subdivisions and local h vectors in part i a general theory of f vectors of simplicial subdivisions or triangulations of simplicial complexes is developed based on the concept of lo cal h vector as an application we prove that the h vector of a cohen macaulay complex increases under quasi geometric subdivision thus establishing a spe cial case of a conjecture of kalai and this author techniques include com mutative algebra homological algebra and the intersection homology of toric varieties in part ii we extend the work of part i to more general situations first a formal generalization of subdivision is given based on incidence alge bras special cases are then developed in particular one based on subdivisions of eulerian posets and involving generalized h vectors other cases deal with kazhdan lusztig polynomials ehrhart polynomials and a q analogue of eule rian posets many applications and examples are given throughout department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address rstan math mit edu this content downloaded from 157 55 39 210 on sat 30 jul 2016 05 59 16 utc all use subject to http about jstor org terms

generalizing the hough transform to detect arbitrary shapes abstract the hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve the initial work showed how to detect both analytic curves 1 2 and non analytic curves 3 but these methods were restricted to binary edge images this work was generalized to the detection of some analytic curves in grey level images specifically lines 4 circles 5 and parabolas 6 the line detection case is the best known of these and has been ingeniously exploited in several applications 7 8 9 we show how the boundaries of an arbitrary non analytic shape can be used to construct a mapping between image space and hough transform space such a mapping can be exploited to detect instances of that particular shape in an image furthermore variations in the shape such as rotations scale changes or figure ground reversals correspond to straightforward transformations of this mapping however the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes this makes the generalized hough transform a kind of universal transform which can be used to find arbitrarily complex shapes

a theoretical framework for relaxation processes in pattern recognition application to robust nonparametric contour generalization while various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives the wider problem addressed here is to find the best suited relaxation process for a given assignment problem or better still to construct a task dependent relaxation process for this we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition the resulting structure enables 1 a description of all known relaxation processes in general terms and 2 the design of task dependent relaxation processes we show that the well known standard relaxation formulas verify our approach referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail important characteristics of the constructed task dependent relaxation process are 1 the independency of the segmentation from any parameters 2 the invariance to geometric transformations 3 the simplicity and 4 efficiency

locating perceptually salient points on planar curves this paper describes the underlying ideas and algorithmic details of a computer program that performs at a human level of competence for a significant subset of the curve partitioning task it extends and rounds out the technique and philosophical approach originally presented by fischler and bolles 1986 in particular it provides a unified strategy for selecting and dealing with interactions between salient points even when these points are salient at different scales of resolution experimental results are presented involving on the order of 1000 real and synthetically generated images

parts of visual form computational aspects underlying recognition is an organization of objects and their parts into classes and hierarchies a representation of parts for recognition requires that they be invariant to rigid transformations robust in the presence of occlusions stable with changes in viewing geometry and be arranged in a hierarchy these constraints are captured in a general framework using notions of a part line and a partitioning scheme a proposed general principle of form from function motivates a particular partitioning scheme involving two types of parts neck based and limb based neck based parts arise from narrowings in shape or the local minima in distance between two points on the boundary while limb based parts arise from a pair of negative curvature minima which have co circular tangents in this paper we present computational support for the limb based and neck based parts by showing that they are invariant robust stable and yield a hierarchy of parts examples illustrate that the resulting decompositions are robust in the presence of occlusion and clutter for a range of man made and natural objects and lead to natural and intuitive parts which can be used for recognition

a shape representation with elastic quadratic polynomials preservation of high curvature points under noisy conditions we present a new shape representation technique for a planar shape using overlapping quadratic splines the technique refines the shape by iteratively updating each spline to reduce the cost associated with c 1 discontinuity it consists of a series of affine commutative linear operators producing a smooth bandpass frequency response the primary purpose of the technique is to remove minute high curvature points while preserving salient ones we compare the performance of the technique against those that are based on either linear splines cubic splines or wavelets we consider three criteria sensitivity of detecting salient high curvature points hausdorff distance between the representation and the original shape and computation time the results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small hausdorff distance and a computational cost

on the curvature of piecewise flat spaces we consider analogs of the lipschitz killing curvatures of smooth riemannian manifolds for piecewise flat spaces in the special case of scalar curvature the definition is due to t regge considerations in this spirit date back to j steiner we show that if a piecewise flat space approximates a smooth space in a suitable sense then the corresponding curvatures are close in the sense of measures

