry the approach is bayesian and the contribution three fold first a new bayesian description of the problem is laid out that supersedes the author s previous maximum likelihood formulations this formulation will reveal some hidden elements of the problem second an algorithm mapsac is provided to obtain the robust map estimate of an arbitrary manifold third a bayesian model selection paradigm is proposed the bayesian formulation of the manifold fitting problem uncovers an elegant solution to this problem for which a new method gric for approximating the posterior probability of each putative model is derived this approximations bears some similarity to the penalized likelihoods used by aic bic and mdl however it is far more accurate in situations involving large numbers of latent variables whose number increases with the data this will be empirically and theoretically demonstrated

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

template based shell clustering using a line segment representation of data this paper presents the algorithms and experimental results for template based shell clustering when the datasets are represented by line segments compared with point datasets such representations have several advantages which include better scalability and noise immunity as well as the availability of orientation information using both synthetic and real world image datasets we have experimentally demonstrated that line segment based representations result in both better accuracy and better efficiency in shell clustering

a multilevel tabu search algorithm for the feature selection problem in biomedical data the automated analysis of patients biomedical data can be used to derive diagnostic and prognostic inferences about the observed patients many noninvasive techniques for acquiring biomedical samples generate data that are characterized by a large number of distinct attributes i e features and a small number of observed patients i e samples using these biomedical data to derive reliable inferences such as classifying a given patient as either cancerous or noncancerous requires that the ratio r of the number of samples to the number of features be within the range 5

u curve a branch and bound optimization algorithm for u shaped cost functions on boolean lattices applied to the feature selection problem this paper presents the formulation of a combinatorial optimization problem with the following characteristics i the search space is the power set of a finite set structured as a boolean lattice ii the cost function forms a u shaped curve when applied to any lattice chain this formulation applies for feature selection in the context of pattern recognition the known approaches for this problem are branch and bound algorithms and heuristics that explore partially the search space branch and bound algorithms are equivalent to the full search while heuristics are not this paper presents a branch and bound algorithm that differs from the others known by exploring the lattice structure and the u shaped chain curves of the search space the main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here several experiments with well known public data indicate the superiority of the proposed method to the sequential floating forward selection sffs which is a popular heuristic that gives good results in very short computational time in all experiments the proposed method got better or equal results in similar or even smaller computational time

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

spatio temporal segmentation based on region merging this paper proposes a technique for spatio temporal segmentation to identify the objects present in the scene represented in a video sequence this technique processes two consecutive frames at a time a region merging approach is used to identify the objects in the scene starting from an oversegmentation of the current frame the objects are formed by iteratively merging regions together regions are merged based on their mutual spatio temporal similarity we propose a modified kolmogorov smirnov test for estimating the temporal similarity the region merging process is based on a weighted directed graph two complementary graph based clustering rules are proposed namely the strong rule and the weak rule these rules take advantage of the natural structures present in the graph experimental results on different types of scenes demonstrate the ability of the proposed technique to automatically partition the scene into its constituent objects

a method to improve integer linear programming problem with branch and bound procedure abstract integer linear programming ilp problems are harder to solve than linear programming lp problems it doesn t work if try to round off the results of lp problems and claim they are the optimum solution the branch and bound b b is the popular method to solve ilp problems in this paper we propose a revised b b which is demonstrated to be more efficient most of time this method is extraordinarily useful when facing ilp problems with large differences between constraints and variables it could reduce the number of constraint and work efficiently when handling ilp problems with many constraints and less variables even if the ilp problems have fewer constraints but many variables we suggest using duality concept to interchange variables with constraints then the revised b b could be used to compute results very quickly

an a contrario decision framework for region based motion detection the aim of motion detection is to decide whether a given part of an image belongs to a moving object or to the static background this paper proposes an automatic decision rule for the detection of moving regions the proposed framework is derived from a perceptual grouping principle namely the helmholtz principle this principle basically states that perceptually relevant events are perceived because they deviate from a model of complete randomness detections are then said to be performed a contrario moving regions appear as low probability events in a model corresponding to the absence of moving objects in the scene a careful design of the events considered under the hypothesis of absence of moving objects results in a general and robust motion detection algorithm no posterior parameter tuning is necessary furthermore a confidence level is attached to each detected region

