pattern recognition by graph matching using the potts mft neural networks this paper is concerned with programming of the potts mean field theory neural networks for pattern recognition by homomorphic mapping of the attributed relational graphs arg in order to generate the homomorphic mapping from the scene relational graph to the model graph we make use of the recently introduced suganthan technical report nanyang technical university 1994 compatibility functions in relation to the hopfield network an efficient pose clustering algorithm is used to separate and localize different occurrences of any particular object model in the scene the pose clustering algorithm also eliminates spurious hypotheses generated by the network and resolves ambiguities in the final interpretation the performance of the proposed approach to pattern recognition by homomorphism is demonstrated using a number of line patterns silhouette images and circle patterns

three dimensional shape analysis using local shape descriptors the three dimensional shape analysis problem is a very demanding test of shape analysis algorithms previous approaches to the problem have employed global features such as moments and fourier descriptors global features lack the capacity for solving the partial shape recognition problem in which only part of the unknown shape is available previous approaches to local shape analysis have employed structural syntactic methods but these methods have so far failed to solve the three dimensional problem this paper describes a hybrid structural statistical local shape analysis algorithm which is applied to the three dimensional problem

critical properties of electron eigenstates in incommensurate systems this paper describes some properties of the eigenvalue equation n 1 n 1 2 cos 2 n n e n this is an example of the more general problem of a hermitian eigenvalue equation in the form of a difference equation with periodic coefficients these equations arise in solid state physics they occur in connection with tight binding models for electrons in one dimensional solids with an incommensurate modulation of the structure and in models for the energy bands of bloch electrons moving in a plane with a perpendicular magnetic field the model studied has a critical point when 1 following some earlier work by azbel azbel m ya phys rev lett 43 1954 1979 an approximate renormalization group transformation is derived this predicts that the spectrum and eigenstates have a remarkable recursive structure at the critical point which is dependent on the expansion of as a continued fraction also when is an irrational number there is a localization transition from extended states to localized states as increases through the critical point this localization transition which was previously discovered by aubry andre aubry s andre g ann israel phys soc 3 133 1979 using the thouless formula for the localization length is explained by the renormalization group transformation derived here

an exact renormalisation group for bloch electrons in a magnetic field bloch electrons in a magnetic field can be modelled by a one dimensional hamiltonian h h x p which is periodic in x and p when beta the ratio of planck s constant h to the area of a unit cell is a rational number p q the spectrum is a set of q bloch bands if beta is perturbed away from this rational value the spectrum becomes a cantor set but it is still possible to define a set of generalised bloch waves which form a complete basis set for a given band projecting these states into the band and taking matrix elements of the hamiltonian leads to a new effective hamiltonian h1v x p and planck constant h v describing the spectrum of the vth band since degrees of freedom have been eliminated by projecting into a band this is a renormalisation group rg transformation the rg transformation can be iterated indefinitely if the measure of the spectrum is zero or if beta is a liouville number the measure of the spectrum vanishes if h x p has centres of threefold or fourfold symmetry in the phase plane and the rg transformation explains the hierarchical structure of the spectrum observed in these cases

a probabilistic analytic center cutting plane method for feasibility of uncertain lmis many robust control problems can be formulated in abstract form as convex feasibility programs where one seeks a solution x that satisfies a set of inequalities of the form f f x d 0 d d this set typically contains an infinite and uncountable number of inequalities and it has been proved that the related robust feasibility problem is numerically hard to solve in general in this paper we discuss a family of cutting plane methods that solve efficiently a probabilistically relaxed version of the problem specifically under suitable hypotheses we show that an analytic center cutting plane scheme based on a probabilistic oracle returns in a finite and pre specified number of iterations a solution x which is feasible for most of the members of f except possibly for a subset having arbitrarily small probability measure

