interpreting perspective images a fundamental problem in computer vision is how to determine the 3 d spatial orientation of curves and surfaces appearing in an image the problem is generally underconstrained and is complicated by the fact that metric properties such as orientation and length are not invariant under projection under perspective projection the correct model for most real images the transform is nonlinear and therefore hard to invert two constructive methods are presented the first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines the second determines the orientation of planes by backprojection of two intrinsic properties of contours angle magnitude and curvature

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

a fast method for robot location determination abstract a fast single view method for determining the location of mobile robot in 3 d space is proposed in the method a tetragon mark is used as the reference target and no prerequisite condition is imposed in grabbing the image the method utilizes the 3 d vector analysis technique and simple algebraic computation to achieve the fast location determination error analysis on the effects of sensor resolution in different distances and elevation angles is included experimental results show that the location determination time is about 0 22 s in a 12 mhz ibm compatible pc at computer system and the location error is less than 2 in average

pseudodistance measures for recognition of curved objects a method for the description and identification of curved objects is described in this paper the shape of a curved object is considered as a surface which is an accumulation of horizontal section boundaries this is described by the coefficients of a fourier series expansion of the proposed representative function each complicated feature of the shape of the object is decomposed into five simple features elongatedness horizontal strain section shape torsion and displacement differences of objects as patterns are defined as pseudodistances of corresponding features some essential properties such as completeness of the pseudodistance family are explained theoretically finally experimental results of identification of wooden block models and a doll are displayed

a modified forward backward splitting method for maximal monotone mappings we consider the forward backward splitting method for finding a zero of the sum of two maximal monotone mappings this method is known to converge when the inverse of the forward mapping is strongly monotone we propose a modification to this method in the spirit of the extragradient method for monotone variational inequalities under which the method converges assuming only the forward mapping is lipschitz continuous on some closed convex subset of its domain the modification entails an additional forward step and a projection step at each iteration applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed

asymptotic subword complexity of fixed points of group substitutions the subword complexity of fixed points of some types of substitutions was studied by various authors here we introduce a family of substitutions arising from multiplication tables of finite groups and other similar structures and analyze their subword complexity

some experiments in relaxation image matching using corner features abstract a relaxation method based on patterns of local features is used to find matches between pairs of images or subimages that differ in position or orientation a local operator is applied to the two images to detect two sets of corners c1 cm and d1 dn each of them characterized by position orientation contrast and sharpness of the angle for each pair ci dj a figure of merit is computed and a relaxation process is used to iteratively adjust these figures of merit based on the merits of other pairs in approximately corresponding positions after a few iterations of this process good matches pairs having much better merit than their next best choices are clustered yielding sets of transformation parameters shift vectors or rotation angles under which many corners correspond this method has yielded good results for tv images of objects such as tools and industrial parts as well as for aerial images of terrain

matching perspective views of a polyhedron using circuits we present a novel approach for finding corresponding points between two line drawings extracted from perspective views of a moving object whose surface is composed of planar polygons in our approach each circuit of the drawings is encoded with a boundary shape code which we call the rlcc code run length code of convex and concave strings then a clustering technique is used to obtain the matching result recursively a series of measures are taken to make the algorithm tolerate considerable dissimilarities which may exist between the two drawings such as missing lines scale differences rotation perspective shape distortions etc experimental results are presented

a new halfspace relaxation projection method for the split feasibility problem abstract let c and q be nonempty closed convex sets in r n and r m respectively and a an m by n real matrix the problem to find x c with ax q if such x exist is called the split feasibility problem sfp this problem is important in intensity modulated radiation therapy signal processing image reconstruction and so on in this paper based on a new reformulation for the sfp we propose a new halfspace relaxation projection method for the sfp the method is implemented very easily and is proven to be fully convergent to the solution for the case where the solution set of the sfp is nonempty preliminary computational experience is also reported

on the joint subword complexity of automatic sequences let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m denotes the number of distinct blocks u n u n m 1 of size m in u in this paper we study the complexity of u n u 1 n u r n n 0 when each u i u i n n 0 i 1 r is a q i automatic sequence over a finite set s i and q 1 q r 2 are pairwise coprime integers as an application we answer a question of allouche and shallit regarding morphic real numbers

