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

3d object modeling and recognition using local affine invariant image descriptors and multi view spatial constraints this article introduces a novel representation for three dimensional 3d objects in terms of local affine invariant descriptors of their images and the spatial relationships between the corresponding surface patches geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide matching and reconstruction allowing the acquisition of true 3d affine and euclidean models from multiple unregistered images as well as their recognition in photographs taken from arbitrary viewpoints the proposed approach does not require a separate segmentation stage and it is applicable to highly cluttered scenes modeling and recognition results are presented

simulation of a cellular automat with an oriented bootstrap rule abstract the evolution of a cellular automat with a culling or bootstrap condition on the minimum number of neighbours for survival has been simulated the introduction of an orientational constraint converts the lattice from isotropic to semidirected simulations of systems of up to 230 million sites are found to be compatible with a threshold value of p 0 966 0 01

co frobenius coalgebras abstract we investigate left and right co frobenius coalgebras and give equivalent characterizations which prove statements dual to the characterizations of frobenius algebras we prove that a coalgebra is left and right co frobenius if and only if c rat c c as right c modules and also that this is equivalent to the fact that the functors hom k k and hom c c from m c to m c are isomorphic this allows a definition of a left right symmetric concept of co frobenius coalgebras that is perfectly dual to the one of frobenius algebras and coincides to the existing notion left and right co frobenius coalgebra

rotation invariant local frequency descriptors for texture classification this paper presents a novel rotation invariant method for texture classification based on local frequency components the local frequency components are computed by applying 1 d fourier transform on a neighboring function defined on a circle of radius r at each pixel we observed that the low frequency components are the major constituents of the circular functions and can effectively represent textures three sets of features are extracted from the low frequency components two based on the phase and one based on the magnitude the proposed features are invariant to rotation and linear changes of illumination moreover by using low frequency components the proposed features are very robust to noise while the proposed method uses a relatively small number of features it outperforms state of the art methods in three well known datasets brodatz outex and curet in addition the proposed method is very robust to noise and can remarkably improve the classification accuracy especially in the presence of high levels of noise

robust partial shape classification using invariant breakpoints and dynamic alignment abstract a system for classifying partially occluded noisy shapes in varying positions orientations and dimensions is described an iterative algorithm derived from the colinearity principle is developed to locate invariant breakpoints on a shape contour the set of invariant breakpoints partitions the contour into a sequence of contour segments each contour segment is described by an ordered sequence that represents the euclidean distance between the pixels in the contour segment and the centroid of the region formed by connecting the end points of the contour segment by a straight line two stages of dynamic alignment with the appropriate constraints are formulated to determine shape similarity the first stage gives a distance measure of contour segment similarity and in the second stage the intersegment distances are used to optimally align contour segments so that a final measure of shape similarity is obtained the performance of the system is demonstrated by considering the classification of aircraft shapes belonging to four classes and classification results are presented as functions of noise and occlusion levels the results indicate that reasonable classification is obtained for noisy shapes with 0 to 30 occlusion

direct curvature scale space theory and corner detection the curvature scale space css technique is considered to be a modern tool in image processing and computer vision direct curvature scale space dcss is defined as the css that results from convolving the curvature of a planar curve with a gaussian kernel directly in this paper we present a theoretical analysis of dcss in detecting corners on planar curves the scale space behavior of isolated single and double corner models is investigated and a number of model properties are specified which enable us to transform a dcss image into a tree organization and so that corners can be detected in a multiscale sense to overcome the sensitivity of dcss to noise a hybrid strategy to apply css and dcss is suggested

comparison between simultaneous and sequential updating in 2n 1 1 cellular automata properties of cellular automata with packard wolfram code 2n 1 1 have been studied without and with noise on square n 4 and triangular n 6 lattices the outer totalistic rule used assign a central spin opposite to the majority spin of its neighbourhood and flips it in the case of equality starting from random configurations with a variable proportion r of up spins different relaxation behaviours and equilibrium structures are obtained a ferromagnetic f structure and an antiferromagnetic af structure for simultaneous and sequential updatings respectively on a square lattice when the spins are processed simultaneously in the presence of noise a first order transition f af is observed for a square lattice and a second order transition for a triangular lattice the results show similarities with ising models domains but also strong differences magnetization as a function of r