phase space lattices with threefold symmetry this paper presents a semiclassical analysis of the spectrum of the hamiltonian ir cos p e cos ci v 3 5 cos f p a 5 which is a model for bloch electrons in a magnetic field the energy levels are determined to a first approximation by bohr sommerfeld quantisation because of the translational symmetry in phase space this leads to a lattice of infinitely degenerate states this degeneracy is lifted by tunnelling effects which can be described by an effective hamiltonian of the same form as that above but with different values of 0 and h the calculation of the effective hamiltonian therefore defines a renormalisation group transformation and it predicts that the spectrum has a complex recursive structure which is confirmed by numerical experiments the results complement earlier work on lattices with fourfold symmetry in which a similar type of spectrum occurs the greater complexity of the problem in lattices with threefold symmetry necessitated developing simpler canonically invariant methods of analysis

an exact effective hamiltonian for a perturbed landau level considers the effect of a scalar potential v x y on a landau level in two dimensions an exact effective hamiltonian is derived which describes the effect of the potential on a single landau level expressed as a power series in v ec where ec is the cyclotron energy the effective hamiltonian can be represented as a function h x p in a one dimensional phase space the function h x p resembles the potential v x y when the area of a flux quantum is much smaller than the square of the characteristic length scale of v then h approximately v also h x p retains the translational and rotational symmetries of v x y exactly but reflection symmetries are not retained beyond the lowest order of the perturbation expansion

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

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

an efficient and accurate method for the relaxation of multiview registration error this paper presents a new method for the relaxation of multiview registration error the multiview registration problem is represented using a graph each node and each edge in the graph represents a 3 d data set and a pairwise registration respectively assuming that all the pairwise registration processes have converged to fine results this paper shows that the multiview registration problem can be converted into a quadratic programming problem of lie algebra parameters the constraints are obtained from every cycle of the graph to eliminate the accumulation errors of global registration a linear solution is proposed to distribute the accumulation error to proper positions in the graph as specified by the quadratic model since the proposed method does not involve the original 3 d data it has low time and space complexity additionally the proposed method can be embedded into a trust region algorithm and thus can correctly handle the nonlinear effects of large accumulation errors while preserving the global convergence property to the first order critical point experimental results confirm both the efficiency and the accuracy of the proposed method

determination of three dimensional object location and orientation from range images a technique for determining the distortion parameters location and orientation of general three dimensional objects from a single range image view is introduced the technique is based on an extension of the straight line hough transform to three dimensional space it is very efficient and robust since the dimensionality of the feature space is low and since it uses range images directly with no preprocessing such as segmentation and edge or gradient detection because the feature space separates the translation and rotation effects a hierarchical algorithm to detect object rotation and translation is possible the new hough space can also be used as a feature space for discriminating among three dimensional objects

representation and shape matching of 3 d objects a three dimensional scene analysis system for the shape matching of real world 3 d objects is presented various issues related to representation and modeling of 3 d objects are addressed a new method for the approximation of 3 d objects by a set of planar faces is discussed the major advantage of this method is that it is applicable to a complete object and not restricted to single range view which was the limitation of the previous work in 3 d scene analysis the method is a sequential region growing algorithm it is not applied to range images but rather to a set of 3 d points the 3 d model of an object is obtained by combining the object points from a sequence of range data images corresponding to various views of the object applying the necessary transformations and then approximating the surface by polygons a stochastic labeling technique is used to do the shape matching of 3 d objects the technique matches the faces of an unknown view against the faces of the model it explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification it is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels the objective here is to match the individual views of the object taken from any vantage point details of the algorithm are presented and the results are shown on several unknown views of a complicated automobile casting

structural pattern recognition using genetic algorithms this paper presents a genetic algorithm ga based optimization procedure for the solution of structural pattern recognition problem using the attributed relational graph representation and matching technique in this study candidate solutions are represented by integer strings and the population is randomly initialized the ga is employed to generate a monomorphic mapping as all the mapping constraints are not enforced during the search phase in order to speedup the search an efficient pose clustering algorithm is used to eliminate spurious matches and to determine the presence of the model in the scene the performance of the proposed approach to pattern recognition by subgraph isomorphism is demonstrated using line patterns and silhouette images

