object representation and recognition in shape spaces in this paper we describe a shape space based approach for invariant object representation and recognition in this approach an object and all its similarity transformed versions are identified with a single point in a high dimensional manifold called the shape space object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space this approach produced promising results in 2d object recognition experiments it is invariant to similarity transformations and is relatively insensitive to noise and occlusion potentially it can also be used for 3d object recognition

using polygons to recognize and locate partially occluded objects we present computer vision algorithms that recognize and locate partially occluded objects the scene may contain unknown objects that may touch or overlap giving rise to partial occlusion the algorithms revolve around a generate test paradigm the paradigm iteratively generates and tests hypotheses for compatibility with the scene until it identifies all the scene objects polygon representations of the object s boundary guide the hypothesis generation scheme choosing the polygon representation turns out to have powerful consequences in all phases of hypothesis generation and verification special vertices of the polygon called corners help detect and locate the model in the scene polygon moment calculations lead to estimates of the dissimilarity between scene and model corners and determine the model corner location in the scene an association graph represents the matches and compatibility constraints extraction of the largest set of mutually compatible matches from the association graph forms a model hypothesis using a coordinate transform that maps the model onto the scene the hypothesis gives the proposed model s location and orientation hypothesis verification requires checking for region consistency the union of two polygons and other polygon operations combine to measure the consistency of the hypothesis with the scene experimental results give examples of all phases of recognizing and locating the objects

global description of edge patterns using moments abstract shape recognition has traditionally been accomplished using well bounded segmented regions or their closed contours in this way the internal edge details of the objects are ignored there are cases such as in character recognition and in object recognition when patterns are not closed contours in this paper such patterns are defined as edge patterns and edge standard moments esm are developed which are invariant to location scale and rotation results of patterns matching with character recognition and polyhedral object recognition are presented

onset of chaotic kolmogorov flows resulting from interacting oscillatory modes on the basis of rigorous analysis supported by numerical computation a systematic study is presented to locate and examine chaotic kolmogorov flows resulting from the interaction of a basic steady state flow and oscillatory modes referenced to suitably chosen initial conditions of the kolmogorov flow model these oscillatory modes are derived from the equation linearized around the basic steady state flow the numerical experiments provide insight into the transition process from secondary self oscillation flows or secondary steady state flows to chaotic kolmogorov flows

a note on scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan abstract in a recent paper chen j s chen scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan european journal of operational research 190 2008 90 102 proposes a heuristic algorithm to deal with the problem scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan chen also provides computational results to demonstrate its effectiveness in this note we first show that the worst case performance bound of this heuristic algorithm is 2 then we show that there is no polynomial time approximation algorithm with a worst case performance bound less than 2 unless p np which implies that chen s heuristic algorithm is the best possible polynomial time approximation algorithm for the considered scheduling problem

learning shape metrics with monte carlo optimization abstract quantifying and modeling shape variation within a population identifying morphological contrasts across groups and categorizing individuals or objects according to morphological similarity are central problems in numerous domains of science and applications in this paper we present an approach to optimal shape categorization through a new family of metrics for shapes presented as a finite collection of labeled landmark points we develop a technique to learn metrics that optimally differentiate and categorize shapes using monte carlo optimization methods we discuss the theory and the practice of the methods and apply them to the analysis of synthetic data and the classification of multiple species of fruit flies based on the shape of their wings

classification of partially occluded objects using 3 point matching and distance transformation abstract recognition of partially occluded objects has been recently made possible by describing an object boundary with a sequence of local feature segments localized with control or dominant points and then matching the representations with those of a set of known reference shapes when part of the object boundary is being occluded contiguous intact feature segments will be used for identifying the object and distorted elements will be rejected in the matching process the main problem associated with this method is that the nature of occlusion may separate the object contour into discrete regions resulting in the degeneration of an individual representation into small isolated clusters reflecting only weak evidence on the object identity in this paper a new scheme capable of combining the isolated clusters for object classification is presented in essence curvature guided polygonal approximation is employed for detecting the dominant points of the boundaries a 3 point matching technique is developed for extracting cluster s of dominant points on an unknown boundary which matched against reference objects and to link up the scattered clusters to form a complete representation the chamfer 3 4 distance transform together with a quantitative measurement on the boundary covered by the matched dominant points is employed for calculating the similarity between the unknown and the reference contours the scheme has been successfully applied for recognizing multiple overlapped handtools in different sizes and orientations