2d affine invariant contour matching using b spline model this paper presents a new affine invariant matching algorithm based on b spline modeling which solves the problem of the nonuniqueness of b spline in curve matching this method first smoothes the b spline curve by increasing the degree of the curve it is followed by a reduction of the curve degree using the least square error lse approach to construct the curvature scale space css image css matching is then carried out our method combines the advantages of b spline that are continuous curve representation and the robustness of css matching with respect to noise and affine transformation it avoids the need for other matching algorithms that have to use the resampled points on the curve thus the curve matching error is reduced the proposed algorithm has been tested by matching similar shapes from a prototype database the experimental results showed the robustness and accuracy of the proposed method in b spline curve matching

noncomputability arising in dynamical triangulation model of four dimensional quantum gravity computations in dynamical triangulation models of four dimensional quantum gravity involve weighted averaging over sets of all distinct triangulations of compact four dimensional manifolds in order to be able to perform such computations one needs an algorithm which for any givenn and a given compact four dimensional manifoldm constructs all possible triangulations ofm with n simplices our first result is that such algorithm does not exist then we discuss recursion theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four dimensional manifold

relaxation labeling in stereo image matching this paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives a relaxation scheme is the technique commonly used by existing methods to solve this problem these techniques generally impose the following competing constraints similarity smoothness ordering and uniqueness and assume a bound on the disparity range the smoothness constraint is basic in the relaxation process we have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem this problem also arises when repetitive structures appear in the scene i e complex images where the existing methods produce a high number of failures we develop our approach from a relaxation labeling method 1 w j christmas j kittler m petrou structural matching in computer vision using probabilistic relaxation ieee trans pattern anal mach intell 17 8 1995 749 764 which allows us to map the above constraints the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit consequently we improve the stereovision matching process a better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods

triangulations of subanalytic sets and locally subanalytic manifolds if two polyhedrons are locally subanalytically homeomorphic that is the graph is locally subanalytic they are pl homeomorphic a lo cally subanalytic manifold is one whose coordinate transformations are locally subanalytic it is proved that a locally subanalytic manifold has a unique pl manifold structure a semialgebraic manifold also is considered

on the solvability of domino snake problems abstract in this paper we present an extensive treatment of tile connectability problems sometimes called domino snake problems the interest in such problems stems from their relationship to classical tiling problems which have been established as an important simple and useful tool for obtaining basic lower bound results in complexity and computability theory we concentrate on the following two contrasting results the general snake problem is undecidable in a half plane due to ebbinghaus but is decidable in the whole plane this surprising decidability result was announced without proof by myers in 1979 we provide here the first full proof and show that the problem is actually pspace complete we also prove many results concerning the difficulty of variants of these general snake problems and their extension to infinite snakes in addition we establish a resemblance between snake problems and classical tiling problems considering the corresponding bounded unbounded and recurring cases

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

a constrained approach to multifont chinese character recognition the constraint graph is introduced as a general character representation framework for recognizing multifont multiple size chinese characters each character class is described by a constraint graph model sampling points on a character skeleton are taken as nodes in the graph connection constraints and position constraints are taken as arcs in the graph for patterns of the same character class the model captures both the topological invariance and the geometrical invariance in a general and uniform way character recognition is then formulated as a constraint based optimization problem a cooperative relaxation matching algorithm that solves this optimization problem is developed a practical optical character recognition ocr system that is able to recognize multifont multiple size chinese characters with a satisfactory performance was implemented

feature extraction of handwritten japanese characters by spine functions for relaxation matching abstract this paper proposes a method of extracting features of handwritten japanese characters by using spline approximation this method represents a character by contours expressed by well approximating functions and stable breakpoints which characterize the connection of the strokes so that it provides proper features for handwritten japanese character recognition with relaxation matching its effectiveness tested on a japanese character database is also shown

effectiveness non effectiveness in semialgebraic and pl geometry f acquistapace r benedetti and f broglia dipartimento di matematica universit i di pisa via f buonarroti 2 1 56127 pisa italy oblatum 14 iv 1989 25 i 1990 0 introduction and statement of the main results working in real semialgebraic geometry one could easily have the feeling that the main facts can be realized by algorithms e g path connecting points triangul ations good stratifications and the main trouble is to construct reasonably fast algorithms in fact it is this in principle constructive nature of semialgebraic geometry and the existence of powerful computers which make it interesting in view of concrete applications on the other hand nabutovsky s examples of non recursive functions associ ated to natural semialgebraic constructions see i n tell us that there are some conceptual limitations to the above attitude in this paper we consider some further examples of effectiveness non effect iveness results in semialgebraic and pl geometry our starting point was the study of shiota yokoi solution of the subanalytic hence semialgebraic hauptvermutung sy and the attempt to make it effective before starting we need to introduce some notations we shall use systematically the notation

encoding of a priori information in active contour models the theory of active contours models the problem of contour recovery as an energy minimization process the computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions in this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models the grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images the variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework we propose an algorithmic solution that combines a nondeterministic version of the knuth morris pratt algorithm for string matching with a time delayed discrete dynamic programming algorithm for energy minimization the numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion

entropy and distance of random graphs with application to structural pattern recognition the notion of a random graph is formally defined it deals with both the probabilistic and the structural aspects of relational data by interpreting an ensemble of attributed graphs as the outcomes of a random graph we can use its lower order distribution to characterize the ensemble to reflect the variability of a random graph shannon s entropy measure is used to synthesize an ensemble of attributed graphs into the distribution of a random graph or a set of distributions we propose a distance measure between random graphs based on the minimum change of entropy before and after their merging when the ensemble contains more than one class of pattern graphs the synthesis process yields distributions corresponding to various classes this process corresponds to unsupervised learning in pattern classification using the maximum likelihood rule and the probability computed for the pattern graph based on its matching with the random graph distributions of different classes we can classify the pattern graph to a class

