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

derivations vanishing on s lets be the group of finite permutations on countably many symbols we exhibit an embedding ofs into a uhf algebra mathfrak a of glimm typen such that if is a derivation vanishing ons and satisfying 0 where is the unique trace on mathfrak a then admits an extension which is the generator of ac dynamics

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

noncommutative topological dynamics and compact actions on c algebras the classical notions of topological transitivity and minimality of a topological dynamical system are extended and analyzed in the context of c dynamical systems these notions are compared with other notions naturally arising in noncommutative ergodic theory as an application a c algebra version of a theorem of araki haag kastler and takesaki comm math phys 53 1977 97 134 about the correspondence between a compact automorphism group here assumed to be abelian and its fixed point subalgebra is proved in the presence of a commuting topologically transitive action a variation of this theorem in the setting of standard w inclusions is also presented

pp is as hard as the polynomial time hierarchy in this paper two interesting complexity classes pp and oplus text p are compared with ph the polynomial time hierarchy it is shown that every set in ph is polynomial time turing reducible to a set in pp and ph is included in text bp cdot oplus text p as a consequence of the results it follows that text pp subseteq text ph or oplus text p subseteq text ph implies a collapse of ph a stronger result is also shown every set in pp ph is polynomial time turing reducible to a set in pp

noncommutative topological dynamics ii this part deals with almost periodic and weakly mixing c flows and with disjointness and weak disjointness of c flows flows on c algebras the main result is a generalization to c flows of keynes and robertson s characteriza tion of minimal weakly mixing flows examples are discussed exhibiting anomalous behaviour of disjointness in the c flow case

complexity classes of optimization functions in this paper complexity classes of functions defined via taking maxima or minima cf the work of krentel or taking middle elements cf the work of toda are examined a number of axioms for a class to be a so called p founded class of optimization functions are given it is shown that many natural function classes fulfill these axioms then these classes are examined concerning their relationship to complexity classes of sets to this end complexity preserving operators s and f for encoding function classes into set classes and vice versa are introduced it is shown how these operators translate closure properties from one class to another how they relate operators on classes of functions and classes of sets and how they encode classes of maximum minimum or median functions into well studied classes of sets the fixpoints of the compositional operator f s are examined and shown to be exactly those function classes closed under binary search let f1 and f2 be two such fixpoints and k1 and k2 be their corresponding classes of sets i e their images under the operator s then f1 f2 if and only if k1 k2 and f1 f2 if and only if k1 k2 a number of natural classes of functions are shown to be such fixpoints thus we build hierachies of function classes with the same inclusional relationships as the polynomial time hierarchy of sets and the counting hierarchy of sets and we prove many interesting structural properties of these hierarchies

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

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

unbounded derivations tangential to compact groups of automorphisms ii let g be a compact abelian group and an action of g on a c algebra u such that u u u 0 u for all g where u is the spectral subspace of u corresponding to the character on g derivations which are defined on the algebra uf of g finite elements are considered in the special case u 0 these derivations are characterized by a cocycle on g with values in the relative commutant of u in the multiplier algebra of u and these derivations are inner if and only if the cocycles are coboundaries and bounded if and only if the cocycles are bounded under various restrictions on g and properties of the cocycle are deduced which again give characterizations of in terms of decompositions into generators of one parameter subgroups of g and approximately inner derivations finally a perturbation technique is devised to reduce the case uf uf to the case uf uf and u 0 this is used to show that any derivation with d uf is wellbehaved and if furthermore g t1 and uf uf the closure of generates a one parameter group of automorphisms of u in the case g td d 2 3 finite and uf uf it is shown that extends to a generator of a group of automorphisms of the weak closure of u in any g covariant representation

simple and prime crossed products of c algebras by compact quantum group coactions let g a be a compact quantum group and a coaction of g on a c algebra b we give necessary and sufficient conditions for the simplicity and primeness of the crossed product b g in terms of certain fixed point algebras

locally compact group actions on c algebras and compact subgroups be a compact subgroup in this paper we shall give necessary and sufficient conditions in order that the crossed product g x a be simple or prime our conditions are in terms of the dual 2 of the com pact subgroup k the paper is organized as follows in the second section we summarize some preliminary definitions and results about continuous banach representations of compact groups the same section contains the definitions of the subspaces of spherical functions sn nl l 7 n e e those of the algebras s i and the relations between these subspaces section 3 contains a study of saturated actions of g on a in terms of the ideals s s we mention that for compact groups the notion of saturated action has been defined by rieffel see 19 chap 73 the same section contains conditions in order that the crossed product be simple for compact abelian groups g our result reduces to the following g x

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

spectra for compact quantum group coactions and crossed products we present definitions of both connes spectrum and strong connes spectrum for actions of compact quantum groups on c algebras and obtain necessary and sufficient conditions for a crossed product to be a prime or a simple c algebra our results extend to the case of compact quantum ac tions the results in 8 which in turn generalize results by connes olesen and pedersen and kishimoto for abelian group actions we prove in addition that the connes spectra are closed under tensor products these results are new for compact nonabelian groups as well

a strong connes spectrum for finite group actions of simple rings abstract in this paper we give necessary and sufficient conditions for a skew group ring to be simple our conditions are in terms of the irreducible representations of the group g we also introduce a version of the strong connes spectrum for finite group actions of simple rings