a parallel algorithm for detecting dominant points on multiple digital curves abstract a new parallel algorithm is proposed for detecting corners of multiple planar curves or shapes this algorithm is based on an analysis of morphological residues and corner characteristics the method is different from traditional chain code based corner detection algorithms which associate with a chain coding and floating point computation for multiple objects in an image the proposed algorithm treats them uniformly and applies simultaneously on curves and shapes of multiple objects the experiments demonstrate that the algorithm can be effectively executed on an simd parallel computer a boundary constrained morphological method is presented for filling closed curves into shapes which are subsequently used for corner detection

population shape regression from random design data regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable and in particular it is applicable to the study of anatomical growth and shape change when the underlying process can be modeled by parameters in a euclidean space classical regression techniques hardle applied nonparametric regression 1990 wand and jones kernel smoothing 1995 are applicable and have been studied extensively however recent work suggests that attempts to describe anatomical shapes using flat euclidean spaces undermines our ability to represent natural biological variability fletcher et al ieee trans med imaging 23 8 995 1005 2004 grenander and miller q appl math 56 4 617 694 1998 in this paper we develop a method for regression analysis of general manifold valued data specifically we extend nadaraya watson kernel regression by recasting the regression problem in terms of frechet expectation although this method is quite general our driving problem is the study anatomical shape change as a function of age from random design image data we demonstrate our method by analyzing shape change in the brain from a random design dataset of mr images of 97 healthy adults ranging in age from 20 to 79 years to study the small scale changes in anatomy we use the infinite dimensional manifold of diffeomorphic transformations with an associated metric we regress a representative anatomical shape as a function of age from this population

on shape of plane elastic curves we study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending stretching or compressing line segments non uniformly along their extensions shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape preserving transformations the elastic properties of the curves are encoded in riemannian metrics on these spaces geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques the shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

on random tomography with unobservable projection angles we formulate and investigate a statistical inverse problem of a random tomographic nature where a probability density function on mathbb r 3 is to be recovered from observation of finitely many of its two dimensional projections in random and unobservable directions such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable the problem arises in single particle electron microscopy a powerful method that biophysicists employ to learn the structure of biological macromolecules strictly speaking the problem is unidentifiable and an appropriate reformulation is suggested hinging on ideas from kendall s theory of shape within this setup we demonstrate that a consistent solution to the problem may be derived without attempting to estimate the unknown angles if the density is assumed to admit a mixture representation

on the distribution of a deforming triangle this paper presents the mathematical treatment of a new measure sphericity which is used to quantify the similarity between two triangles various properties of sphericity such as maximal invariance and its probability density function are derived

robust multidimensional matched subspace classifiers based on weighted least squares we propose and design two classes of robust subspace classifiers for classification of multidimensional signals our classifiers are based on robust m estimators and the least median of squares principle and we show that they may be unified as iterated reweighted oblique subspace classifiers the performance of the proposed classifiers are demonstrated by two examples noncoherent detection of space time frequency shift keying signals and shape classification of partially occluded two dimensional 2 d objects in both cases the proposed robust subspace classifiers outperform the conventional subspace classifiers

statistical analysis of unlabeled point sets comparing molecules in chemoinformatics we consider bayesian methodology for comparing two or more unlabeled point sets application of the technique to a set of steroid molecules illustrates its potential utility involving the comparison of molecules in chemoinformatics and bioinformatics we initially match a pair of molecules where one molecule is regarded as random and the other fixed a type of mixture model is proposed for the point set coordinates and the parameters of the distribution are a labeling matrix indicating which pairs of points match and a concentration parameter an important property of the likelihood is that it is invariant under rotations and translations of the data bayesian inference for the parameters is carried out using markov chain monte carlo simulation and it is demonstrated that the procedure works well on the steroid data the posterior distribution is difficult to simulate from due to multiple local modes and we also use additional data partial charges on atoms to help with this task an approximation is considered for speeding up the simulation algorithm and the approximating fast algorithm leads to essentially identical inference to that under the exact method for our data extensions to multiple molecule alignment are also introduced and an algorithm is described which also works well on the steroid data set after all the steroid molecules have been matched exploratory data analysis is carried out to examine which molecules are similar also further bayesian inference for the multiple alignment problem is considered