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

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

on automatic threshold selection for polygonal approximations of digital curves polygonal approximation is a very common representation of digital curves a polygonal approximation depends on a parameter e which is the error value in this paper we present a method for an automatic selection of the error value e let e be a polygonal approximation of the original curve with an error value e we define a set of function ns e s s s such that for a given value of s ns e is the number of edges that contain at least s vertices in e the time complexity for computing the set of functions ns e s ss s is almost linear in n the number of vertices in in this paper we analyse the ns graph and show that for adequate values of s a wide plateau is expected to appear at the top of the graph this plateau corresponds to a stable state in the multi scale representation of e we show that the functions ns s s are a statistical representation of some kind of scale space image

nonparametric segmentation of curves into various representations this paper describes and demonstrates the operation and performance of an algorithm for segmenting connected points into a combination of representations such as lines circular elliptical and superelliptical arcs and polynomials the algorithm has a number of interesting properties including being scale invariant nonparametric general purpose and efficient

undecidability principle and the uncertainty principle even for classical systems it is shown that for any physical system there is an infinite number of measurements which are related to one of the undecidable problems the undecidability of the physical systems indicates that there is an infinite number of incomputable correlation functions for each physical system these results show that there is an inherent and irreducible limitation on the knowledge of the nature of physical systems this uncertainty principle is caused by the undecidability principle

the wave equation with computable initial data such that its unique solution is not computable we consider the three dimensional wave equation it is well known that the solution u x y z t is uniquely determined by two initial conditions the values of u and au at at time t 0 our question is can computable initial data give rise to noncomputable solutions the answer is yes and two quite different types of noncomputability can occur theorem 1 below gives an example in which the solution u x y z t takes a noncomputable real value at a computable point in space time by contrast theorem 2 provides an example in which the solution maps each computable sequence of points in space time into a computable sequence nevertheless u x y z t is not a computable function we note in passing that computability as used in this paper is a technical term familiar to mathematical logicians the precise definitions are spelled out in the next section the proof of theorem 1 is quite short that for theorem 2 is considerably more intricate it should be mentioned that these noncomputable solutions of the wave equation are of the type commonly referred to as weak solutions i e although continuous they are not twice differentiable at all points weak solutions describe creases cusps and other non differentiable patterns which frequently appear in models of wave phenomena the use of weak solutions is inevitable we will prove that no cz solutions of the desired kind exist for the convenience of readers unfamiliar with weak solutions we have put them into a coherent framework in an addendum basing our presentation on the energy integral associated with the wave just as the initial conditions are computable the energy integral in our examples is also a computable real finally the proof that all noncomputable solutions must be of weak type is sketched at the end of this addendum we note however that the main part of the paper may be read without reference to the addendum the results in this paper are related to comments of kreisel in 4 kreisel asks whether existing physical theories e g classical mechanics or quantum mechanics can predict theoretically the existence of a physical constant which is not a recursive real previous work of the authors in this area 9 was concerned with ordinary differential equations it was proved that there exists a computable and hence continuous function f such that 215 oool 8708 81 030215 25905 00 o

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

physical limits of inference abstract we show that physical devices that perform observation prediction or recollection share an underlying mathematical structure we call devices with that structure inference devices we present a set of existence and impossibility results concerning inference devices these results hold independent of the precise physical laws governing our universe in a limited sense the impossibility results establish that laplace was wrong to claim that even in a classical non chaotic universe the future can be unerringly predicted given sufficient knowledge of the present alternatively these impossibility results can be viewed as a non quantum mechanical uncertainty principle the mathematics of inference devices has close connections to the mathematics of turing machines tms in particular the impossibility results for inference devices are similar to the halting theorem for tms furthermore one can define an analog of universal tms utms for inference devices we call those analogs strong inference devices we use strong inference devices to define the inference complexity of an inference task which is the analog of the kolmogorov complexity of computing a string a task independent bound is derived on how much the inference complexity of an inference task can differ for two different inference devices this is analogous to the encoding bound governing how much the kolmogorov complexity of a string can differ between two utms used to compute that string however no universe can contain more than one strong inference device so whereas the kolmogorov complexity of a string is arbitrary up to specification of the utm there is no such arbitrariness in the inference complexity of an inference task we informally discuss the philosophical implications of these results e g for whether the universe is a computer we also derive some graph theoretic properties governing any set of multiple inference devices we also present an extension of the framework to address physical devices used for control we end with an extension of the framework to address probabilistic inference

