rulegraphs for graph matching in pattern recognition abstract in pattern recognition the graph matching problem involves the matching of a sample data graph with the subgraph of a larger model graph where vertices and edges correspond to pattern parts and their relations in this paper we present rulegraphs a new method that combines the graph matching approach with rule based approaches from machine learning this new method reduces the cardinality of the np complete graph matching problem by replacing model part and their relational attribute states by rules which depict attribute bounds and evidence for different classes we show how rulegraphs when combined with techniques for checking feature label compatibilities not only reduce the search space but also improve the uniqueness of the matching process

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

two dimensional local moment surface fitting and their fast computation abstract it is proved that local moments are related to their surface fitting coefficients by a linear transform and by this the surface fitting based feature extraction is converted into the computation of 2d local moments a npt recursive method is proposed to compute 2d local moments quickly and then to efficiently implement surface fitting the new method has a novel advantage that its computational complexity for both 2d local moment computation and surface fitting is independent of the mask size which much efficiently speed up the feature extraction

computation of surface geometry and segmentation using covariance techniques in this correspondence the application of covariance techniques to surface representation of 3 d objects is discussed and such ways of computing surface geometry are compared with traditional methods using differential geometry it is shown how the covariance method provides surface descriptors that are invariant to rigid motions without explicitly using surface parameterizations or derivatives analogous covariance operators for both the gauss and weingarten maps are defined and a range image segmentation technique is presented that labels pixels as jump or crease discontinuities or planar parabolic or curved region types

range image segmentation based on differential geometry a hybrid approach the authors describe a hybrid approach to the problem of image segmentation in range data analysis where hybrid refers to a combination of both region and edge based considerations the range image of 3 d objects is divided into surface primitives which are homogeneous in their intrinsic differential geometric properties and do not contain discontinuities in either depth of surface orientation the method is based on the computation of partial derivatives obtained by a selective local biquadratic surface fit then by computing the gaussian and mean curvatures an initial region gased segmentation is obtained in the form of a curvature sign map two additional initial edge based segmentations are also computed from the partial derivatives and depth values namely jump and roof edge maps the three image maps are then combined to produce the final segmentation experimental results obtained for both synthetic and real range data of polyhedral and curved objects are given

3d free form surface registration and object recognition a new technique to recognise 3d free form objects via registration is proposed this technique attempts to register a free form surface represented by a set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d sensed data points to the model surface represented by another set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d model data points without prior knowledge of correspondence or view points between the two point sets with an initial assumption that the sensed surface be part of a more complete model surface the algorithm begins by selecting three dispersed reliable points on the sensed surface to find the three corresponding model points the method uses the principal curvatures and the darboux frames to restrict the search over the model space invariably many possible model 3 typles will be found for each hypothesized model 3 tuple the transformation to match the sensed 3 tuple to the model 3 tuple can be determined a heuristic search is proposed to single out the optimal transformation in low order time for realistic object recognition or registration where the two range images are often extracted from different view points of the model the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on with this the sensed 3 tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views we propose an algorithm to select a minimal non redundant set of 3 tuples such that at least one of the 3 tuples will lie on the overlap applying the previous algorithm to each 3 tuple within this set the optimal transformation can be determined experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases if the optimal registrations between the sensed data candidate and each of a set of model data are found then for 3d object recognition purposes the minimal best fit error can be used as the decision rule

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

range data based object surface segmentation via edges and critical points a novel method for range image segmentation is presented in this paper it is based on an integration of edge and region information the algorithm consists of three steps edge and critical point detection triangulation and region growing experimental results show that the method is efficient for segmentation of the range images that contain polyhedral objects a three dimensional 3 d surface structure graph ssg obtained from the segmentation is a description of the surface structure about an object therefore a segmentation result also presents a data set that can be used to establish a surface model for computer aided design based cad based vision and object recognition

second order implicit polynomials for segmentation of range images abstract in this paper we present an algorithm for segmentation and feature extraction for noisy range images we use the edge and region based approach for obtaining reliable segmentation maps for edge detection regions having much higher values of planar fit error are assumed to contain edges these edge regions are explored for detection of crease edges which can be located at the maxima of the curvature however due to noise the maximas are generated at a number of points other than the actual edges these extraneous curvature maximas have a substantially smaller value of curvature compared with the curvature of the actual edges the true edges are detected using an approach based on local thresholding within edge regions the detected edges segment the range image into smooth patches on each of the smooth patches a planar quadric fit is obtained using a novel non iterative procedure to obtain reliable fits we had to restrict the permissible class of quadrics to surfaces of revolution the quadric fit obtained gives a very reliable estimate of the position and orientation of the axis for curved surfaces the approach has been demonstrated on real range data and has been found to give good results

on certain new nonlinear retarded integral inequalities in two independent variables and applications abstract the purpose of this paper is to establish some new non linear retarded integral inequalities in two independent variables which can be used as handy tools to study the boundedness of solutions of differential integral equations with the initial conditions an application is given to illustrate the usefulness of our results

on some new inequalities related to certain inequalities in the theory of differential equations in the present paper we establish some new integral inequalities related to a certain inequality arising in the theory of differential equations the discrete analogues of the main results are also given the analysis used in the proofs is elementary and the results established here provide new estimates for these types of inequalities

on the convergence of infinite products of matrices abstract in the normed metric space of n square complex matrices convergence of i ai implies convergence of i u i a i with u i 1 i if and only if i q u i converges for any integer q the limit of i u i a i may be considered a function u a of the summable sequence a a i the function u is parametrized by u u i the sequences of summable matrices a a i constitute a normed metric space e with norm a e i a i the family of functions u a i u i a i is equicontinuous at a if a e u i