universal bounds on the attractor of the navier stokes equation in the energy enstrophy plane we continue our examination of the projection of the global attractor of the two dimensional navier stokes equations in a normalized dimensionless energy enstrophy plane in this plane the attractor must lie above the line of slope 1 through the origin an immediate consequence of the poincare inequality we showed in dascaliuc et al j dyn differ equ 17 629 649 2005 that the attractor must also lie below a parabola the square root curve here we optimize this parabola to obtain a sharper bound these bounds are universal they are independent of viscosity domain size and strength of the force the effectiveness of the bounds is demonstrated on galerkin approximations of modest size up to 1372 modes

on edge detection edge detection is the process that attempts to characterize the intensity changes in the image in terms of the physical processes that have originated them a critical intermediate goal of edge detection is the detection and characterization of significant intensity changes this paper discusses this part of the edge detection problem to characterize the types of intensity changes derivatives of different types and possibly different scales are needed thus we consider this part of edge detection as a problem in numerical differentiation we show that numerical differentiation of images is an ill posed problem in the sense of hadamard differentiation needs to be regularized by a regularizing filtering operation before differentiation this shows that this part of edge detection consists of two steps a filtering step and a differentiation step following this perspective the paper discusses in detail the following theoretical aspects of edge detection 1 the properties of different types of filters with minimal uncertainty with a bandpass spectrum and with limited support are derived minimal uncertainty filters optimize a tradeoff between computational efficiency and regularizing properties 2 relationships among several 2 d differential operators are established in particular we characterize the relation between the laplacian and the second directional derivative along the gradient zero crossings of the laplacian are not the only features computed in early vision 3 geometrical and topological properties of the zero crossings of differential operators are studied in terms of transversality and morse theory

scheduling deteriorating jobs subject to job or machine availability constraints we consider two problems of scheduling a set of independent non preemptable and proportionally deteriorating jobs on a single machine in the first problem the machine is not continuously available for processing but the number of non availability periods the start time and end time of each period are known in advance in the second problem the machine is available all the time but for each job a ready time and a deadline are defined in both problems the criterion of schedule optimality is the maximum completion time we show that the decision version of the first the second problem is np complete in the ordinary or in the strong sense depending on the number of non availability periods the number of ready times and deadlines

partially occluded object recognition using statistical models in this paper we present a new bayesian framework for partially occluded object recognition based on matching extracted local features on a one to one basis with object features we introduce two different statistical models for occlusion one model assumes that each feature in the model can be occluded independent of whether any other features are occluded whereas the second model uses spatially correlated occlusion to represent the extent of occlusion using these models the object recognition problem reduces to finding the object hypothesis with largest generalized likelihood we develop fast algorithms for finding the optimal one to one correspondence between scene features and object features to compute the generalized likelihoods under both models we conduct experiments illustrating the differences between the two occlusion models using different quantitative metrics we also evaluate the recognition performance of our algorithms using examples extracted from object silhouettes and synthetic aperture radar imagery and illustrate the performance advantages of our approach over alternative algorithms

inverse wishart distributions based on singular elliptically contoured distribution abstract assuming that the random matrix x has a singular or non singular matrix variate elliptically contoured distribution the density function of the moore penrose inverse z x x is given with respect to the hausdorff measure the result is applied to bayesian inference for a general multivariate linear regression model with matrix variate elliptically distributed errors some results concerning the posterior joint and marginal distributions of the parameters are obtained