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

metastability effects in bootstrap percolation bootstrap percolation models or equivalently certain types of cellular automata exhibit interesting finite volume effects these are studied at a rigorous level the authors find that for an initial configuration obtained by placing particles independently with probability p or 2 the density of the bootstrapped final configurations in the sequence of cubes l 2 l 2 d typically undergoes an abrupt transition as l is increased from being close to 0 to the value 1 with l fixed at a large value the mean final density as a function of p changes from 0 to 1 around a value which varies only slowly with l the pertinent parameter being lambda p1 d 1 ln l the driving mechanism is the capture of a critical droplet this behaviour is analogous to the decay of a metastable state near a first order phase transition for which the analysis offers some suggestive ideas

segmentation of two dimensional curve contours abstract segmentation of digitized planar curves is one of the most important elements in early image processing because a segmented image can describe the object profile in a compact form to facilitate higher level vision processing in many applications it is necessary to decompose an object boundary contour into several primitives such as segments and curves in this paper a two stage hybrid technique for the segmentation of two dimensional 2d curves is presented in which the number of segments is assumed to be known first the boundary is iteratively approximated using a split and merge method next an end point adjustment procedure is applied to reach the best fitting polygonal approximation a computational comparison with two existing methods shows that the proposed technique is fast and accurate an application of the new segmentation technique to industrial part inspection is also provided

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

critical points of two dimensional bootstrap percolation like cellular automata cellular automata in two dimensions that generalize the bootstrap percolation dynamics are considered focusing on the thresholdp c of the initial density for convergence to total occupancy to occur these models are classified according top c being 0 1 or strictly between these extreme values explicit upper and lower bounds are provided in the third case

an improved curvature scale space corner detector and a robust corner matching approach for transformed image identification there are many applications such as image copyright protection where transformed images of a given test image need to be identified the solution to this identification problem consists of two main stages in stage one certain representative features such as corners are detected in all images in stage two the representative features of the test image and the stored images are compared to identify the transformed images for the test image curvature scale space css corner detectors look for curvature maxima or inflection points on planar curves however the arc length used to parameterize the planar curves by the existing css detectors is not invariant to geometric transformations such as scaling as a solution to stage one this paper presents an improved css corner detector using the affine length parameterization which is relatively invariant to affine transformations we then present an improved corner matching technique as a solution to the stage two finally we apply the proposed corner detection and matching techniques to identify the transformed images for a given image and report the promising results

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area

robust image corner detection through curvature scale space this paper describes a novel method for image corner detection based on the curvature scale space css representation the first step is to extract edges from the original image using a canny detector 1986 the corner points of an image are defined as points where image edges have their maxima of absolute curvature the corner points are detected at a high scale of the css and tracked through multiple lower scales to improve localization this method is very robust to noise and we believe that it performs better than the existing corner detectors an improvement to canny edge detector s response to 45 spl deg and 135 spl deg edges is also proposed furthermore the css detector can provide additional point features curvature zero crossings of image edge contours in addition to the traditional corners

boundary simplification using a multiscale dominant point detection algorithm abstract in this paper we intend to characterize boundaries using the scale space theory the aim we try to achieve is the description of a boundary in relation to a subset of points dominant points that are obtained from a new multiscale representation of the boundary dominant points are characterized by a high curvature value in the original or smoothed boundary as a result the boundary is represented using those points as well as an appropriate interpolation method the linear one in the simplest case among them as the basic tool of our work we will introduce a new multiscale dominant point detection algorithm that detects the points at their natural scales through a reliability condition with respect to the original curve because we want to apply the algorithms on complex enough boundaries we use cartographic boundaries in which several structures can be obtained at different scales to evaluate the results