multimodal estimation of discontinuous optical flow using markov random fields the estimation of dense velocity fields from image sequences is basically an ill posed problem primarily because the data only partially constrain the solution it is rendered especially difficult by the presence of motion boundaries and occlusion regions which are not taken into account by standard regularization approaches in this paper the authors present a multimodal approach to the problem of motion estimation in which the computation of visual motion is based on several complementary constraints it is shown that multiple constraints can provide more accurate flow estimation in a wide range of circumstances the theoretical framework relies on bayesian estimation associated with global statistical models namely markov random fields the constraints introduced here aim to address the following issues optical flow estimation while preserving motion boundaries processing of occlusion regions fusion between gradient and feature based motion constraint equations deterministic relaxation algorithms are used to merge information and to provide a solution to the maximum a posteriori estimation of the unknown dense motion field the algorithm is well suited to a multiresolution implementation which brings an appreciable speed up as well as a significant improvement of estimation when large displacements are present in the scene experiments on synthetic and real world image sequences are reported

optimal image and video closure by superpixel grouping detecting independent objects in images and videos is an important perceptual grouping problem one common perceptual grouping cue that can facilitate this objective is the cue of contour closure reflecting the spatial coherence of objects in the world and their projections as closed boundaries separating figure from background detecting contour closure in images consists of finding a cycle of disconnected contour fragments that separates an object from its background searching the entire space of possible groupings is intractable and previous approaches have adopted powerful perceptual grouping heuristics such as proximity and co curvilinearity to constrain the search we introduce a new formulation of the problem by transforming the problem of finding cycles of contour fragments to finding subsets of superpixels whose collective boundary has strong edge support few gaps in the image our cost function a ratio of a boundary gap measure to area promotes spatially coherent sets of superpixels moreover its properties support a global optimization procedure based on parametric maxflow extending closure detection to videos we introduce the concept of spatiotemporal closure analogous to image closure we formulate our spatiotemporal closure cost over a graph of spatiotemporal superpixels our cost function is a ratio of motion and appearance discontinuity measures on the boundary of the selection to an internal homogeneity measure of the selected spatiotemporal volume the resulting approach automatically recovers coherent components in images and videos corresponding to objects object parts and objects with surrounding context providing a good set of multiscale hypotheses for high level scene analysis we evaluate both our image and video closure frameworks by comparing them to other closure detection approaches and find that they yield improved performance

definition and properties of lagrangian coherent structures from finite time lyapunov exponents in two dimensional aperiodic flows this paper develops the theory and computation of lagrangian coherent structures lcs which are defined as ridges of finite time lyapunov exponent ftle fields these ridges can be seen as finite time mixing templates such a framework is common in dynamical systems theory for autonomous and time periodic systems in which examples of lcs are stable and unstable manifolds of fixed points and periodic orbits the concepts defined in this paper remain applicable to flows with arbitrary time dependence and in particular to flows that are only defined computed or measured over a finite interval of time previous work has demonstrated the usefulness of ftle fields and the associated lcss for revealing the lagrangian behavior of systems with general time dependence however ridges of the ftle field need not be exactly advected with the flow the main result of this paper is an estimate for the flux across an lcs which shows that the flux is small and in most cases negligible for well defined lcss or those that rotate at a speed comparable to the local eulerian velocity field and are computed from ftle fields with a sufficiently long integration time under these hypotheses the structures represent nearly invariant manifolds even in systems with arbitrary time dependence the results are illustrated on three examples the first is a simplified dynamical model of a double gyre flow the second is surface current data collected by high frequency radar stations along the coast of florida and the third is unsteady separation over an airfoil in all cases the existence of lcss governs the transport and it is verified numerically that the flux of particles through these distinguished lines is indeed negligible