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

on detecting dominant points abstract detecting dominant points is a crucial preprocessing step for shape recognition and point based motion estimation polygonal approximation has been a commonly used approach in detecting dominant points this paper presents two alternatives which detect stable dominant points in the first method we find a set of positive maximum and negative minimum curvature points along the gaussian smoothed boundary followed by a split and merge polygonal approximation algorithm the resulting break points vertices of the approximated polygon are the dominant points experimental results show that dominant points obtained by this method are less sensitive to the orientation of the boundary than other polygonal approximation algorithms in the sense that the number and the location of the dominant points along the contour remain relatively unchanged in the second method we smooth a boundary by a gaussian filter using various widths until the extreme curvature points remain relatively unchanged for a range of filter widths the resulting extreme curvature points which are stable to orientation and a reasonable range of scaling are the dominant points

variable sized bin packing tight absolute worst case performance ratios for four approximation algorithms in this paper we consider a one dimensional bin packing problem where the bins do not have identical sizes or a variable sized bin packing problem to minimize the bin consumption i e the total size of the opened bins the identical size problem has been extensively studied in the literature both for static and dynamic settings the worst case or average case performance has been analyzed our problem setting particularly arises in metal cutting industries therefore it presents a great practical relevance four greedy approximation algorithms based on a construction approach called largest object first with least absolute waste lflaw largest object first with least relative waste lflrw least absolute waste law and least relative waste lrw are examined their absolute worst case performances are analyzed the worst case bounds are 2 for lflaw and lflrw 3 for law and 2 ln 2 for lrw we also show that these worst case bounds are tight

regularized reconstruction of shapes with statistical a priori knowledge the reconstruction of geometry or in particular the shape of objects is a common issue in image analysis starting from a variational formulation of such a problem on a shape manifold we introduce a regularization technique incorporating statistical shape knowledge the key idea is to consider a riemannian metric on the shape manifold which reflects the statistics of a given training set we investigate the properties of the regularization functional and illustrate our technique by applying it to region based and edge based segmentation of image data in contrast to previous works our framework can be considered on arbitrary finite dimensional shape manifolds and allows the use of riemannian metrics for regularization of a wide class of variational problems in image processing

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

deformotion deforming motion shape average and the joint registration and approximation of structures in images what does it mean for a deforming object to be moving how can we separate the overall motion a finite dimensional group action from the more general deformation a diffeomorphism in this paper we propose a definition of motion for a deforming object and introduce a notion of shape average as the entity that separates the motion from the deformation our definition allows us to derive novel and efficient algorithms to register non identical shapes using region based methods and to simultaneously approximate and align structures in greyscale images we also extend the notion of shape average to that of a moving average in order to track moving and deforming objects through time the algorithms we propose extend prior work on landmark based matching to smooth curves and involve the numerical integration of partial differential equations which we address within the framework of level set methods

a single machine scheduling problem with maintenance activities to minimize makespan we study a single machine scheduling problem with periodic maintenance activity under two maintenance stratagems although the scheduling problem with single or periodic maintenance and nonresumable jobs has been well studied most of past studies considered only one maintenance stratagem this research deals with a single machine scheduling problem where the machine should be stopped for maintenance after a fixed periodic interval t or after a fixed number of jobs k have been processed the objective is to minimize the makespan for the addressed problem a two stage binary integer programming bip model is provided for driving the optimal solution up to 350 job instances for the large sized problems two efficient heuristics are provided for the different combinations of t and k computational results show that the proposed algorithm best fit butterfly bbf performs well because the total average percentage error is below 1 once the constraint of the maximum number of jobs k processed in the machine s available time interval t is equal or larger than half of jobs the heuristic best fit decreasing dbf is strongly recommended

3 d structure from visual motion modeling representation and observability abstract the problem of structure from motion concerns the reconstruction of the three dimensional structure of a scene from its projection onto a moving two dimensional surface such a problem is solved effectively by the human visual system judging from the ease with which we perform delicate control tasks involving vision as a sensor such as reaching for objects in the environment or driving a car in this paper we study structure from motion from the point of view of dynamical systems we first formalize the problem of 3 d structure and motion reconstruction as the estimation of the state of certain nonlinear dynamical models then we study the feasibility of structure from motion by analyzing the observability of such models the models that define the visual motion estimation problem for feature points in the euclidean 3 d space are not locally observable however the non observable manifold can be easily isolated by imposing metric constraints on the state space one of the peculiarities of vision as a sensor is its richness which can be a disadvantage when we are interested only in few of the unknown parameters for instance if we want to control the direction of heading of our car by measuring brightness values on our retina we have to overcome the effects that the shape of the environment its reflectance properties illumination and other quantities have on our measurements invariance to undesired parameters can be achieved by appropriate modeling or by choice of representation of the parameter space we propose and analyze models for 3 d structure that are independent of 3 d motion and vice versa estimating unknown parameters from such models amounts to the identification of nonlinear and implicit systems with parameters on differentiable manifolds such as a sphere or the so called essential manifold 1997 elsevier science ltd