reduced resolution and scale space for dominant feature detection in contours abstract analysis of contours or curves at various scales or levels of smoothing scale space is an important tool in curve segmentation and feature detection in this paper we propose the application of the hierarchical discrete correlation algorithm for efficiently calculating and creating a scale space of curves in conjunction with this procedure we also investigate the use of the reduced resolution or gaussian pyramid representation of the set of smoothed curves as the basis for initially localizing and detecting features we also create an approximation to the above algorithms that is computationally less expensive finally we propose a new inter scale method for curve segmentation and feature detection based on the motion of a curve through scale space

piecewise approximation of contours through scale space selection of dominant points this paper describes a method of approximating a shape contour with a polygon the polygon vertices are extracted from the curvature extremes through a scale space description of the contour via linear diffusion these vertices are located on the contour points where the sharper changes of the contour directions occur using a proper strategy a set of extremes that result in a given approximation level is chosen by adding new vertices the approximation level can be improved and a scalable representation of the contour is identified this method results in an approximation that discriminates local from global geometric features and provides a good visual representation of the original contour this polygonal approximation method is used for scalable encoding of the shape contours in this regard an encoding technique suitable for scalable polygonal approximation has been developed we show that encoding the approximated polygons result in a good relation between the distortion and the bitrate finally we show that in addition to coding this method can be efficiently used for shape comparison and shape retrieval

fast decomposition of digital curves into polygons using the haar transform the perimeters of features in digital images are decomposed into sets of straight lines using the haar transform the haar basis functions preserve sharp changes in direction along the perimeter while still allowing smoothing the coefficients of the haar transform are simply related to the error between the polygonal decomposition and the true perimeter the haar transform can be calculated efficiently with a computational overhead linear in the number of data points

robust contour decomposition using a constant curvature criterion the problem of decomposing an extended boundary or contour into simple primitives is addressed with particular emphasis on laplacian of gaussian zero crossing contours a technique is introduced for partitioning such contours into constant curvature segments a nonlinear blip filter matched to the impairment signature of the curvature computation process an overlapped voting scheme and a sequential contiguous segment extraction mechanism are used this technique is insensitive to reasonable changes in algorithm parameters and robust to noise and minor viewpoint induced distortions in the contour shape such as those encountered between stereo image pairs the results vary smoothly with the data and local perturbations induce only local changes in the result robustness and insensitivity are experimentally verified

towards effective planar shape representation with multiscale digital curvature analysis based on signal processing techniques abstract this paper presents and discusses a new approach to multiscale curvature analysis of digital contours that is based on digital signal processing techniques the shape contour is expressed in terms of two one dimensional signals linearized x and y coordinates and the derivative theorem is applied as a means of obtaining an interesting expression relating contour curvature and the spectra of its parametrized x and y signals multiscale curvature analysis is achieved through gaussian lowpass filtering and the shrinkage of the original signals implied by such a process is effectively circumvented by an energy based compensation scheme which has allowed accurate quantitative identification of the curvature value the concept of curvegram is introduced and exemplified and the overall performance of the proposed technique for curvature estimation is formally assessed with respect to a contour defined in terms of b splines application examples to synthetic and real images have been included

fuzzy cognitive maps for stereovision matching this paper outlines a method for solving the stereovision matching problem using edge segments as the primitives in stereovision matching the following constraints are commonly used epipolar similarity smoothness ordering and uniqueness we propose a new matching strategy under a fuzzy context in which such constraints are mapped the fuzzy context integrates both fuzzy clustering and fuzzy cognitive maps with such purpose a network of concepts nodes is designed each concept represents a pair of primitives to be matched each concept has associated a fuzzy value which determines the degree of the correspondence the goal is to achieve high performance in terms of correct matches the main findings of this paper are reflected in the use of the fuzzy context that allows building the network of concepts where the matching constraints are mapped initially each concept value is loaded via the fuzzy clustering and then updated by the fuzzy cognitive maps framework this updating is achieved through the influence of the remainder neighboring concepts until a good global matching solution is achieved under this fuzzy approach we gain quantitative and qualitative matching correspondences this method works as a relaxation matching approach and its performance is illustrated by comparative analysis against some existing global matching methods