non parametric dominant point detection abstract a new method for detecting dominant points is presented it does not require any input parameter and the dominant points obtained by this method remain relatively the same even when the object curve is scaled or rotated in this method for each boundary point a support region is assigned to the point based on its local properties each point is then smoothed by a gaussian filter with a width proportional to its determined support region a significance measure for each point is then computed dominant points are finally obtained through nonmaximum suppression unlike other dominant point detection algorithms which are sensitive to scaling and rotation of the object curve the new method will overcome this difficulty furthermore it is robust in the presence of noise the proposed new method is compared to the teh chin algorithm see c teh and r t chin ieee trans pattern anal mach intell 11 859 872 1989 in terms of the computational complexity the approximation errors and the number of detected dominant points of an object curve

recognition and inspection of two dimensional industrial parts using subpolygons abstract a model based scene analysis for the recognition of imperfect and possibly occluded two dimensional 2d industrial parts is described the means of recognition leads reliably to the correct association of the sides making up the unknown object to those of the model both the scene polygon and the model are divided into pairs of complementary subpolygons this is done by a cutting line drawn parallel and close to a selected side the subpolygons from the object are compared to all possible subpolygons from the model invariant moments are used in the analysis a matching process using clusters of mutually consistent features is used to hypothesize the identity of the object examples are given to illustrate the method

laplacian scale space behavior of planar curve corners scale space behavior of corners is important for developing an efficient corner detection algorithm in this paper we analyze the scale space behavior with the laplacian of gaussian log operator on a planar curve which constructs laplacian scale space lss the analytical expression of a laplacian scale space map lss map is obtained demonstrating the laplacian scale space behavior of the planar curve corners based on a newly defined unified corner model with this formula some laplacian scale space behavior is summarized although lss demonstrates some similarities to curvature scale space css there are still some differences first no new extreme points are generated in the lss second the behavior of different cases of a corner model is consistent and simple this makes it easy to trace the corner in a scale space at last the behavior of lss is verified in an experiment on a digital curve

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

global propagation of affine invariant features for robust matching local invariant features have been successfully used in image matching to cope with viewpoint change partial occlusion and clutters however when these factors become too strong there will be a lot of mismatches due to the limited repeatability and discriminative power of features in this paper we present an efficient approach to remove the false matches and propagate the correct ones for the affine invariant features which represent the state of the art local invariance first a pair wise affine consistency measure is proposed to evaluate the consensus of the matches of affine invariant regions the measure takes into account both the keypoint location and the region shape size and orientation based on this measure a geometric filter is then presented which can efficiently remove the outliers from the initial matches and is robust to severe clutters and non rigid deformation to increase the correct matches we propose a global match refinement and propagation method that simultaneously finds a optimal group of local affine transforms to relate the features in two images the global method is capable of producing a quasi dense set of matches even for the weakly textured surfaces that suffer strong rigid transformation or non rigid deformation the strong capability of the proposed method in dealing with significant viewpoint change non rigid deformation and low texture objects is demonstrated in experiments of image matching object recognition and image based rendering

on two conjectures of faith abstract we prove that a profinite algebra whose left right cyclic modules are torsionless is finite dimensional and qf we give a relative version of the notion of left right pf ring for pseudocompact algebras and prove it is left right symmetric and dual to the notion of quasi co frobenius coalgebras we also prove two ring theoretic conjectures of faith in the setting and supplementary hypothesis of profinite algebras any profinite semiartinian selfinjective algebra is finite dimensional and qf and any fgf profinite algebra is finite dimensional qf