estimates for the two dimensional navier stokes equations in terms of the reynolds number the tradition in navier stokes analysis of finding estimates in terms of the grashof number gr whose character depends on the ratio of the forcing to the viscosity means that it is difficult to make comparisons with other results expressed in terms of reynolds number re whose character depends on the fluid response to the forcing the first task of this paper is to apply the approach of doering and foias c r doering and c foias j fluid mech 467 289 2002 to the two dimensional navier stokes equations on a periodic domain 0 l 2 by estimating quantities of physical relevance particularly long time averages in terms of the reynolds number re ul where u2 l 2 u 22 and l is the forcing scale in particular the constantin foias temam upper bound p constantin c foias and r temam physica d 30 284 1988 on the attractor dimension converts to al2re 1 lnre 1 3 while the estimate for the inverse kraichnan length is al2re 1 2 where al is the aspect ratio of the forcing other in

shape space smoothing splines for planar landmark data a method is developed for fitting smooth curves through a series of shapes of landmarks in two dimensions using unrolling and unwrapping procedures in riemannian manifolds an explicit method of calculation is given which is analogous to that of jupp kent 1987 for spherical data the resulting splines are called shape space smoothing splines the method resembles that of fitting smoothing splines in real spaces in that if the smoothing parameter is zero the resulting curve interpolates the data points and if it is infinitely large the curve is a geodesic line the fitted path to the data is defined such that its unrolled version at the tangent space of the starting point is a cubic spline fitted to the unwrapped data with respect to that path computation of the fitted path consists of an iterative procedure which converges quickly and the resulting path is given in a discretised form in terms of a piecewise geodesic path the procedure is applied to the analysis of some human movement data and a test for the appropriateness of a mean geodesic curve is given

kolmogorov theory via finite time averages abstract several relations from the kolmogorov theory of fully developed three dimensional turbulence are rigorously established for finite time averages over leray hopf weak solutions of the navier stokes equations the navier stokes equations are considered with periodic boundary conditions and an external forcing term the main parameter is the grashof number associated with the forcing term the relations rigorously proved in this article include estimates for the energy dissipation rate the kolmogorov wavenumber the taylor wavenumber the reynolds number and the energy cascade process for some estimates the averaging time depends on the macroscale wavenumber and the kinematic viscosity alone while for others such as the kolmogorov energy dissipation law and the energy cascade the estimates depend also on the grashof number as compared with earlier works by some of the authors the more physical concept of finite time average is replacing the concept of infinite time average used before

the shapes of non generic figures and applications to collinearity testing the singular values decomposition of matrices determines a local representation v of the shape space for k labelled points in r m which has been used to describe its riemannian structure here we use to compute the geodesic distance of a shape from the dimensionally deficient k ads which can be used as a statistic for dimensional deficiency we also characterize in terms of v the coincidence set which can be used to assess whether the deficiencies are genuine or merely apparent these can be used to treat the appropriate analogue in such curved shape spaces of the classical multivariate procedure in which one projects the multivariate sample points onto an interesting hyperplane and then regards the foot of the perpendicular as an estimate and the length of the perpendicular as an goodness of fit statistic finally we discuss some probabilistic properties of such geometrical statistics

auto regressive shape classifiers in time varying noise abstract good results have been reported in a number of recent studies where auto regressive shape classifiers have been used to allocate objects to a pre determined number of classes it is shown that this approach may give unsatisfactory results when applied to imaging systems whose noise characteristics vary substantially over time such variation may be due to changes in atmospheric conditions or the relative effect of discretization errors observations are based on the reconstruction of a number of noisy synthetic templates