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

on the growth of infinite products of slowly varying primitive matrices abstract let a t be a sequence of bounded nonnegative matrices each with perron root t satisfying a condition of uniform primitivity and having nonzero entries bounded away from 0 in a generalization of a result on powers of primitive matrices it is shown that if the matrices a t vary slowly enough i e a t 1 a t e for all t and some small e then as soon as the entries p i j t of the backward product a t a t 1 a 1 are positive the ratios p i j t p i j t 1 are equal to t h i j t where for all t 0 each h i j t 0 is small in a precisely quantified manner the larger t 0 is and the slower the probability normed perron vectors v t of a t have changed in the recent past preceding t 0 the smaller h i j t 0 will be other similar results are derived the resulting approximation p i j t p i j t 1 t is illustrated with two numerical examples

generalized gronwall bellman type delay dynamic inequalities on time scales and their applications abstract in this paper we establish some new gronwall bellman type delay dynamic inequalities on time scales which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales our results generalize the main results of ou iang l ou iang the boundedness of solutions of linear differential equations y a t y 0 shuxue jinzhan 3 1957 409 415 jiang f c jiang f w meng explicit bounds on some new nonlinear integral inequality with delay j comput appl math 205 2007 479 486 and yuan z l yuan x w yuan f w meng some new delay integral inequalities and their applications appl math comput 208 2009 231 237

a theorem on products of matrices a new result on products of matrices is proved in the following theorem let mi i 1 2 be a bounded sequence of square matrices and k be the l u b of the spectral radii mi then for any positive number e there is a constant a and an ordering p j j 1 2 of the matrices such that j 1nmp j a k e n n 1 2 the ordering is well defined by p j a one to one mapping on the set of positive integers in general the inequality does not hold for any ordering p j a counterexample is provided however some sufficient conditions are given for the result to remain true irrespective of the order of the matrices

a generalization of retarded integral inequalities in two independent variables and their applications the object of this paper is to establish some nonlinear retarded integral inequalities in two independent variables which can be used as handy tools in the theory of partial differential and integral equations with time delays

inferring surface trace and differential structure from 3 d images early image understanding seeks to derive analytic representations from image intensities the authors present steps towards this goal by considering the inference of surfaces from three dimensional images only smooth surfaces are considered and the focus is on the coupled problems of inferring the trace points the points through which the surface passes and estimating the associated differential structure given by the principal curvature and direction fields over the estimated smooth surfaces computation of these fields is based on determining an atlas of local charts or parameterizations at estimated surface points algorithm robustness and the stability of results are essential for analyzing real images to this end the authors present a functional minimization algorithm utilizing overlapping local charts to refine surface points and curvature estimates and develop an implementation as an iterative constraint satisfaction procedure based on local surface smoothness properties examples of the recovery of local structure are presented for synthetic images degraded by noise and for clinical magnetic resonance images

strong ergodicity for perturbed dual semigroups and application to age dependent population dynamics abstract in this paper we first summarize the perturbation theory in a sun reflexive banach space next we shall introduce the concept of strong ergodicity for the evolutionary system and then we investigate conditions under which the evolutionary system generated by the perturbation of a c 0 semigroup in a sun reflexive banach space becomes strongly ergodic subsequently we construct the evolutionary system corresponding to lotka s renewal equation and apply it to prove strong ergodicity of the age structured population with time dependent vital rates finally we study the controllability of the age structured population controlled by changing its total fertility rate

compact global attractors of discrete inclusions abstract the paper is dedicated to the study of the problem of the existence of compact global attractors of discrete inclusions and to the description of its structure we consider a family of continuous mappings of a metric space w into itself and w f i i i is the family of discrete dynamical systems on the metric space w we consider a discrete inclusion 1 u t 1 f u t associated with m f i i i where f u f u f m for all u w we give sufficient conditions the family of maps m is contracting in the extended sense for the existence of a compact global attractor of 1 if the family m consists of a finite number of maps then the corresponding compact global attractor is chaotic we study this problem in the framework of non autonomous dynamical systems cocyles

integral inequalities in two independent variables for retarded volterra equations in this paper we obtain some retarded volterra integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

on retarded integral inequalities and their applications abstract the main results of j math anal appl 285 2003 436 443 are here generalized to the following retarded integral inequalities u m t c m m n m m n 0 t f s u n s w u s g s u n s d s and u m t c m m n m m n 0 t f s u n s w u s d s m m n 0 t g s u n s w u s d s where m n 0 are constants and t r 0 the results given here can be applied to the global existence of solutions to differential equations with time delay

a retarded gronwall like inequality and its applications we prove a gronwall like inequality and present some of its applications to the qualitative study of retarded differential equations the problems of global continuation of the solutions and the existence of nonoscillatory solutions are considered by means of examples we show the usefulness of our results

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

on certain integral inequalities in two independent variables for retarded equations in this paper we establish some new retarded integral inequalities in two independent variables which can be used as tools in the theory of integral equations with time delays applications are given to illustrate the usefulness of the inequalities

on retarded integral inequalities in two independent variables and their applications the object of this paper is to establish some nonlinear retarded integral inequalities in two independent variables which can be used as handy tools in the theory of partial differential and integral equations with time delays

approximation of granular textures by quadric surfaces abstract the method to compute the best biquadratic form approximating an image on neighbourhoods of sizes 3 3 to 9 9 pixels is given when this quadric surface is an elliptic paraboloid various geometric parameters are expressed in terms of quadric coefficients they are the exact position of the apex the height direction eccentricity projected area and mean and gaussian curvatures two examples of approximation by elliptic paraboloids are then presented on two kinds of images radiographs of metallic pieces and histological sections

a retarded integral inequality and its applications we prove a retarded nonlinear integral inequality and present some applications of it to the global existence of solutions to differential equations with time delay