curvature scale space driven object recognition with an indexing scheme based on artificial neural networks this paper addresses the problem of recognizing real flat objects from two dimensional images in particular a new object recognition technique which performs under occlusion and geometric transformations is presented the method has mainly been designed to handle complex objects and incorporates two main ideas first matching operates hierarchically guided by a curvature scale space segmentation scheme and takes advantage of important object features that is features which distinguish an object from other objects this is different from many classical approaches which employ a rather large number of very local features second the model database is built by using artificial neural networks anns this is also different from traditional approaches where classical indexing schemes such as hashing are utilized to organize and search the model database important object features are obtained in two steps first by segmenting the object boundary at multiple scales using its resampled curvature scale space rcss and second by concentrating at each scale separately searching for groups of segments which distinguish an object from other objects these groups of segments are then used to build a model database which stores associations between segments and models the model database is implemented using a set of anns which provide the essential mechanism not only for establishing correct associations between groups of segments and models but also for enabling efficient searching and robust retrieval the method has been tested using both artificial and real data illustrating good performance

the splitting problem for coalgebras abstract let r be a ring and let t be a torsion preradical r is said to have the splitting property provided that for every left r module m the torsion submodule t m of m is a direct summand of m the characterization of rings with this property is a classical problem in particular the goldie and dickson torsion theories have been studied that for noncommutative rings remains open we consider the problem for the algebra c associated to a coalgebra c and the torsion preradical rat it is shown that if c has the splitting property with respect a rat then c is finite dimensional

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

new polygonal approximation schemes for object shape representation abstract object shape representation is an important issue in pattern recognition and computer vision applications a set of new polygonal approximation schemes namely the internal maximum area polygonal approximation imapa the external minimum area polygonal approximation emapa and the minimum area deviation polygonal approximation madpa are proposed for object shape representation the area deviation between the initial object shape and its approximation polygon is defined as the cost function instead of outputting a unique approximation polygon each proposed scheme outputs a sequence of approximation polygons with different numbers of line segments and different area deviations for various application situations for a given area deviation bound and an initial object shape each proposed scheme can give a corresponding optimal approximation polygon with a minimum number of line segments a performance comparison among the proposed schemes is included the proposed schemes are compared with two other existing schemes some experimental results show the feasibility of the proposed approaches

enhanced figure ground classification with background prior propagation we present an adaptive figure ground segmentation algorithm that is capable of extracting foreground objects in a generic environment starting from an interactively assigned background mask an initial background prior is defined and multiple soft label partitions are generated from different foreground priors by progressive patch merging these partitions are fused to produce a foreground probability map the probability map is then binarized via threshold sweeping to create multiple hard label candidates a set of segmentation hypotheses is formed using different evaluation scores from this set the hypothesis with maximal local stability is propagated as the new background prior and the segmentation process is repeated until convergence similarity voting is used to select a winner set and the corresponding hypotheses are fused to yield the final segmentation result experiments indicate that our method performs at or above the current state of the art on several data sets with particular success on challenging scenes that contain irregular or multiple connected foregrounds

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

performance comparisons of contour based corner detectors corner detectors have many applications in computer vision and image identification and retrieval contour based corner detectors directly or indirectly estimate a significance measure e g curvature on the points of a planar curve and select the curvature extrema points as corners while an extensive number of contour based corner detectors have been proposed over the last four decades there is no comparative study of recently proposed detectors this paper is an attempt to fill this gap the general framework of contour based corner detection is presented and two major issues curve smoothing and curvature estimation which have major impacts on the corner detection performance are discussed a number of promising detectors are compared using both automatic and manual evaluation systems on two large datasets it is observed that while the detectors using indirect curvature estimation techniques are more robust the detectors using direct curvature estimation techniques are faster

phase diagram of the one state potts model on the cayley tree the phase diagram of the one state potts model on the closed asymmetric cayley tree with branching ratior 2 is obtained from the bethe peierls map the route to chaos via the period doubling cascade is obtained by considering the antiferromagnetic coupling limit the connection of the potts model with the percolation problem is shown by calculating the order parameter its susceptibility the internal energy and the specific heat as well as their asymptotic behavior at the paramagnetic ferromagnetic critical point due to the type of the lattice and to the polynomial character of the map this is the simplest known example of a mckay berker kirkpatrick spin glass