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

recognition of occluded objects a cluster structure algorithm clustering techniques have been used to perform image segmentation to detect lines and curves in images and to solve several other problems in pattern recognition and image analysis in this paper we apply clustering methods to a new problem domain and present a new method based on a cluster structure approach for the recognition of 2 d partially occluded objects basically the technique consists of three steps clustering of border segment transformations finding continuous sequences of segments in appropriately chosen clusters and clustering of sequence average transformation values as compared to some of the earlier methods which identify an object based on only one sequence of matched segments the new approach allows the identification of all parts of the model which match in the occluded scene we also discuss the application of the clustering techniques to 3 d scene analysis in both cases the cluster structure algorithm entails the application of clustering concepts in a hierarchical manner resulting in a decrease in the computational effort as the recognition algorithm progresses the implementation of the techniques discussed for the 2 d case has been completed and the algorithm has been evaluated with respect to a large number of examples where several objects partially occlude one another the method is able to tolerate a moderate change in scale and a significant amount of shape distortion arising as a result of segmentation and or the polygonal approximation of the boundary of the object a summary of the results is presented

partial shape recognition a landmark based approach a method of recognizing partially occluded objects is presented in which each object is represented by a set of landmarks given a scene consisting of partially occluded objects a model object in the scene is hypothesized by matching the landmarks of the model with those in the scene a measure of similarity between two landmarks is needed to perform this matching a local shape measure sphericity is introduced it is shown that any invariant function under a similarity transformation is a function of the sphericity to match landmarks between the model and the scene a table of compatibility is constructed a technique known as hopping dynamic programming is described to guide the landmark matching through the compatibility table the location of the model in the scene is estimated with a least squares fit among the matched landmarks a heuristic measure is then computed to decide if the model is in the scene

some specific mathematical constraints on 2d turbulence abstract we derive upper and lower bounds for ensemble averages of energy enstrophy and palinstrophy for the 2d periodic navier stokes equations this is carried out both in the general case and in the case where the energy power law for fully developed turbulence holds in the turbulent case the bounds are sharp up to a logarithm and provide a new lower bound on the landau lifschitz degrees of freedom we also prove two properties of the inertial term under the turbulence assumption one is that as the grashof number is increased the ensemble average of this term approaches the force the other is that an estimate of it via the ladyzhenskaya inequality is sharp on a considerable portion of the global attractor

reduction theory and the lagrange routh equations reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of euler jacobi lagrange hamilton routh poincare and others the modern vision of mechanics includes besides the traditional mechanics of particles and rigid bodies field theories such as electromagnetism fluid mechanics plasma physics solid mechanics as well as quantum mechanics and relativistic theories including gravity symmetries in these theories vary from obvious translational and rotational symmetries to less obvious particle relabeling symmetries in fluids and plasmas to subtle symmetries underlying integrable systems reduction theory concerns the removal of symmetries and their associated conservation laws variational principles along with symplectic and poisson geometry provide fundamental tools for this endeavor reduction theory has been extremely useful in a wide variety of areas from a deeper understanding of many physical theories including new variational and poisson structures to stability theory integrable systems as well as geometric phases this paper surveys progress in selected topics in reduction theory especially those of the last few decades as well as presenting new results on non abelian routh reduction we develop the geometry of the associated lagrange routh equations in some detail the paper puts the new results in the general context of reduction theory and discusses some future directions

geodesic distance on a grassmannian for monitoring the progression of alzheimer s disease we propose a geodesic distance on a grassmannian manifold that can be used to quantify the shape progression patterns of the bilateral hippocampi amygdalas and lateral ventricles in healthy control hc mild cognitive impairment mci and alzheimer s disease ad longitudinal magnetic resonance imaging mri scans of 754 subjects 3092 scans in total were used in this study longitudinally the geodesic distance was found to be proportional to the elapsed time separating the two scans in question cross sectionally utilizing a linear mixed effects statistical model we found that each structure s annualized rate of change in the geodesic distance followed the order of ad mci hc with statistical significance being reached in every case in addition for each of the six structures of interest within the same time interval e g from baseline to the 6th month we observed significant correlations between the geodesic distance and the cognitive deterioration as quantified by the adas cog increase and the mmse decrease furthermore as the disease progresses over time this linkage between the inter shape geodesic distance and the cognitive decline becomes considerably stronger and more significant