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

recursion theoretic characterizations of complexity classes of counting functions abstract there has been a great effort in giving machine independent algebraic characterizations of complexity classes especially of functions astonishingly no satisfactory characterization of the prominent class p is known up to now here we characterize p as the closure of a set of simple arithmetical functions under summation and weak product based on that result the hierarchy of counting functions which is the closure of p under substitution is characterized remarkably without using the operator of substitution since we can show that in the context of this hierarchy the operation of modified subtraction is as powerful as substitution this leads us to a number of consequences concerning closure of p under certain arithmetical operations analogous results are achieved for the class gap p which is the closure of p under subtraction

correlation filters with controlled scale response correlation filtering methods are becoming increasingly popular for image recognition and location the recent introduction of optimal tradeoff circular harmonic function filters allowed the user to specify the response of a correlation filter to in plane rotation distortion in this paper we introduce a new correlation filter design that can provide a user specified response to in plane scale distortion the design is based on the mellin radial harmonic mrh transform and incorporates multiple harmonics into the correlation filter for improved discrimination capability additionally the filter design minimizes the average correlation energy in order to achieve sharp correlation peaks and thus we refer to these filters as minimum average correlation energy mellin radial harmonic mace mrh filters we present underlying theory a mace mrh filter design method and numerical simulation results

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

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

some observations on the connection between counting and recursion abstract based on valiant s class p of all functions counting the number of accepting computations of nondeterministic polynomial time turing machines the polynomial time hierarchy of counting functions is introduced the class phcf of all functions of this hierarchy and some of its subclasses are characterized by recursion theoretic means it turns out that from the recursion theoretic point of view phcf is an analogue to kalmar s class e of elementary functions to the class pspace of polynomial space computable functions as well as to the class p of polynomial time computable functions

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

multiresolution circular harmonic decomposition a dictionary of complex waveforms suited for multiresolution analysis and individually steerable by multiplication by a complex factor is presented it is based on circular harmonic wavelets chw and is useful for pattern analysis under rotations the main theoretical aspects of chws are illustrated and an example of application to motion estimation is provided

free joinings of c dynamical systems joinings of c dynamical systems are defined in terms of free products of c algebras as an analogue of joinings of classical dynamical systems we then consider disjointness in this context in particular for ergodic versus identity systems lastly we show how multi time correlation functions appearing in quantum statistical mechanics naturally fit into this joining framework

maximal subalgebras of c algebras associated with periodic flows we find necessary and sufficient conditions for the subalgebra of analytic elements associated with a periodic c dynamical system to be a maximal norm closed subalgebra our conditions are in terms of the arveson spectrum of the action we also describe equivalent properties of the system in terms of the strong connes spectrum and the simplicity of the crossed product c 2012 elsevier inc all rights reserved

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

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

topological automorphism groups of compact quantum groups we study the topological structure of the automorphism groups of compact quantum groups showing that in parallel to a classical result due to iwasawa the connected component of identity of the automorphism group and of the inner automorphism group coincide for compact matrix quantum groups which can be thought of as quantum analogues of compact lie groups we prove that the inner automorphism group is a compact lie group and the outer automorphism group is discrete applications of this to the study of group actions on compact quantum groups are highlighted we end by providing examples of compact matrix quantum groups with infinitely generated fusion rings in stark contrast with the classical situation along the way we study the invariant theory of finite group actions on free laurent rings and show that the rings of invariants are in general not finitely generated

a note on noncommutative unique ergodicity and weighted means abstract in this paper we study unique ergodicity of c dynamical system a t consisting of a unital c algebra a and a markov operator t a a relative to its fixed point subspace in terms of riesz summation which is weaker than cesaro one namely it is proven that a t is uniquely ergodic relative to its fixed point subspace if and only if its riesz means 1 p 1 p n k 1 n p k t k x converge to e t x in a for any x a as n here e t is an projection of a to the fixed point subspace of t it is also constructed a uniquely ergodic entangled markov operator relative to its fixed point subspace which is not ergodic

mixing properties of quantum systems we generalize the classical notion of topological mixing for automorphisms ofc algebras in two ways we show that for galilean invariant fermi systems the weaker form of mixing is satisfied with some additional requirement on the range of the interaction we can also demonstrate the stronger mixing property

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

reforming the theory of invariant moments for pattern recognition abstract the relationship between the algebraic invariants and the fourier mellin spectrum of an image irradiance distribution is clarified and a new approach for generating the two dimensional 2d invariant moments is proposed fifty two invariant functions of the second to the ninth order image moments are tabulated which are invariant with respect to image translation shift orientation and size changes and can be used as library functions in computer programs for automatic image identification the invariant functions derived in this study are shown useful in a numerical example concerned with a character recognition model