robust automatic selection of optimal views in multi view free form object recognition this paper addresses the issue of automatic selection of the best and the optimum number of representative views for each object in a database that can enable the accurate recognition of that object from any single arbitrary view of the object the object boundary in each view is represented by its curvature scale space css image the css representation has been selected for mpeg 7 standardisation as a contour shape descriptor the paper also presents a novel method for fusion of results from combined shape descriptors the utilisation of this method for multi view three dimensional 3 d object recognition has been explored the object boundary of each view is represented effectively using the css technique moment invariants and fourier descriptors it has been shown that the results obtained from the fusion method are superior to the results obtained from any single technique the method has been tested on a collection of free form 3 d objects each object has been modelled using an optimal number of silhouette contours obtained from different viewpoints this number varies depending on the complexity of the object and the measure of expected accuracy a comprehensive analysis of the performance of the system has been given

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

perceptually relevant and piecewise linear matching of silhouettes in this paper a novel alignment method for silhouettes is proposed this method is based on the establishment of correspondences between landmarks on their boundaries and in turn on the establishment of correspondences of the boundary pieces in between these landmarks the method yields more correct correspondences than conventional methods that scale the arc length descriptions of silhouettes to align them the selection of landmarks is investigated as to the robustness of their localization and their perceptual relevance matching of silhouettes is then achieved by quantifying the dissimilarity of a pair of silhouette boundaries based on a novel dissimilarity metric the matching procedure is evaluated based on retrieval experiments and it is concluded that the precision of the results is higher than that obtained by conventional pointwise comparison methods

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

simulation of three dimensional bootstrap percolation on a simple cubic lattie which is initially occupied randomly with concentration p a site is emptied if it does not have at least four of its six neighbors occupied the threshold concentration below which all sites are emptied after sufficiently many iterations is found to vary logarithmically with l for l l l lattices and l between 32 and 704 it is extrapolated to about 0 936 for infinite lattices two other cases are roughly compatible with the theoretical prediction of unity as a threshold concentration

bootstrap automata the dynamics of destruction abstract simulations for bootstrap cellular automata on an oriented square lattice are shown to be consistent with exact results on the critical threshold p c 1 and a finite size scaling bound regimes above below and close to p c for finite samples are detailed and characterized by a wide choice of updating and coding algorithms

the use of maximum curvature points for the recognition of partially occluded objects abstract a graph theoretic optimization method is used to recognize partially occluded objects from a 2 d image through the use of maximal cliques and a weight matching algorithm the vertices of an occluded object image with high curvature values are classified by the objects which are hypothesized to be involved in the occlusion a heuristic method is also developed to further improve the computational speed a few typical examples are given to illustrate the accuracy of the optimization model as well as the simplicity of the companion heuristic method

matching widely separated views based on affine invariant regions invariant regions are self adaptive image patches that automatically deform with changing viewpoint as to keep on covering identical physical parts of a scene such regions can be extracted directly from a single image they are then described by a set of invariant features which makes it relatively easy to match them between views even under wide baseline conditions in this contribution two methods to extract invariant regions are presented the first one starts from corners and uses the nearby edges while the second one is purely intensity based as a matter of fact the goal is to build an opportunistic system that exploits several types of invariant regions as it sees fit this yields more correspondences and a system that can deal with a wider range of images to increase the robustness of the system two semi local constraints on combinations of region correspondences are derived one geometric the other photometric they allow to test the consistency of correspondences and hence to reject falsely matched regions experiments on images of real world scenes taken from substantially different viewpoints demonstrate the feasibility of the approach