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

acord an adaptive corner detector for planar curves abstract in contrast to the conventional method of smoothing a curve at multiple scales and integrating the information at various scales a technique for smoothing a curve adaptively based on the roughness present in the curve is suggested the procedure does not require smoothing at all levels of detail and it does not require construction of complete scale space map and representation of the map by tree the procedure has been applied on a number of digital curves and the results have been compared with those of the recent work

wavelet based approach to character skeleton character skeleton plays a significant role in character recognition the strokes of a character may consist of two regions i e singular and regular regions the intersections and junctions of the strokes belong to singular region while the straight and smooth parts of the strokes are categorized to regular region therefore a skeletonization method requires two different processes to treat the skeletons in theses two different regions all traditional skeletonization algorithms are based on the symmetry analysis technique the major problems of these methods are as follows 1 the computation of the primary skeleton in the regular region is indirect so that its implementation is sophisticated and costly 2 the extracted skeleton cannot be exactly located on the central line of the stroke 3 the captured skeleton in the singular region may be distorted by artifacts and branches to overcome these problems a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper this scheme consists of two main steps namely a extraction of primary skeleton in the regular region and b amendment processing of the primary skeletons and connection of them in the singular region a direct technique is used in the first step where a new wavelet based symmetry analysis is developed for finding the central line of the stroke directly a novel method called smooth interpolation is designed in the second step where a smooth operation is applied to the primary skeleton and thereafter the interpolation compensation technique is proposed to link the primary skeleton so that the skeleton in the singular region can be produced experiments are conducted and positive results are achieved which show that the proposed skeletonization scheme is applicable to not only binary image but also gray level image and the skeleton is robust against noise and affine transform

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

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

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

an approach to the parameterization of structure for fast categorization a decomposition is described which parameterizes the geometry and appearance of contours and regions of gray scale images with the goal of fast categorization to express the contour geometry a contour is transformed into a local global space from which parameters are derived classifying its global geometry arc inflexion or alternating and describing its local aspects degree of curvature edginess symmetry regions are parameterized based on their symmetric axes which are evolved with a wave propagation process enabling to generate the distance map for fragmented contour images the methodology is evaluated on three image sets the caltech 101 set and two sets drawn from the corel collection the performance nearly reaches the one of other categorization systems for unsupervised learning

fundamental group and contractible closed geodesics we prove the existence of a nonempty class of finitely presented groups with the following property if the fundamental group of a compact riemannian manifold m belongs to this class then there exists a constant c m 1 such that for any sufficiently large x the number of contractible closed geodesics on m of length not exceeding x is greater than c m x in order to prove this result we give a lower bound for the number of contractible closed geodesics of length x on a compact riemannian manifold m in terms of the resource bounded kolmogorov complexity of the word problem for 1 m thus answering a question posed by gromov 1996 john wiley sons inc

on line signature verification based on logarithmic spectrum in this paper an on line signature verification scheme based on similarity measurement of logarithmic spectrum is proposed the principal components of the logarithmic spectrum of each signature are extracted we then compute the similarity of logarithmic spectrum between input signature and the reference template by comparing the similarity of logarithmic spectrum with the verification threshold we can determine the authenticity of the input signature based on the experimentation the rates of false rejection errors and false acceptance errors are as low as 1 4 and 2 8 respectively this demonstrates the effectiveness of the proposed scheme

handwritten character recognition using a 2 layer random graph model by relaxation matching abstract a handwritten character recognizer is proposed in this paper first using components and strokes of a character as primitives a 2 layer attributed graph is constructed to represent the character next a relaxation matching technique is used in the learning stage to synthesize different attributed graphs which are due to writing variations and belong to a same character into a 2 layer random graph as a reference data model of the character and the relaxation matching technique is also used in the recognition stage to match the attributed graph of an input character to the random graph of each reference character then a similarity measure between an attributed graph and a random graph based on whether the attributed graph is a possible outcome of the random graph is presented in the recognition stage according to the similarity measure an input character can be classified into correct reference character experimental results are finally provided to show the effectiveness of the proposed approach

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

handwritten numerical recognition based on multiple algorithms abstract in this paper the authors combine two algorithms for application to the recognition of unconstrained isolated handwritten numerals the first algorithm employs a modified quadratic discriminant function utilizing direction sensitive spatial features of the numeral image the second algorithm utilizes features derived from the profile of the character in a structural configuration to recognize the numerals while both algorithms yield very low error rates the authors combine the two algorithms in different ways to study the best polling strategy and realize very low error rates 0 2 or less and rejection rates below 4

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

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

a multiscanning approach based on morphological filtering it is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of gaussian shaped filters of different sizes to show the validity of this method the authors concentrated on an application that involves forming scale space image of a 2 d shape using morphological opening filtering a proof is given to show that morphological opening filtering has a property of not introducing additional zero crossings as one moves to a coarser scale this is a different result from the conclusion by a l yuille and t a poggio ibid vol pami 8 jan 1986 that the gaussian filter is the only filter with this property in addition opening filtering is computationaly simpler than the gaussian filter

a robust boundary based object recognition in occlusion environment by hybrid hopfield neural networks this paper presents a new method of occluded object matching for machine vision applications the current methods for occluded object matching lack robustness and require high computational effort in this paper a new hybrid hopfield neural network hhn algorithm which combines the advantages of both a continuous hopfield network chn and a discrete hopfield network dhn will be described and applied for partially occluded object recognition in a multi context scenery the hhn proposed as a new approach provides great fault tolerance and robustness and requires less computation time also advantages of hhn such as reliability and speed will be discussed