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

the riemannian structure of euclidean shape spaces a novel environment for statistics the riemannian metric structure of the shape space sum k m for k labelled points in mathbb r m was given by kendall for the atypically simple situations in which m 1 or 2 and k geq 2 here we deal with the general case m geq 1 k geq 2 by using the properties of riemannian submersions and warped products as studied by o neill the approach is via the associated size and shape space that is the warped product of the shape space and the half line mathbb r carrying size the warping function being equal to the square of the size when combined with parallel studies by le of the corresponding global geodesic geometry the results obtained here determine the environment in which shape statistical calculations have to be acted out finally three different applications are discussed that illustrate the theory and its use in practice

bilinear models for spatio temporal point distribution analysis in this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter subject variation and to the intrinsic dynamics of the human heart we show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle provided we are given a small number of shape instances representing the same heart at different points in the same cycle we can use the bilinear model to establish this using a temporal and a spatial alignment step in the preprocessing of the shapes around half of the reconstruction errors were on the order of the axial image resolution of 2 mm and over 90 was within 3 5 mm from this we conclude that the dynamics were indeed separated from the inter subject variability in our dataset

error analysis in stereo determination of 3 d point positions the relationship between the geometry of a stereo camera setup and the accuracy in obtaining three dimensional position information is of great practical importance in many imaging applications assuming a point in a scene has been correctly identified in each image its three dimensional position can be recovered via a simple geometrical method known as triangulation the probability that position estimates from triangulation are within some specified error tolerance is derived an ideal pinhole camera model is used and the error is modeled as known spatial image plane quantization a point s measured position maps to a small volume in 3 d determined by the finite resolution of the stereo setup with the assumption that the point s actual position is uniformly distributed inside this volume closed form expressions for the probability distribution of error in position along each coordinate direction horizontal vertical and range are derived following this the probability that range error dominates over errors in the point s horizontal or vertical position is determined it is hoped that the results presented will have an impact upon both sensor design and error modeling of position measuring systems for computer vision and related applications

scheduling of nonresumable jobs and flexible maintenance activities on a single machine to minimize makespan abstract this study addresses a single machine scheduling problem with periodic maintenance where the machine is assumed to be stopped periodically for maintenance for a constant time w during the scheduling period meanwhile the maintenance period u v is assumed to have been previously arranged and the time w is assumed not to exceed the available maintenance period u v i e w v u the time u v is the earliest latest time at which the machine starts stops its maintenance the objective is to minimize the makespan two mixed binary integer programming bip models are provided for deriving the optimal solution additionally an efficient heuristic is proposed for finding the near optimal solution for large sized problems finally computational results are provided to demonstrate the efficiency of the models and the effectiveness of the heuristics the mixed bip model can optimally solve up to 100 job instances while the average percentage error of the heuristic is below 1

moshfit algorithms for occlusion tolerant mean shape and rigid motion from 3d movement data this work addresses the use of 3d point data to measure rigid motions in the presence of occlusion and without reference to a prior model of relative point locations this is a problem where cluster based measurement techniques are used e g for measuring limb movements and no static calibration trial is available the same problem arises when performing the task known as roving capture in which a mobile 3d movement analysis system is moved through a volume with static markers in unknown locations and the ego motion of the system is required in order to understand biomechanical activity in the environment to provide a solution for both of these applications the new concept of a visibility graph is introduced and is combined with a generalised procrustes method adapted from ones used by the biological shape statistics and computer graphics communities recent results on shape space manifolds are applied to show sufficient conditions for convergence to unique solution algorithm source code is available and referenced here processing speed and rate of convergence are demonstrated using simulated data positional and angular accuracy are shown to be equivalent to approaches which require full calibration to within a small fraction of input resolution typical processing times for sub micron convergence are found to be fractions of a second so the method is suitable for workflows where there may be time pressure such as in sports science and clinical analysis

statistical estimates for the navier stokes equations and the kraichnan theory of 2 d fully developed turbulence a mathematical formulation of the kraichnan theory for 2 d fully developed turbulence is given in terms of ensemble averages of solutions to the navier stokes equations a simple condition is given for the enstrophy cascade to hold for wavenumbers just beyond the highest wavenumber of the force up to a fixed fraction of the dissipation wavenumber up to a logarithmic correction this is followed by partial rigorous support for kraichnan s eddy breakup mechanism a rigorous estimate for the total energy is found to be consistent with kraichnan s theory finally it is shown that under our conditions for fully developed turbulence the fractal dimension of the attractor obeys a sharper upper bound than in the general case