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

a rotationally invariant descriptor based on mixed intensity feature histograms abstract this paper proposes a novel method to build a rotation invariant local descriptor by mixed intensity feature histogram most existing local descriptors based on intensity ordinal information typically encode only one local feature for each sampling point in the image patch to address this problem we proposed a method to encode more than one different local features for each pixel in the image patch and construct a 2d mixed intensity feature histogram from which our proposed mifh descriptor is then constructed since the rotation invariant coordinate system is adopted the mifh descriptor does not need to estimate the reference orientation in order to evaluate the performance and the robustness of the mifh with other well known local descriptors e g sift gloh daisy hri csltp liop mrogh image matching experiments were carried out on standard oxford dataset additional image pairs with complex illumination changes and image sequences with different noises to further investigate the discriminative ability of the mifh descriptor a simple object recognition experiment was conducted on three public datasets the experimental results demonstrate that our descriptor mifh exhibits better performance and robustness than other evaluated local descriptors

determination of optimal polygon from digital curve using l1 norm abstract a technique to determine optimal polygons of digital curves is proposed it determines the longest possible line segments with the minimum possible error the l 1 norm is used to measure the closeness of a polygon to a digital curve the algorithm runs in linear time the procedure is applied to several digital curves and promising results are obtained

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

classification of square lattice cellular automata abstract all 65 536 automata on the square lattice with nearest neighbor interactions ignoring the central spin were simulated we determined which percentage of them ended up in a fixed point with all spins parallel in other fixed points in up down oscillations with all spins parallel and in other oscillations of period two nine tenths of the rules did not fall into these classes we also checked for chaos i e how does the damage spread if one line of spins is reversed for 62 percent of the possible rules it spread over the lattice 31 percent had the damage remaining localized but nonzero and in 7 percent of all rules the damage healed out after some time these simulations were done with a speed of up to 120 updates per microsecond and cray xmp processor

proof of straley s argument for bootstrap percolation we prove thatpc 1 for bootstrap percolation with large void instabilities in particular ifm 3 on the square lattice

sphorb a fast and robust binary feature on the sphere in this paper we propose sphorb a new fast and robust binary feature detector and descriptor for spherical panoramic images in contrast to state of the art spherical features our approach stems from the geodesic grid a nearly equal area hexagonal grid parametrization of the sphere used in climate modeling it enables us to directly build fine grained pyramids and construct robust features on the hexagonal spherical grid thus avoiding the costly computation of spherical harmonics and their associated bandwidth limitation we further study how to achieve scale and rotation invariance for the proposed sphorb feature extensive experiments show that sphorb consistently outperforms other existing spherical features in accuracy efficiency and robustness to camera movements the superior performance of sphorb has also been validated by real world matching tests

comparison of two algorithms for bootstrap percolation models abstract two different algorithms for determining the percolation threshold in bootstrap percolation models are compared one algorithm is the usual literal bootstrap prescription whereby each site with less than the required number of neighbours is removed by a repetitive culling process the second algorithm was proposed for diffusion percolation models and has some similarities with multigrid or swendsen wang algorithms for thermal systems since it considers entire clusters in a single step it is called the rectangle algorithm because the clusters of the models under investigation are compact for small systems and concentrations where not all lattices percolate the literal algorithm is more efficient however there is some indication that for large systems and concentrations closer to the threshold value of the infinite system the rectangle algorithm is faster this has interesting implications for calculations in some other cellular automata systems

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

dynamical properties of a new fast algorithm for the simulation of the ising model a new algorithm recently proposed by pomeau 1984 and herrmann 1986 for the microcanonical simulation of the ising model is very efficiently implemented on a dap computer its dynamical properties are studied and compared with those of the standard metropolis algorithm