silhouette based isolated object recognition through curvature scale space a complete fast and practical isolated object recognition system has been developed which is very robust with respect to scale position and orientation changes of the objects as well as noise and local deformations of shape due to perspective projection segmentation errors and non rigid material used in some objects the system has been tested on a wide variety of three dimensional objects with different shapes and material and surface properties a light box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave convex curves are recognized using their four high scale curvature extrema points curvature scale space css representations are computed for concave curves the css representation is a multi scale organization of the natural invariant features of a curve curvature zero crossings or extrema and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects a three stage coarse to fine matching algorithm prunes the search space in stage one by applying the css aspect ratio test the maxima of contours in css representations of the surviving models are used for fast css matching in stage two finally stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves transformation parameter optimization is then used to find the best fit of the input object to the correct model

a robust solution for object recognition by mean field annealing techniques abstract object recognition in multi context scene is one of the very difficult problems to find a robust solution in many applications the annealed hopfield networks have been developed to find global solutions of a non linear system in the study it has been proven that the system temperature of mfa is equivalent to the gain of sigmoid function of hopfield network in our early work we developed the hybrid hopfield network hhn on the purpose of fast and reliable matching in the object recognition process however hhn does not guarantee global solutions and yields false matching under heavily occluded conditions because hhn is depending on initial states by its nature in this paper we present the annealed hopfield network ahn to find a robust solution for occluded object matching problems in multi context scenery in ahn the mean field theory is applied to the hybrid hopfield network in order to improve computational complexity of the annealed hopfield network and provide reliable matching under heavily occluded conditions ahn is slower than hhn however ahn provides near global solutions without initial restrictions and provides less false matching than hhn the robustness of the algorithm is proved by identifying occluded target objects with large tolerance of their features also we present a optimal boundary smoothing algorithm to extract reliable features from the boundary representation of the object heavily contaminated by noise

laplacian and orthogonal wavelet pyramid decompositions in coarse to fine registration the authors develop orthogonal wavelet pyramid methods for registration and matching the registration algorithm described compensates for the representation s lack of translation invariance it shows better performance when tested with laplacian pyramids for matching applications they derive filters that directly generate coarse representations of candidates for comparison to library prototypes

on machine recognition of hand painted chinese characters by feature relaxation abstract a new relaxation matching method based on features is introduced for the recognition of hand printed chinese characters the types of features are selected carefully to reflect the structural information of characters matching probabilities between two features one from the mask and the other from input are computed by the relaxation method a new distance measure between two characters based on these matching probabilities is defined we demonstrate through examples the utility of the new approach in the recognition of hand printed chinese characters it is especially powerful in distinguishing similarly shaped characters within a cluster produced by preclassification

bengali alpha numeric character recognition using curvature features abstract this paper is concerned with recognition of hand written and or printed multifont alpha numeric bengali characters it is assumed that characters are present in an isolated fashion in the present work characters have been represented in terms of the primitives and structural constraints between the primitives imposed by the junctions present in the characters the primitives have been characterized on the basis of the significant curvature events like curvature maxima curvature minima and inflexion points observed along their extent curvature properties have been extracted after thinning the smoothed character images and filtering the thinned images using a gaussian kernel the unknown samples are classified using a two stage feed forward neural net based recognition scheme experimental results have established the effectiveness of the technique

geometry of the space of triangulations of a compact manifold in this paper we study the spacetm of triangulations of an arbitrary compact manifoldm of dimension greater than or equal to four this space can be endowed with the metric defined as the minimal number of bistellar operations required to transform one of two considered triangulations into the other recently this space became and object of study in quantum gravity because it can be regarded as a toy discrete model of the space of riemannian structures onm

representing curves at their natural scales abstract the shapes of curves generally contain several structures at different scales an expressive curve representation should explicitly describe each structure at its appropriate scale this greatly simplifies any reasoning processes e g matching applied to the curve rather than exhaustively represent the curve over a full range of scales just the most significant ones should be retained for a compact and useful representation a technique is presented that identifies the significant or natural scales in a curve

matching of partially occluded planar curves abstract an algorithm for curves partial matching up to a similarity transformation is presented the matching is based on the total curvature graph which is the direction of the first derivative of the curve no higher derivatives are required the algorithm uses dynamic programming it is not dependent on reference or feature points the base step consists of a comparison of the total curvatures of neighborhoods the neighborhoods are dynamically chosen according to local characteristics of the curve in the recursive step ratios of lengths of matched curve segments are compared in order to extend the matches the matching is not sensitive to local deviations of the curves the algorithm is fast and simple its worst case time complexity is o mn where m and n are the number of points in the two digital curves experimental results are presented

proposed solution of the quantum measurement problem a discussion of quantum measurement theory is presented it is argued that the quantum measurement problem consists in the failure of any formalism based on unitary evolution to describe fully the observed behaviour in measurement like processes it is shown that the problem is essentially concerned with the phase of the coherence between orthogonal eigenstates of an object measuring device system it is then proposed that the observed behaviour is fully described if the value of this phase is formally undecidable