two view multibody structure and motion with outliers through model selection multibody structure and motion msam is the problem in establishing the multiple view geometry of several views of a 3d scene taken at different times where the scene consists of multiple rigid objects moving relative to each other we examine the case of two views the setting is the following given are a set of corresponding image points in two images which originate from an unknown number of moving scene objects each giving rise to a motion model furthermore the measurement noise is unknown and there are a number of gross errors which are outliers to all models the task is to find an optimal set of motion models for the measurements it is solved through monte carlo sampling careful statistical analysis of the sampled set of motion models and simultaneous selection of multiple motion models to best explain the measurements the framework is not restricted to any particular model selection mechanism because it is developed from a bayesian viewpoint different model selection criteria are seen as different priors for the set of moving objects which allow one to bias the selection procedure for different purposes

trajectory triangulation 3d reconstruction of moving points from a monocular image sequence we consider the problem of reconstructing the 3d coordinates of a moving point seen from a monocular moving camera i e to reconstruct moving objects from line of sight measurements only the task is feasible only when some constraints are placed on the shape of the trajectory of the moving point we coin the family of such tasks as trajectory triangulation we investigate the solutions for points moving along a straight line and along conic section trajectories we show that if the point is moving along a straight line then the parameters of the line and hence the 3d position of the point at each time instant can be uniquely recovered and by linear methods from at least five views for the case of conic shaped trajectory we show that generally nine views are sufficient for a unique reconstruction of the moving point and fewer views when the conic is of a known type like a circle in 3d euclidean space for which seven views are sufficient the paradigm of trajectory triangulation in general pushes the envelope of processing dynamic scenes forward thus static scenes become a particular case of a more general task of reconstructing scenes rich with moving objects where an object could be a single point

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

how easy is matching 2d line models using local search local search is a well established and highly effective method for solving complex combinatorial optimization problems here local search is adapted to solve difficult geometric matching problems matching is posed as the problem of finding the optimal many to many correspondence mapping between a line segment model and image line segments image data is assumed to be fragmented noisy and cluttered the algorithms presented have been used for robot navigation photo interpretation and scene understanding this paper explores how local search performs as model complexity increases image clutter increases and additional model instances are added to the image data expected run times to find optimal matches with 95 percent confidence are determined for 48 distinct problems involving six models nonlinear regression is used to estimate run time growth as a function of problem size both polynomial and exponential growth models are fit to the run time data for problems with random clutter the polynomial model fits better and growth is comparable to that for tree search for problems involving symmetric models and multiple model instances where tree search is exponential the polynomial growth model is superior to the exponential growth model for one search algorithm and comparable for another

a fast branch and bound algorithm for u curve feature selection abstract we introduce a fast branch and bound algorithm for optimal feature selection based on a u curve assumption for the cost function the u curve assumption which is based on the peaking phenomenon of the classification error postulates that the cost over the chains of the boolean lattice that represents the search space describes a u shaped curve the proposed algorithm is an improvement over the original algorithm for u curve feature selection introduced recently extensive simulation experiments are carried out to assess the performance of the proposed algorithm iubb comparing it to the original algorithm ubb as well as exhaustive search and generalized sequential forward search the results show that the iubb algorithm makes fewer evaluations and achieves better solutions under a fixed computational budget we also show that the iubb algorithm is robust with respect to violations of the u curve assumption we investigate the application of the iubb algorithm in the design of imaging w operators and in classification feature selection using the average mean conditional entropy mce as the cost function for the search

residue complexes over noncommutative rings abstract residue complexes were introduced by grothendieck in algebraic geometry these are canonical complexes of injective modules that enjoy remarkable functorial properties traces in this paper we study residue complexes over noncommutative rings these objects have a more intricate structure than in the commutative case since they are complexes of bimodules we develop methods to prove uniqueness existence and functoriality of residue complexes for a polynomial identity algebra over a field admitting a noetherian connected filtration we prove existence of the residue complex and describe its structure in detail

homological transcendence degree let d be a division algebra over a base field k the homological transcendence degree of d denoted by text htr d is defined to be the injective dimension of the algebra d otimes k d circ we show that text htr has several useful properties which the classical transcendence degree has we extend some results of resco rosenberg schofield and stafford and compute text htr for several classes of division algebras the main tool for the computation is van den bergh s rigid dualizing complex