recognize objects with three kinds of information in landmarks abstract object recognition is one of the most important tasks in computer vision domain and it has been extensively applied in many areas during the last three decades in this paper a method is proposed to recognize objects in shape spaces in which landmarks have three kinds of information i e landmarks position angle and feature vector by comparing angle and feature vector a landmark in an image can correspond with a few number of landmarks in another image then the pixel s positions of landmarks from two images are used to calculate the procrustean distance in a shape space if the value of the procrustean distance is smaller than a predefined threshold the two sets of landmarks will be considered to match each other applying the proposed method two dimensional objects including occluded objects can be recognized quickly

on the landau lifschitz degrees of freedom in 2 d turbulence we show that if the kraichnan theory of fully developed turbulence holds then the landau lifschitz degrees of freedom is bounded up to a logarithmic term by g1 2 where g is the grashof number

kraichnan turbulence via finite time averages relations central to kraichnan s theory of fully developed two dimensional turbulence are rigorously established for finite time averages in particular we prove that if the ratio of the averages of palinstrophy to enstrophy is large then a large inertial range displaying an enstrophy cascade exists moreover if this ratio is comparable up to a logarithm to the dissipation wave number a necessary condition for turbulence then the power law for the energy spectrum until now derived only heuristically is rigorously shown to provide up to a logarithm an upper bound for the energy spectrum finally we show that deep in the dissipation range the palinstrophy contributed by eddies smaller than a specified length decays exponentially in the corresponding wave number the averaging times needed for these relations are bounded in terms of the generalized grashof number independent of the solution for which the time averages are taken solutions are not assumed to be on the global attractor merely within the absorbing ball an easily verified condition

a control point matching algorithm abstract a general procedure for point matching is outlined which deals effectively with the dual problems of finding matches between two point sets and correctly identifying missing or spurious points

a scale space filtering approach for visual feature extraction this paper presents a new integrated approach for detecting visual features which include corners ends arcs and lines the effect of scale space filtering on visual features is studied in detail as it forms the theoretical basis of our work in this approach the outline of the object is first extracted and it is then smoothed by scale space filtering at different scale levels subsequently the local extreme curvature points extracted from the smoothed curve and end candidates are determined to guide the termination of the filtering process information about the curvature of each point at the largest scale level is used to detect the different kinds of visual features several algorithms are proposed to determine corners ends arcs and lines experimental results show that our approach is robust to translation rotation and scaling of the object as well as noise corruption in addition efficient visual features can also be successfully extracted with this approach

notes on some single machine scheduling problems with general position dependent and time dependent learning effects this paper provides a continuation of the idea presented by yin et al yin et al some scheduling problems with general position dependent and time dependent learning effects inform sci 179 2009 2416 2425 for each of the following three objectives total weighted completion time maximum lateness and discounted total weighted completion time this paper presents an approximation algorithm which is based on the optimal algorithm for the corresponding single machine scheduling problem and analyzes its worst case bound it shows that the single machine scheduling problems under the proposed model can be solved in polynomial time if the objective is to minimize the total lateness or minimize the sum of earliness penalties it also shows that the problems of minimizing the total tardiness discounted total weighted completion time and total weighted earliness penalty are polynomially solvable under some agreeable conditions on the problem parameters

intrinsic sample mean in the space of planar shapes in this paper we consider the shape space as the set of smooth simple closed curves in r 2 parameterized curves modulo translations rotations and scale changes an algorithm to obtain the intrinsic average of a sample data set of planar shape realizations from the identification of the shape space with an infinite dimensional grassmannian is proposed using a gradient descent type algorithm a simulation study is carried out to check the performance of the algorithm highlightswe propose an algorithm to obtain the intrinsic mean of sample data planar shapes shape space is identified with a grassmann manifold of infinite dimension the frechet mean for manifolds and the gradient descent algorithm are used a simulation study is carried out to check the performance of the methodology