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

complexity for finite factors of infinite sequences abstract we define several notions of language complexity for finite words and use them to define and compute some new complexity functions for infinite sequences in particular they give a new characterization of sturmian sequences and discriminate between sturmian sequences with bounded or unbounded partial quotients

on the convergence of a class of outer approximation algorithms for convex programs abstract this paper presents a new class of outer approximation methods for solving general convex programs the methods solve at each iteration a subproblem whose constraints contain the feasible set of the original problem moreover the methods employ quadratic objective functions in the subproblems by adding a simple quadratic term to the objective function of the original problem while other outer approximation methods usually use the original objective function itself throughout the iterations by this modification convergence of the methods can be proved under mild conditions furthermore it is shown that generalized versions of the cut construction schemes in kelley cheney goldstein s cutting plane method and veinott s supporting hyperplane method can be incorporated with the present methods and a cut generated at each iteration need not be retained in the succeeding iterations

algorithms for subsequence combinatorics a subsequence is obtained from a string by deleting any number of characters thus in contrast to a substring a subsequence is not necessarily a contiguous part of the string counting subsequences under various constraints has become relevant to biological sequence analysis to machine learning to coding theory to the analysis of categorical time series in the social sciences and to the theory of word complexity we present theorems that lead to efficient dynamic programming algorithms to count 1 distinct subsequences in a string 2 distinct common subsequences of two strings 3 matching joint embeddings in two strings 4 distinct subsequences with a given minimum span and 5 sequences generated by a string allowing characters to come in runs of a length that is bounded from above

three view matching algorithm for multipolyhedron reconstruction using genetic algorithm abstract in this paper a novel stereo matching algorithm based on genetic algorithm ga is proposed to find the correspondences among multipolyhedron objects in a three view system optimal camera configuration in the approach is used to reduce the feature searching area on the image plane and ga is then used to refine the matching results due to optimal camera configuration we can achieve a smaller searching area less ambiguity and a faster matching process the features on the second image near the intersection of the two epipolar lines derived from the first and the third images considered as possible triplets are refined using ga the fitness function for every corresponding triplet is assigned according to the corresponding distance between the feature location and the intersection of two epipolar lines the consistent connection relationship is then enforced in the evolution process to resolve the ambiguous correspondence triplets experimental results show that the 3 d multiple polyhedra in a complex scene can be successfully reconstructed in a three view system

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

polyhedral object recognition using hough space features abstract we propose a new technique for three dimensional 3 d polyhedral object recognition on the basis of a single two dimensional 2 d view of a 3 d scene the binary gradient image of the captured scene is converted into the hough space domain the cluster patterns originating from straight line features of the image are explored by reasoning in hough space this yields an attributed graph representation of the object to be recognized which is compared to similar representations of cad designed wire frame model objects by means of a new attributed subgraph isomorphism algorithm simulation experiments illustrate this promising new approach

subword complexity of uniform d0l words over finite groups we deal with the subword complexity of uniform d0l words obtained from group substitutions our main interest is whether the subword complexity is almost proportional to the length of the factor we find necessary and sufficient conditions for that for some cases we show that this is impossible