digitized circular arcs characterization and parameter estimation the digitization of a circular arc causes an inherent loss of geometrical information arcs with slightly different local curvature or position may lead to exactly the same digital pattern in this paper the authors give a characterization of all centers and radii of circular arcs yielding the same digitization pattern the radius of the arcs varies over the set however only one curvature or radius estimate can be assigned to the digital pattern the authors derive an optimal estimator and give expressions for the bound on the precision of estimation this bound due to digitization is the deterministic equivalent of the cramer rao bound known from parameter estimation theory consider the estimation of the local curvature and local radius of a smooth object typically such parameters are estimated by moving a window along the digital boundary methods in literature show a poor precision in estimating curvature values relative errors of over 40 are often found from the definition of curvature it follows that locally the curve can be considered a circular arc and hence the method presented in this paper can be applied to the pattern in the window giving estimates with optimal precision and a measure for the remaining error on the practical side the authors present examples of the residual error due to the discrete grid the estimation of the radius or curvature of a circular arc at random position with an estimation window containing 10 points coded with nine freemancodes has a relative deviation exceeding 2 for a full disk the deviation is below 1 when the radius r exceeds four grid units the presented method is particularly useful for problems where some prior knowledge on the distribution of radii is known and where there is a noise free sampling

directional analysis of images in scale space the authors propose a computational technique for the directional analysis of piecewise linear patterns in images based on the notion of zero crossings in gradient images a given image is preprocessed by a sequence of filters that are second derivatives of 2 d gaussian functions with different scales this gives a set of zero crossing maps the scale space from which a stability map is generated significant linear patterns are detected from measurements on the stability map information regarding orientation of the linear patterns in the image and the area covered by the patterns in specific directions is then computed the performance of the method is illustrated through applications to a simple test image made up of straight bar patterns as well as to scanning electron microscope images of collagen fibrils in rabbit ligaments the method has significant applications in quantitative analysis of ligament healing and in comparison of treatment methods for ligament injuries

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

fast polygonal approximation of digital curves using relaxed straightness properties several existing digital straight line segment dss recognition algorithms can be used to determine the digital straightness of a given one pixel thick digital curve because of the inherent geometric constraints of digital straightness these algorithms often produce a large number of segments to cover a given digital curve representing a real life object image thus a curve segment which is not exactly digitally straight but appears to be visually straight is fragmented into multiple dss when these algorithms are run in this paper a new concept of approximate straightness is introduced by relaxing certain conditions of dss and an algorithm is described to extract those segments from a digital curve the number of such segments required to cover the curve is found to be significantly fewer than that of the exact dss cover as a result the data set required for representing a curve also reduces to a large extent the extracted set of segments can further be combined to determine a compact polygonal approximation of a digital curve based on certain approximation criteria and a specified error tolerance the proposed algorithm involves only primitive integer operations and thus runs very fast compared to those based on exact dss the overall time complexity becomes linear in the number of points present in the representative set experimental results on several digital curves demonstrate the speed elegance and efficacy of the proposed method

non recursive functions knots with thick ropes and self clenching thick hyperspheres we introduce an approach to certain geometric variational problems based on the use of the algorithmic unrecognizability of the n dimensional sphere for n 5 sometimes this approach allows one to prove the existence of infinitely many solutions of a considered variational problem this recursion theoretic approach is applied in this paper to a class of functionals on the space of c1 1 smooth hypersurfaces diffeomorphic to sn in rn 1 where n is any fixed number 5 the simplest of these functionals kv is defined by the formula kv n vol n 1 n r n where r n denotes the radius of injectivity of the normal exponential map for n rn l we prove the existence of an infinite set of distinct locally minimal values of kv on the space of c1 1 smooth topological hyperspheres in rn 1 for any n 5 the functional kv naturally arises when one attempts to generalize knot theory in order to deal with embeddings and isotopies of thick circles and more generally thick spheres into euclidean spaces we introduce the notion of knot with thick rope types the theory of knot with thick rope types turns out to be quite different from the classical knot theory because of the following result there exists an infinite set of non trivial knot with thick rope types in codimension one for every dimension greater than or equal to five

deb definite error bounded tangent estimator for digital curves we propose a simple and fast method for tangent estimation of digital curves this geometric based method uses a small local region for tangent estimation and has a definite upper bound error for continuous as well as digital conics i e circles ellipses parabolas and hyperbolas explicit expressions of the upper bounds for continuous and digitized curves are derived which can also be applied to nonconic curves our approach is benchmarked against 72 contemporary tangent estimation methods and demonstrates good performance for conic nonconic and noisy curves in addition we demonstrate a good multigrid and isotropic performance and low computational complexity of o 1 and better performance than most methods in terms of maximum and average errors in tangent computation for a large variety of digital curves