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

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

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

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

diffusion percolation i infinite time limit and bootstrap percolation several models for the dynamic growth of percolation clusters or diffusion percolation dp are introduced and analysed in these models a random walker an ant walks on percolation clusters which are occupied with initial site concentration pi the ant is allowed to step off such clusters and add new sites to them if certain conditions are met some of these models are shown to have a one to one correspondence with models of bootstrap percolation bp in which sites which do not have a required number of neighbours are successively culled two new percolation thresholds have been calculated for two diffusion percolation models on the square lattice

self similarity and points of interest in this work we present a new approach to interest point detection different types of features in images are detected by using a common computational concept the proposed approach considers the total variability of local regions the total sum of squares computed on the intensity values of a local circular region is divided into three components between circumferences sum of squares between radii sum of squares and the remainder these three components normalized by the total sum of squares represent three new saliency measures namely radial tangential and residual the saliency measures are computed for regions with different radii and scale spaces are built in this way local extrema in scale space of each of the saliency measures are located they represent features with complementary image properties blob like features corner like features and highly textured points results obtained on image sets of different object classes and image sets under different types of photometric and geometric transformations show high robustness of the method to intraclass variations as well as to different photometric transformations and moderate geometric transformations and compare favorably with the results obtained by the leading interest point detectors from the literature the proposed approach gives a rich set of highly distinctive local regions that can be used for object recognition and image matching

finite size effects for some bootstrap percolation models the consequences of schonmann s new proof that the critical threshold is unity for certain bootstrap percolation models are explored it is shown that this proof provides an upper bound for the finite size scaling in these systems comparison with data for one case demonstrates that this scaling appears to give the correct asymptotics we show that the threshold for a finite system of sizel scales aso ln lnl for the isotropic model in three dimensions where sites that fail to have at least four neighbors are culled

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

the dickson subcategory splitting conjecture for pseudocompact algebras abstract let a be a pseudocompact or profinite algebra so a c where c is a coalgebra we show that the if the semiartinian part the dickson part of every a module m splits off in m then a is semiartinian giving thus a positive answer in the case of algebras arising as dual of coalgebras pseudocompact algebras to a well known conjecture of faith

the detection of dominant points on digital curves by scale space filtering the detection of dominant points is an important preprocessing step for shape recognition an effective method of scale space filtering with a gaussian kernel is introduced to detect dominant points on digital curves the conventional polygonal approximation algorithms are time consuming and need input parameter tuning for gaussian smoothing the noise and quantization error also they are sensitive to scaling and rotation of the object curve the above dit culty can be overcome by finding out the dominant points at each scale by scale space filtering by tracing back the dominant point contours in the scale space image the stable cardinal curvature points can be detected very accurately this new method requires no input parameters and the resultant dominant points do not change under translation rotation and scaling meanwhile a fast convolution algorithm is proposed to detect the dominant points at each scale dominant points scale space gaussian smoothing curvature

simultaneous object recognition and segmentation from single or multiple model views we present a novel object recognition approach based on affine invariant regions it actively counters the problems related to the limited repeatability of the region detectors and the difficulty of matching in the presence of large amounts of background clutter and particularly challenging viewing conditions after producing an initial set of matches the method gradually explores the surrounding image areas recursively constructing more and more matching regions increasingly farther from the initial ones this process covers the object with matches and simultaneously separates the correct matches from the wrong ones hence recognition and segmentation are achieved at the same time the approach includes a mechanism for capturing the relationships between multiple model views and exploiting these for integrating the contributions of the views at recognition time this is based on an efficient algorithm for partitioning a set of region matches into groups lying on smooth surfaces integration is achieved by measuring the consistency of configurations of groups arising from different model views experimental results demonstrate the stronger power of the approach in dealing with extensive clutter dominant occlusion and large scale and viewpoint changes non rigid deformations are explicitly taken into account and the approximative contours of the object are produced all presented techniques can extend any view point invariant feature extractor

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

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed

localized image watermarking based on feature points of scale space representation this paper proposes a novel method for content based watermarking based on feature points of an image at each feature point the watermark is embedded after scale normalization according to the local characteristic scale characteristic scale is the maximum scale of the scale space representation of an image at the feature point by binding watermarking with the local characteristics of an image resilience against affine transformations can be obtained easily experimental results show that the proposed method is robust against various image processing steps including affine transformations cropping filtering and jpeg compression