von neumann lattices of wannier functions for bloch electrons in a magnetic field the problem of bloch electrons in a magnetic field in two dimensions can be reduced to a one dimensional problem with a hamiltonian h that is a periodic function of x and p wannier functions can be defined for the sub bands of the spectrum of this effective hamiltonian when the chern class quantized hall conductance integer of the sub band is zero the weyl wigner formalism can be used to represent these wannier functions by a von neumann lattice it is shown how this von neumann lattice of wannier functions can be defined for irrational as well as rational magnetic fields an important benefit from using the weyl wigner formalism is that symmetries of the periodic potential are reflected by symmetries of the effective hamiltonian in phase space it is shown how the wannier functions can be defined so that their wigner functions have the point symmetries of the effective hamiltonian an example of how these results can prove useful is given if we take matrix elements of the hamiltonian between the wannier states of a sub band we derive a new effective hamiltonian describing this sub band which is again a periodic function of coordinate and momentum operators since by projecting onto a sub band we have also reduced the number of degrees of freedom this operation is a renormalization group transformation it is shown that the symmetry of the new effective hamiltonian in phase space is the same as that of the original one this preservation of symmetry helps to explain some unusual properties of the spectrum when the hamiltonian has fourfold symmetry

principal component analysis with missing data and its application to polyhedral object modeling observation based object modeling often requires integration of shape descriptions from different views to overcome the problems of errors and their accumulation we have developed a weighted least squares wls approach which simultaneously recovers object shape and transformation among different views without recovering interframe motion we show that object modeling from a range image sequence is a problem of principal component analysis with missing data pcamd which can be generalized as a wls minimization problem an efficient algorithm is devised after we have segmented planar surface regions in each view and tracked them over the image sequence we construct a normal measurement matrix of surface normals and a distance measurement matrix of normal distances to the origin for all visible regions over the whole sequence of views respectively these two matrices which have many missing elements due to noise occlusion and mismatching enable us to formulate multiple view merging as a combination of two wls problems a two step algorithm is presented after surface equations are extracted spatial connectivity among the surfaces is established to enable the polyhedral object model to be constructed experiments using synthetic data and real range images show that our approach is robust against noise and mismatching and generates accurate polyhedral object models

cantor spectrum for the almost mathieu equation for a dense g of pairs in r2 we prove that the operator hu n u n 1 u n 1 cos 2 n u n has a nowhere dense spectrum along the way we prove several interesting results about the case pq of which we mention a if q is not an integral multiple of then all gaps are open and b if q is even and is chosen suitably then the middle gap is closed for all

computation of surface orientation and structure of objects using grid coding in this correspondence algorithms are introduced to infer surface orientation and structure of visible object surfaces using grid coding we adopt the active lighting technique to spatially encode the scene for analysis the observed objects which can have surfaces of arbitrary shape are assumed to rest on a plane base plane in a scene which is encoded with light cast through a grid plane two orthogonal grid patterns are used where each pattern is obtained with a set of equally spaced stripes marked on a glass pane the scene is observed through a camera and the object surface orientation is determined using the projected patterns on the object surface if the surfaces under consideration obey certain smoothness constraints a dense orientation map can be obtained through proper interpolation the surface structure can then be recovered given this dense orientation map both planar and curved surfaces can be handled in a uniform manner the algorithms we propose yield reasonably accurate results and are relatively tolerant to noise especially when compared to shape from shading techniques in contrast to other grid coding techniques reported which match the grid junctions for depth reconstruction under the stereopsis principle our techniques use the direction of the projected stripes to infer local surface orientation and do not require any correspondence relationship between either the grid lines or the grid junctions to be specified the algorithm has the ability to register images and can therefore be embedded in a system which integrates knowledge from multiple views

an integral approach to free form object modeling presents an approach to free form object modeling from multiple range images in most conventional approaches successive views are registered sequentially in contrast to the sequential approaches we propose an integral approach which reconstructs statistically optimal object models by simultaneously aggregating all data from multiple views into a weighted least squares wls formulation the integral approach has two components first a global resampling algorithm constructs partial representations of the object from individual views so that correspondence can be established among different views second a weighted least squares algorithm integrates resampled partial representations of multiple views using the techniques of principal component analysis with missing data pcamd experiments show that our approach is robust against noise and mismatch

polyhedron recognition using three view analysis abstract using three view analysis this paper proposes a new approach for single polyhedron recognition both the 3d surface data and 2d image projection patterns are used to find the exact corresponding model of an unknown input object the recognition process first applies a hypothesis generation verification process to match the 3d partial object of the unknown input which is reconstructed by applying the three view matching strategy chiou et al proc ics 88 pp 1516 1521 1988 and the polyhedron reconstruction process hung et al pattern recognition 22 231 246 1989 against the data based models for selecting the possible corresponding models candidates it then backprojects each candidate onto the three image planes and matches the outer boundaries of the three backprojections by a simple method for judging the exact corresponding model measurement error is also analyzed theoretically to give a bound of the threshold value so that it can be automatically chosen in each decision making process the approach is implemented on a pc level vision system experimental results show that the system is feasible and reliable even in a noisy environment

identification of three dimensional objects using range information a method for identifying unoccluded three dimensional objects from arbitrary viewing angles is presented the technique uses synthetically generated range data in a model based feature vector classification scheme fourier descriptors and moments are used for feature vector generation from respectively contour imagery and silhouette or range imagery a method is developed for generating an exhaustive set of library views and worst case test views that is based on a polyhedral approximation to a sphere analysis of the success of this approach is made with experiments on a six airplane data set a model of range data noise is developed and results are presented for both ideal and noisy lower resolution image classification tests the use of multiple views for object identification is discussed and results for one two and three view tests are presented

symmetry properties of exact energy solutions to the harper equation and related q normalizations proofs are given that exact solutions to the wavefunctions of the harper equation can be established in an explicit manner by resorting to three term recurrence relations implied by a q calculus approach proposed previously the q normalization of wavefunctions resulting in the appearance of peaks is discussed the exact q 6 energy solution has also been derived and analysed in some more detail there are reasons to say that fractal structures concerning band and gap distributions have to be accounted for if q 6

advanced in plane rotation invariant correlation filters advanced correlation filter synthesis algorithms to achieve rotation invariance are described we use a specified form for the filter as the rotation invariance constraint and derive a general closed form solution for a multiclass rotation invariant filter that can recognize a number of different objects by requiring the filter to minimize the average correlation plane energy we produce a multiclass rotation invariant ri ri mace filter which controls correlation plane sidelobes and improves discrimination against false targets to improve noise performance we require the filter to minimize a weighted sum of correlation plane signal and noise energy initial test results of all filters are provided

first order correction to the renormalization of the phase space lattice hamiltonian we develop a renormalization group analysis for a hamiltonian which is a periodic function of and this is a model for bloch electrons in a magnetic field and includes harper s model as a special case the eigenfunctions are bloch waves when the ratio of to the area of the unit cell is a rational number p q the renormalization procedure produces an effective hamiltonian for a subset of the spectrum which can be expanded in the zeroth order term has been obtained in earlier papers here we obtain the first order term of this expansion in terms of the q dimensional vectors which define the rational bloch states k and are bloch wavevectors the effective hamiltonian is not invariant under gauge transformations multiplying the vector we show that the infinitesimal gauge transformation is equivalent to evolving under a gauge hamiltonian obtained to lowest order in by quantizing

a sum rule for the dispersion relations of the rational harper equation the authors derive an exact sum rule satisfied by the dispersion relations of the commensurable case of harper s equation 1955 they use this result to derive a lower bound for the total bandwidth of the spectrum and to provide a stronger analytical justification for a result due to thouless 1990 concerning the total bandwidth when the commensurability is a high order rational