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

applications of tensor theory to object recognition and orientation determination a method is developed by which images resulting from orthogonal projection of rigid planar patch objects arbitrarily oriented in three dimensional 3 d space may be used to form systems of linear equations which are solved for the affine transform relating the images the technique is applicable to complete images and to unlabeled feature sets derived from images and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation for use in object identification no knowledge of point correspondence between images is required theoretical development of the method and experimental results are presented the method is shown to be computationally efficient requiring o n multiplications and additions where depending on the computation algorithm n may equal the number of object or edge picture elements

several acceleration schemes for solving the multiple sets split feasibility problem abstract in this paper we present several acceleration schemes for solving the multiple sets split feasibility problem msfp which is to find a point which belongs to the intersection of a family of closed convex sets in one space such that its image under a linear transformation belongs to the intersection of another family of closed convex sets in the image space we first modify the existing method and give a self adaptive algorithm to solve the msfp which computes the step size by armijo like searches and performs an additional projection step onto some simple closed convex set x r n at each iteration then we present a special case of this algorithm convergence results are analyzed and further discussions on accelerating relaxed algorithms are lead preliminary numerical experiments shows that these accelerating schemes are practical and promising for solving the msfps

arithmetical complexity of symmetric d0l words we characterize and count words which occur in arithmetical subsequences of fixed points of symmetric morphisms

on the subword complexity of square free dol languages abstract the subword complexity of a language k is the function which to every positive integer n assigns the number of different subwords of length n occuring in words of k a language k is square free if no word in it contains a subword of the form xx where x is a nonempty word the best upper and lower bounds on the subword complexity of infinite square free dol languages are established

on the subword complexity of thue morse polynomial extractions let the subword complexity of a sequence u u n n 0 over a finite set s be the function m p u m where p u m is the number of distinct blocks of length m in u let t t n n 0 denote the thue morse sequence in this paper we study the complexity of the sequences t h t h n n 0 when h n q n is a polynomial with h n n in particular we solve an open problem of allouche and shallit regarding t n 2 n 0 we also study the vector space over z 2z spanned by the sequences t h

on the combinatorics of finite words in this paper we consider a combinatorial method for the analysis of finite words recently introduced in colosimo and de luca special factors in biological strings preprint 97 42 dipt matematica univ di roma for the study of biological macromolecules the method is based on the analysis of right special factors of a given word a factor u of a word w is special if there exist at least two occurrences of the factor u in w followed on the right by two distinct letters we show that in the combinatorics of finite words two parameters play an essential role the first denoted by r represents the minimal integer such that there do not exist special factors of w of length r the second that we denote by k is the minimal length of a factor of w which cannot be extended on the right in a factor of w some new results are proved in particular a new characterization in terms of special factors and of r and k is given for the set per of all words w having two periods p and q which are coprimes and such that w p q 2

palindrome complexity we study the palindrome complexity of infinite sequences on finite alphabets i e the number of palindromic factors blocks of given length occurring in a given sequence we survey the known results and obtain new results for some sequences in particular for rote sequences and for fixed points of primitive morphisms of constant length belonging to class p of hof knill simon we also give an upper bound for the palindrome complexity of a sequence in terms of its block complexity

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability

matching three dimensional objects using silhouettes a method for matching three dimensional objects against a library of models from an observed sequence of silhouettes is presented in this correspondence based upon the observed silhouettes the three dimensional structure of the object is constructed and refined the principal moments and three primary silhouettes are computed for the constructed three dimensional objects to represent the aggregate and detailed structure parameters the adaptive matching technique requires that sufficient silhouettes be added to modify the structure of the unknown object until consistent and steady matching results are obtained the library for matching is based on three primary silhouettes of the model objects experiments conducted show a fast convergence to a consistent result may be achieved provided that a reasonable choice of silhouettes is made

a relaxed projection method for variational inequalities this paper presents a modification of the projection methods for solving variational inequality problems each iteration of the proposed algorithm consists of projection onto a halfspace containing the given closed convex set rather than the latter set itself the algorithm can thus be implemented very easily and its global convergence to the solution can be established under suitable conditions

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

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

hierarchical structures in sturmian dynamical systems the paper is concerned with hierarchical stuctures in subshifis over a finite alphabet in particular we present a hierarchy based approach to sturmian systems this approach is then used to characterize the linearly repetitive sturmian systems among the sturmian systems by uniform positivity of certain weights more generally we discuss various bounds on weights and their relationship finally we combine hierarchies and bounds on a weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts