practical reliable bayesian recognition of 2d and 3d objects using implicit polynomials and algebraic invariants we treat the use of more complex higher degree polynomial curves and surfaces of degree higher than 2 which have many desirable properties for object recognition and position estimation and attack the instability problem arising in their use with partial and noisy data the scenario discussed in this paper is one where we have a set of objects that are modeled as implicit polynomial functions or a set of representations of classes of objects with each object in a class modeled as an implicit polynomial function stored in the database then given partial data from one of the objects we want to recognize the object or the object class or collect more data in order to get better parameter estimates for more reliable recognition two problems arising in this scenario are discussed 1 the problem of recognizing these polynomials by comparing them in terms of their coefficients and 2 the problem of where to collect data so as to improve the parameter estimates as quickly as possible we use an asymptotic bayesian approximation for solving the two problems the intrinsic dimensionality of polynomials and the use of the mahalanobis distance are discussed

skeleton search category specific object recognition and segmentation using a skeletal shape model we describe a top down object detection and segmentation approach that uses a skeleton based shape model and that works directly on real images the approach is based on three components first we propose a fragment based generative model for shape that is based on the shock graph and has minimal dependency among its shape fragments the model is capable of generating a wide variation of shapes as instances of a given object category second we develop a progressive selection mechanism to search among the generated shapes for the category instances that are present in the image the search begins with a large pool of candidates identified by a dynamic programming dp algorithm and progressively reduces it in size by applying series of criteria namely local minimum criterion extent of shape overlap and thresholding of the objective function to select the final object candidates third we propose the partitioned chamfer matching pcm measure to capture the support of image edges for a hypothesized shape this measure overcomes the shortcomings of the oriented chamfer matching and is robust against spurious edges missing edges and accidental alignment between the image edges and the shape boundary contour we have evaluated our approach on the ethz dataset and found it to perform well in both object detection and object segmentation tasks

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

inference and learning with hierarchical shape models in this work we introduce a hierarchical representation for object detection we represent an object in terms of parts composed of contours corresponding to object boundaries and symmetry axes these are in turn related to edge and ridge features that are extracted from the image we propose a coarse to fine algorithm for efficient detection which exploits the hierarchical nature of the model this provides a tractable framework to combine bottom up and top down computation we learn our models from training images where only the bounding box of the object is provided we automate the decomposition of an object category into parts and contours and discriminatively learn the cost function that drives the matching of the object to the image using multiple instance learning using shape based information we obtain state of the art localization results on the uiuc and ethz datasets

shape decomposition and classification by searching optimal part pruning sequence representing shapes in terms of meaningful parts is a fundamental problem in shape analysis and part based object representation decomposition methods typically utilize handcrafted geometric rules in a nondata driven manner however these rules are insufficient to mimic human decomposition behavior which limits the applications of decomposition in vision tasks in this paper we propose a novel shape analysis framework that integrates shape decomposition with shape classification in fundamental level we first train probabilistic models for contours and part cuts involved in decomposition process next we construct a data structure called decomposition graph whose nodes represent intermediate contours and whose edges represent part cut selections the decomposition and classification results are obtained by efficiently searching the optimal path on decomposition graph with minimum energy experimental results show that such integrated framework improves the decomposition performance under various shape deformations and achieves competitive classification performance highlightsintegrating decomposition with classification will benefit both of them part based descriptor is robust to shape deformation and intra class variation class and geometric information are complementary in guiding decomposition learning from human decomposition result improves the decomposition performance the decomposition by optimal pruning sequence is solved in polynomial complexity

three dimensional surface mesh segmentation using curvedness based region growing approach a new parameter free graph morphology based segmentation algorithm is proposed to address the problem of partitioning a 3d triangular mesh into disjoint submeshes that correspond to the physical parts of the underlying object curvedness which is a rotation and translation invariant shape descriptor is computed at every vertex in the input triangulation iterative graph dilation and morphological filtering of the outlier curvedness values result in multiple disjoint maximally connected submeshes such that each submesh contains a set of vertices with similar curvedness values and vertices in disjoint submeshes have significantly different curvedness values experimental evaluations using the triangulations of a number of complex objects demonstrate the robustness and the efficiency of the proposed algorithm and the results prove that it compares well with a number of state of the art mesh segmentation algorithms

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics this paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics we adopt a new point of view which has emerged progressively in recent years and which takes seriously into account the chaotic character of the microscopic time evolution the emphasis is on nonequilibrium steady states rather than the traditional approach to equilibrium point of view of boltzmann the nonequilibrium steady states in presence of a gaussian thermostat are described by srb measures in terms of these one can prove the gallavotti cohen fluctuation theorem one can also prove a general linear response formula and study its consequences which are not restricted to near equilibrium situations at equilibrium one recovers in particular the onsager reciprocity relations under suitable conditions the nonequilibrium steady states satisfy the pairing theorem of dettmann and morriss the results just mentioned hold so far only for classical systems they do not involve large size i e they hold without a thermodynamic limit

a new shape decomposition scheme for graph based representation nowadays the part based representation of a given shape plays a significant role in shape related applications such as those involving content based retrieval object recognition and so on in this paper to represent both 2 d and 3 d shapes as a relational structure i e a graph a new shape decomposition scheme which recursively performs constrained morphological decomposition cmd is proposed the cmd method adopts the use of the opening operation with the ball shaped structuring element and weighted convexity to select the optimal decomposition for the sake of providing a compact representation the merging criterion is applied using the weighted convexity difference therefore the proposed scheme uses the split and merge approach finally we present experimental results for various modified 2 d shapes as well as 3 d shapes represented by triangular meshes based on the experimental results it is believed that the decomposition of a given shape coincides with that based on human insight for both 2 d and 3 d shapes and also provides robustness to scaling rotation noise shape deformation and occlusion

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

euler spiral for shape completion in this paper we address the curve completion problem e g the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion also known as the gap completion or shape completion problem this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared elastica as motivated by a physical analogy our approach is motivated by railroad design methods of the early 1900 s which connect two rail segments by transition curves and by the work of knuth on mathematical typography we propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation the minimization of total curvature variation leads to an euler spiral solution a curve whose curvature varies linearly with arclength the construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving fresnel integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions since the choice of an appropriate initial curve is critical in this optimization we analytically derive an optimal solution in the class of biarc curves which is then used as the initial curve the resulting interpolations yield intuitive interpolation across gaps and occlusions and are extensible in contrast to scale invariant elastica in addition euler spiral segments can be used in other applications of curve completions e g modeling boundary segments between curvature extrema or skeletal branch geometry

representation and self similarity of shapes representing shapes in a compact and informative form is a significant problem for vision systems that must recognize or classify objects we describe a compact representation model for two dimensional 2d shapes by investigating their self similarities and constructing their shape axis trees sa trees our approach can be formulated as a variational one or equivalently as map estimation of a markov random field we start with a 2d shape its boundary contour and two different parameterizations for the contour one parameterization is oriented counterclockwise and the other clockwise to measure its self similarity the two parameterizations are matched to derive the best set of one to one point to point correspondences along the contour the cost functional used in the matching may vary and is determined by the adopted self similarity criteria e g cocircularity distance variation parallelism and region homogeneity the loci of middle points of the pairing contour points yield the shape axis and they can be grouped into a unique free tree structure the sa tree by implicitly encoding the local and global shape information into an sa tree a variety of vision tasks e g shape recognition comparison and retrieval can be performed in a more robust and efficient way via various tree based algorithms a dynamic programming algorithm gives the optimal solution in o n sup 1 where n is the size of the contour

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

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

path similarity skeleton graph matching this paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes the main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints in contrast to typical tree or graph matching methods we do not consider the topological graph structure our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures the proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases the skeletons are pruned by contour partitioning with discrete curve evolution which implies that the endpoints of skeleton branches correspond to visual parts of the objects the experimental results demonstrate that our method is able to produce correct results in the presence of articulations stretching and contour deformations

large deviations and a fluctuation symmetry for chaotic homeomorphisms we consider expansive homeomorphisms with the specification property we give a new simple proof of a large deviation principle for gibbs measures corresponding to a regular potential and we establish a general symmetry of the rate function for the large deviations of the antisymmetric part under time reversal of the potential this generalizes the gallavotti cohen fluctuation theorem to a larger class of chaotic systems

on the intrinsic reconstruction of shape from its symmetries the main question we address is what is the minimal information required to generate closed nonintersecting planar boundaries for this paper we restrict shape to this meaning more precisely we examine whether the medial axis together with dynamics can serve as a language to design shapes and to effect shape changes we represent the medial axis together with a direction of flow along the axis as the shock graph and examine the reconstruction of shape along each of the three types of medial axis points a sub 1 sup 2 a sub 1 sup 3 a sub 3 and the associated six types of shock points first we show that the tangent and curvature of the medial axis and the speed and acceleration of the shock with respect to time of propagation are sufficient to determine the boundary tangent and curvature at corresponding points of the boundary this implies that a rather coarse sampling of the symmetry axis its tangent curvature speed and acceleration is sufficient to regenerate accurately a local neighborhood of shape at regular axis points a sub 1 sup 2 second we examine the reconstruction of shape at branch points a sub 1 sup 3 where three regular branches are joined we show that the three pairs of geometry that is curvature and dynamics that is acceleration must satisfy certain constraints finally we derive similar results for the end points of shock branches a sub 3 points these formulas completely specify the local reconstruction of a shape from its shock graph or medial axis and the conditions required to form a coherent shape from the medial axis

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

shape representation and classification using the poisson equation we present a novel approach that allows us to reliably compute many useful properties of a silhouette our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries this function can be computed by solving poisson s equation with the silhouette contours providing boundary conditions we show how this function can be used to reliably extract various shape properties including part structure and rough skeleton local orientation and aspect ratio of different parts and convex and concave sections of the boundaries in addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms we demonstrate the utility of the extracted properties by using them for shape classification and retrieval

constructing simple stable descriptions for image partitioning a new formulation of the image partitioning problem is presented construct a complete and stable description of an image in terms of a specified descriptive language that is simplest in the sense of being shortest we show that a descriptive language limited to a low order polynomial description of the intensity variation within each region and a chain code like description of the region boundaries yields intuitively satisfying partitions for a wide class of images the advantage of this formulation is that it can be extended to deal with subsequent steps of the image understanding problem or to deal with other attributes such as texture in a natural way by augmenting the descriptive language experiments performed on a variety of both real and synthetic images demonstrate the superior performance of this approach over partitioning techniques based on clustering vectors of local image attributes and standard edge detection techniques

minimum near convex shape decomposition shape decomposition is a fundamental problem for part based shape representation we propose the minimum near convex decomposition mncd to decompose arbitrary shapes into minimum number of near convex parts the near convex shape decomposition is formulated as a discrete optimization problem by minimizing the number of nonintersecting cuts two perception rules are imposed as constraints into our objective function to improve the visual naturalness of the decomposition with the degree of near convexity a user specified parameter our decomposition is robust to local distortions and shape deformation the optimization can be efficiently solved via binary integer linear programming both theoretical analysis and experiment results show that our approach outperforms the state of the art results without introducing redundant parts and thus leads to robust shape representation

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

representation and detection of deformable shapes we describe some techniques that can be used to represent and detect deformable shapes in images the main difficulty with deformable template models is the very large or infinite number of possible nonrigid transformations of the templates this makes the problem of finding an optimal match of a deformable template to an image incredibly hard using a new representation for deformable shapes we show how to efficiently find a global optimal solution to the nonrigid matching problem the representation is based on the description of objects using triangulated polygons our matching algorithm can minimize a large class of energy functions making it applicable to a wide range of problems we present experimental results of detecting shapes in medical images and images of natural scenes we also consider the problem of learning a nonrigid shape model for a class of objects from examples we show how to learn good models while constraining them to be in the form required by the matching algorithm

support vector shape a classifier based shape representation we introduce a novel implicit representation for 2d and 3d shapes based on support vector machine svm theory each shape is represented by an analytic decision function obtained by training svm with a radial basis function rbf kernel so that the interior shape points are given higher values this empowers support vector shape svs with multifold advantages first the representation uses a sparse subset of feature points determined by the support vectors which significantly improves the discriminative power against noise fragmentation and other artifacts that often come with the data second the use of the rbf kernel provides scale rotation and translation invariant features and allows any shape to be represented accurately regardless of its complexity finally the decision function can be used to select reliable feature points these features are described using gradients computed from highly consistent decision functions instead from conventional edges our experiments demonstrate promising results

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

shape evolution with structural and topological changes using blending this paper describes a framework for the estimation of shape from sparse or incomplete range data it uses a shape representation called blending which allows for the geometric combination of shapes into a unified model selected regions of the component shapes are cut out and glued together estimation of shape by this representation is realized using a physics based framework and it also includes a process for deciding how to adapt the structure and topology of the model to improve the fit the blending representation helps avoid abrupt changes in model geometry during fitting by allowing the smooth evolution of the shape which improves the robustness of the technique we demonstrate this framework with a series of experiments showing its ability to automatically extract structured representations from range data given both structurally and topologically complex objects

skeleton pruning by contour partitioning with discrete curve evolution in this paper we introduce a new skeleton pruning method based on contour partitioning any contour partition can be used but the partitions obtained by discrete curve evolution dce yield excellent results the theoretical properties and the experiments presented demonstrate that obtained skeletons are in accord with human visual perception and stable even in the presence of significant noise and shape variations and have the same topology as the original skeletons in particular we have proven that the proposed approach never produces spurious branches which are common when using the known skeleton pruning methods moreover the proposed pruning method does not displace the skeleton points consequently all skeleton points are centers of maximal disks again many existing methods displace skeleton points in order to produces pruned skeletons

shape codification indexing and retrieval using the quad tree structure the author presents in this paper a new approach for indexing and content based image retrieval based on the quad tree structure the 3d objects are represented by their silhouettes and codified following the filling rate of each quadrant at different levels of the quad tree subdivision the author proposes a modified linear codification for silhouettes this method improves the processing time because in opposite to the traditional algorithms the author s algorithm has not a processing time that is proportional to the number of pixels in the image as the same descriptor may characterize a set of different shapes the author proposes also efficient similarity measures to distinguish different objects having the same index in order to apply the approach to the retrieval process