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

structural matching in computer vision using probabilistic relaxation in this paper we develop the theory of probabilistic relaxation for matching features extracted from 2d images derive as limiting cases the various heuristic formulae used by researchers in matching problems and state the conditions under which they apply we successfully apply our theory to the problem of matching and recognizing aerial road network images based on road network models and to the problem of edge matching in a stereo pair for this purpose each line network is represented by an attributed relational graph where each node is a straight line segment characterized by certain attributes and related with every other node via a set of binary relations

experiments in curvature based segmentation of range data this paper focuses on the experimental evaluation of a range image segmentation system which partitions range data into homogeneous surface patches using estimates of the sign of the mean and gaussian curvatures the authors report the results of an extensive testing program aimed at investigating the behavior of important experimental parameters such as the probability of correct classification and the accuracy of curvature estimates measured over variations of significant segmentation variables evaluation methods in computer vision are often unstructured and subjective this paper contributes a useful example of extensive experimental assessment of surface based range segmentation

a comparison of approaches to high level image interpretation abstract a critical comparison of methods of high level interpretation of segmented images is presented and illustrated by examples drawn from two dimensional image analysis the methods discussed include boundary correlation generalized hough transformation relational distance measures graph matching heuristic search and relaxation labelling each technique is considered in terms of its reliability in interpreting noisy and cluttered scenes and in terms of the dynamic complexity of the algorithm as a function of the input data although 2 d analysis of linearly segmented scenes is used as a mechanism for comparison many of the arguments are applicable to three dimensional image interpretation based on surface modelling for example

a general surface approach to the integration of a set of range views this paper presents a new and general solution to the problem of range view integration the integration problem consists in computing a connected surface model from a set of registered range images acquired from different viewpoints the proposed method does not impose constraints on the topology of the observed surfaces the position of the viewpoints or the number of views that can be merged the integrated surface model is piecewise estimated by a set of triangulations modeling each canonical subset of the venn diagram of the set of range views the connection of these local models by constrained delaunay triangulations yields g non redundant surface triangulation describing all surface elements sampled by the set of range views experimental results show that the integration technique can be used to build connected surface models of free form objects no integrated models built from objects of such complexity have yet been reported in the literature it is assumed that accurate range views are available and that frame transformations between all pairs of views can be reliably computed

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

level statistics in a quasiperiodic system the authors examine the level statistics of harper s equation a simple model of a one dimensional quasiperiodic system through the distribution of the spacings between adjacent eigenvalues each normalised by the average local density of states they present exact results for the distribution for both small and large amplitude alpha of the incommensurate potential showing it has a simple form in each of these limits they show numerically that these distributions are preserved as alpha approaches its critical value 2 from each side and also that at the critical point the distribution of the normalised spacings has a distinct but simple form

3 d object recognition using bipartite matching embedded in discrete relaxation the authors show how large efficiencies can be achieved in model based 3 d vision by combining the notions of discrete relaxation and bipartite matching the computational approach presented is capable of pruning large segments of search space an indispensable step when the number of objects in the model library is large and when recognition of complex objects with a large number of surfaces is called for bipartite matching is used for quick wholesale rejection of inapplicable models and for the determination of compatibility of a scene surface with a potential model surface taking into account relational considerations the time complexity function associated with those aspects of the procedure that are implemented via bipartite matching is provided the algorithms do not take more than a couple of iterations even for objects with more than 30 surfaces

fitting an unknown number of lines and planes to image data through compatible cluster merging abstract a compatible cluster merging algorithm is presented that is specially designed to find the optimum number of linear planar and hyperplanar clusters i e clusters that lie in a subspace of the original space when an upper bound on the number of clusters present is known this algorithm is shown to be superior to more traditional validity measure based approaches the effectiveness and advantages of the proposed technique in 2d and 3d applications is demonstrated with both synthetic and real data the proposed applications include character recognition obtaining straight line descriptions of intensity edge images and obtaining planar approximations of 3d range data

constructing intrinsic parameters with active models for invariant surface reconstruction a technique for constructing a canonical surface parameterization in terms of lines of curvature is presented two methods of computing the canonical invariant representation are also presented in the first method a static instance of the controlled continuity spline is used for the stabilizer ways to modify it to reflect a change of parameters to the lines of curvature are described in the second method the dynamic instance of the controlled continuity spline called the deformable model is used a force field defined in terms of the principal vectors is synthesized and applied to the parameter curves of the deformable model to coerce them along the lines of curvature in essence any transformation of parameters requires a modification of the stabilizer in the first method whereas in the second method it is tantamount to synthesizing a new force field experimental results with real and synthetic range data are included