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

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

free products of c algebras small spatial free products of c algebras are constructed under certain conditions they have properties similar to those proved by paschke and salinas for the algebras c gi g2 where g1 g2 are discrete groups the freeproduct analogs of noncommutative bernoulli shifts are discussed 0 introduction let k be a field consider the category of unital algebras over k it is well known that this category admits coproducts free products of algebras 2 heuristically the free product of algebras is the algebra generated by them with no relations except for the identification of unit elements if k c the complex numbers and we consider unital algebras we can easily define a operation on the free products let a b be unital c algebras and a b their free product which is a unital algebra the question arises in what ways may one define a pre c norm on a b that extends the norms on a and b guided by analogy with tensor products we expect to have a choice among many pre c norms giving rise to many c free products of a and b one natural norm is 1c i i sup 1it c ih st representation of a b the representations of a b are in 1 1 correspondence with pairs of representations of a and b which act on the same hilbert space let a b be the completion of a b in this norm it is easy to see that this construction defines a coproduct in the category of c algebras and that a b is the biggest free product of a and b analogous to the biggest tensor product a 0 b if g 1 g2 are discrete groups we obtain c g1 c g2 c gi g2 where g1 g2 is the free product group and this is analogous to the relation c g1 0 c g2 c g1 x g2 this paper is motivated by the question is there a smallest c product a b in analogy to the smallest tensor product a b satisfying a relation cr gi g2 cr gi cr g2 received by the editors january 28 1981 and in revised form may 19 1981 1980 mathematics subject classification primary 46l05 secondary 46l55 1 982 american mathematical society 0002 9947 82 00001022 04 25

compact actions commuting with ergodic actions and applications to crossed products let a k be a c dynamical system with k compact in this paper we prove a duality result for saturated actions theorem 3 3 the proof of this result can also be considered as an alternate proof of the corresponding result for von neumann algebras due to araki haag kastler and takesaki 14 we also obtain results concerning the simplicity and the primeness of the crossed product a k in terms of the ergodicity of the commutant of propositions 5 3 and 5 4

derivations commuting with abelian gauge actions on lattice systems let be an action of a compact abelian groupg on ac algebraa and assume that the fixed point subalgebraa is an af algebra we show that if is a closed derivation ona commuting with and the restriction of toa generates a one parameter group of automorphisms then itself is a generator in particular the result applies if is an infinite product action ofg on a uhf algebra furthermore if in this situation 1 and 2 are two derivations both satisfying the hypotheses on and 1 and 2 have the same restriction toa then there exists a one parameter subgroup of the action with generator 0 such thatd 1 d 2 d 0 is a joint core for the three derivations and 2 1 0 on this core

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

symmetries of quantum spaces subgroups and quotient spaces of quantum su 2 and so 3 groups we prove that each action of a compact matrix quantum group on a compact quantum space can be decomposed into irreducible representations of the group we give the formula for the corresponding multiplicities in the case of the quotient quantum spaces we describe the subgroups and the quotient spaces of quantumsu 2 andso 3 groups

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

an arithmetical characterization of np abstract adleman and manders proc 17th ieee symposium on foundations of computer science 1976 obtained a near characterization of np using diophantine predicates with quantifier bounds we characterize np as the class of sets definable by a polynomial predicate preceded by a string of quantifiers where each universal variable has a bound of the form p n and each existential variable has a bound of the form 2 q n for input n and polynomials p and q

unbounded derivations commuting with compact group actions let be a closed derivation in ac algebra mathfrak a which commutes with an ergodic action of a compact group on mathfrak a then generates ac dynamics of mathfrak a similar results are obtained for non ergodic actions on abelianc algebras and on the algebra of compact operators

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

approximate equivalence for representations of c algebras and c dynamical systems abstract approximate equivalence unitary equivalence up to arbitrarily small compact perturbations is studied for representations of c algebras and covariant representations of c dynamical systems approximate equivalence for representations of c algebras is shown to be determined by a trace condition analogous to the trace condition for unitary equivalence of representations of finite groups for c dynamical systems with a compact abelian group acting approximate equivalence is shown to be determined by certain associated representations of the fixed point algebra of the action

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

expressibility and parallel complexity it is shown that the time needed by a concurrent read concurrent write parallel random access machine cram to check if an input has a certain property is the same as the minimal depth of a first

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

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

a galois correspondence for compact group actions on c algebras abstract in this paper we prove a galois correspondence for compact group actions on c algebras in the presence of a commuting minimal action namely we show that there is a one to one correspondence between the c subalgebras that are globally invariant under the compact action and the commuting minimal action that in addition contain the fixed point algebra of the compact action and the closed normal subgroups of the compact group

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

strong asymptotic abelianness for entropic k systems we prove that in entropick systems of type ii1 the automorphism is strongly asymptotically abelian

maximum likelihood localization of 2 d patterns in the gauss laguerre transform domain theoretic framework and preliminary results usual approaches to localization i e joint estimation of position orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures which allow for position estimation independent of scale and orientation in this paper a maximum likelihood method for pattern localization working in the gauss laguerre transform glt domain is presented the glt is based on an orthogonal family of circular harmonic functions with specific radial profiles which permits optimum joint estimation of position and scale rotation parameters looking at the maxima of a gauss laguerre likelihood map the fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the cramer rao lower bound application of the ml estimation method is discussed and an example is provided