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

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

high accuracy character recognition algorithm using fourier and topological descriptors abstract this paper presents a new two stage character recognition algorithm yielding accuracies in excess of 98 in the first stage a primary classification using fourier descriptors is derived the fourier descriptors are obtained from a fourier analysis of the derived boundaries of the digitized image of the characters due to the rotational invariance of the fourier descriptors no distinction is made between the characters 2 and 5 6 and 9 and occasionally between 4 and 7 in order to resolve this ambiguity a secondary classification that utilized topological descriptors is initiated this combined two stage algorithm yields high recognition accuracies while retaining computational simplicity

using dominant points and variants for profile extraction from chromosomes abstract the most accurate methods for automatic analysis of chromosomes under a light microscope today extract numerical features from band pattern profiles along their longitudinal axes the construction of a reliable axis is a crucial step in this process we propose a new way based on the dominant points of the contour and cubic splines the dominant points serve as candidates for the tips of the chromosome ambiguities are dissolved by the recently developed method of variants for object identification a voronoi diagram decomposes the chromosome in slices for profile extraction the method improves the currently best classification results significantly yielding a test set error rate of 0 61

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

shapes shocks and deformations i the components of two dimensional shape and the reaction diffusion space we undertake to develop a general theory of two dimensional shape by elucidating several principles which any such theory should meet the principles are organized around two basic intuitions first if a boundary were changed only slightly then in general its shape would change only slightly this leads us to propose an operational theory of shape based on incremental contour deformations the second intuition is that not all contours are shapes but rather only those that can enclose physical material a theory of contour deformation is derived from these principles based on abstract conservation principles and hamilton jacobi theory these principles are based on the work of sethian 1985a c the osher sethian 1988 level set formulation the classical shock theory of lax 1971 1973 as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of gage hamilton grayson 1986 1989 the result is a characterization of the computational elements of shape deformations parts bends and seeds which show where to place the components of a shape the theory unifies many of the diverse aspects of shapes and leads to a space of shapes the reaction diffusion space which places shapes within a neighborhood of similar ones such similarity relationships underlie descriptions suitable for recognition

local reproducible smoothing without shrinkage a simple local smoothing filter is defined for curves or surfaces combining the advantages of gaussian smoothing and fourier curve description unlike gaussian filters the filter described has no shrinkage problem repeated application of the filter does not yield a curve or surface smaller than the original but simply reproduces the approximate result that would have been obtained by a single application at the largest scale unlike fourier description the filter is local in space the wavelet transform of y meyer 1989 is also shown to have these properties

non parametric planar shape representation based on adaptive curvature functions this paper presents a non parametric method to extract a very short feature vector from the curvature function of a planar shape curvature is adaptively calculated using a new procedure that removes noise from the contour without missing relevant points then its fourier transform is projected onto a set of vectors which have been chosen to be as representative as possible to obtain the similarity between the input object and each vector of the set these similarity values are the elements of the feature vector the proposed method is very fast and classification has proven that the representation is good

effective transformations on infinite trees with applications to high undecidability dominoes and fairness elementary translations between various kinds of recursive trees are presented it is shown that trees of either finite or countably infinite branching can be effectively put into one one correspondence with infinitely branching trees in such a way that the infinite paths of the latter correspond to the p abiding infinite paths of the former here p can be any member of a very wide class of properties of infinite paths for many properties the converse holds too two of the applications involve a the formulation of large classes of highly undecidable variants of classical computational problems and in particular easily describable domino problems that are iii 1 1 complete and b the existence of a general method for proving termination of nondeterministic or concurrent programs under any reasonable notion of fairness

motion estimation of two dimensional objects based on the straight line hough transform a new approach abstract in this paper we propose a novel technique for estimating motion of two dimensional objects the technique involves representing objects uniquely by straight line approximations of the boundary p and estimating motion from shifts in the p space the straight line approximation of the boundary is obtained by detecting dominant points during contour tracing and then approximating the pixels between adjacent dominant points along the contour by a straight line using the hough transform we have developed a computationally efficient way of detecting dominant points in a single pass during contour tracing the proposed object representation enables us to determine the translation and rotation with significantly fewer computations compared with existing methods our method can also detect the motion parameters correctly for partially overlapping objects

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

optimal estimation of contour properties by cross validated regularization the problem of estimating the properties of smooth continuous contours from discrete noisy samples is used as vehicle to demonstrate the robustness of cross validated regularization applied to a vision problem a method for estimation of contour properties based on smoothing spline approximations is presented generalized cross validation is to devise an automatic algorithm for finding the optimal value of the smoothing regularization parameter from the data the cross validated smoothing splines are then used to obtain optimal estimates of the derivatives of quantized contours experimental results are presented which demonstrate the robustness of the method applied to the estimation of curvature of quantized contours under variable scale rotation and partial occlusion these results suggest the application of generalized cross validation to other computer vision algorithms involving regularization

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