Representation Of Object Shape Research Articles

ｏｃｔｒｅｅと多面体表現を用いた三次元物体間の衝突面検出

We propose an accurate and efficient method for detecting potential collisions among multiple objects with arbitrary motion (translation and rotation) in three-dimensional (3-D) space. The algorithm can be used directly for both convex and concave objects. The method consists of two main stages. In the first, coarse stage, an approximate test is performed to identify interfering objects in the entire workspace using octree representation of object shapes. In the second, fine stage, polyhedral representation of object shapes is used to more accurately identify any object parts that might cause interference and collisions. For this purpose, specific pairs of faces belonging to any of the interfering objects found in the first stage are tested, thus performing detailed computation on a reduced amount of data. Experimental results, which demonstrate the efficiency of the proposed collision detection method with adequate octree are given.

Efficient morphological shape representation

Mathematical morphology is well suited to capturing geometric information. Hence, morphology-based approaches have been popular for object shape representation. The two primary morphology-based approaches-the morphological skeleton and the morphological shape decomposition (MSD)-each represent an object as a collection of disjoint sets. A practical shape representation scheme, though, should give a representation that is computationally efficient to use. Unfortunately, little work has been done for the morphological skeleton and the MSD to address efficiency. We propose a flexible search-based shape representation scheme that typically gives more efficient representations than the morphological skeleton and MSD. Our method decomposes an object into a number of simple components based on homothetics of a set of structuring elements. To form the representation, the components are combined using set union and set difference operations. We use three constituent component types and a thorough cost-based search strategy to find efficient representations. We also consider allowing object representation error, which may yield even more efficient representations.

Efficient representation of object shape for silhouette intersection

A new shape representation-the radial intersection set (RIS)-is presented. The RIS is an object-centred model in which 2-D and 3-D boundaries are represented via their intersection with radial lines from some specific origin. The RIS representation allows efficient 3-D reconstruction using silhouette intersection from an arbitrary number of 2-D perspective views. The relationship between the visual hull (Laurentini, 1994) of the 3-D object and the silhouettes it may generate is defined as a set intersection operator. This operator allows the direct generation of 3-D RIS models from silhouettes. The RIS method is shown to compare favourably, in terms of both speed and storage, with existing octree techniques. Examples of images rendered from RIS models are presented. These show high visual fidelity.

Ridges for image analysis

Representation of object shape by medial structures has been an important aspect of image analysis. Methods for describing objects in a binary image by medial axes are well understood. Many attempts have been made to construct similar medial structures for objects in gray scale images. In particular, researchers have studied images by analyzing the graphs of the intensity data and identifying ridge and valley structures on those surfaces. In this paper we review many of the definitions for ridges. Computational vision models require that medial structures should remain invariant under certain transformations of the spatial locations and intensities. For each ridge definition we point out which invariances the definition satisfies. We also give extensions of the concepts so that we can located-dimensional ridge structures withinn-dimensional images. A comparison of the ridge structures produced by the different definitions is given both by mathematical examples and by an application to a 2-dimensional MR image of a head.

Object shape before boundary shape: Scale-space medial axes

Representing object shape in two or three dimensions has typically involved the description of the object boundary. This paper proposes a means for characterizing object structure and shape that avoids the need to find an explicit boundary. Rather, it operates directly from the imageintensity distribution in the object and its background, using operators that do indeed respond to “boundariness.” It produces a sort of medial-axis description that recognizes that both axis location and object width must be defined according to a tolerance proportional to the object width. This generalized axis is called themultiscale medial axis because it is defined as a curve or set of curves in scale space. It has all of the advantages of the traditional medial axis: representation of protrusions and indentations in the object, decomposition of object-curvature and object-width properties, identification of visually opposite points of the object, incorporation of size constancy and orientation independence, and association of boundary-shape properties with medial locations. It also has significant new advantages: it does not require a predetermination of exactly what locations are included in the object, it provides gross descriptions that are stable against image detail, and it can be used to identify subobjects and regions of boundary detail and to characterize their shape properties.

MuItiscale medial analysis of medical images

The Multiscale Medial Axis is a means for detecting and representing object shape at multiple scales simultaneously. One of its key characteristics is that the scale used to measure object properties (and hence to represent the object) is proportional to the local width of the object. This allows it to separate fine-scale detail from larger-scale gross shape properties of the object in a manner dictated by the object itself. It works directly from image intensities and does not require a prior segmentation of the image or explicit determination of object boundaries. Fuzzy (non-binary) boundary measures are used to compute fuzzy medial measures, and axis points are identified as ridges in this fuzzy medial space. This paper presents some of the basic concepts of the Multiscale Medial Axis, describes ils computation, and demonstrates some preliminary results of its application to medical images from variety of imaging modalities.

Shape and motion from image streams: a factorization method.

Inferring scene geometry and camera motion from a stream of images is possible in principle, but it is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion without computing depth as an intermediate step. An image stream can be represented by the 2F x P measurement matrix of the image coordinates of P points tracked through F frames. Under orthographic projection this matrix is of rank 3. Using this observation, the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices, which represent object shape and camera motion, respectively. The method can also handle and obtain a full solution from a partially filled-in measurement matrix, which occurs when features appear and disappear in the image sequence due to occlusions or tracking failures. The method gives accurate results and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.

New polygonal approximation schemes for object shape representation

Object shape representation is an important issue in pattern recognition and computer vision applications. A set of new polygonal approximation schemes, namely, the internal maximum area polygonal approximation (IMAPA), the external minimum area polygonal approximation (EMAPA), and the minimum area deviation polygonal approximation (MADPA), are proposed for object shape representation. The area deviation between the initial object shape and its approximation polygon is defined as the cost function. Instead of outputting a unique approximation polygon, each proposed scheme outputs a sequence of approximation polygons with different numbers of line segments and different area deviations for various application situations. For a given area deviation bound and an initial object shape, each proposed scheme can give a corresponding “optimal” approximation polygon with a minimum number of line segments. A performance comparison among the proposed schemes is included. The proposed schemes are compared with two other existing schemes. Some experimental results show the feasibility of the proposed approaches.

Shape and motion from image streams under orthography: a factorization method

Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions.

A model-based approach to representation and matching of object shape patterns

Representation and matching of object shapes are two important steps of image analysis and computer vision applications. In most existing approaches, the object shapes for representation and matching are usually described in a ‘deterministic’ manner instead of in a ‘statistical’ form. In this paper, a model-based approach to representation and matching of object shapes involving statistical properties is proposed. To speed up the matching process, a modified distance-weighted correlation (MDWC) map is constructed in the learning stage so that the matching between the input shape pattern T and its corresponding stored model shape pattern S can be performed without any correspondence. Some experimental results show the feasibility of the proposed approaches.

Feature Recognition of Two-Dimensional Object Scenes Using Contour Curvature Representation

The contour curvature representation of object shapes yields a scale-and/or rotation-invariant model-matching technique for object recognition problems. General characteristics associated with the proposed curvature function axe discussed. In addition, an algorithm for computing the curvature function and recognizing object shapes is derived, and numerical results confirming the feasibility of shape recognition based on the proposed algorithm are shown. Finally, a general feature-tracking formulation for celestial bodies, such as comets and asteroids, is presented.

Size invariance in visual object priming.

The magnitude of priming resulting from perception of a briefly presented picture of an object in an earlier trial block, as assessed by naming reaction times (RTs), was independent of whether the primed object was presented at the or a different size as when originally viewed. RTs and error rates for same responses for old-new shape judgments were much increased by a change in object size from initial presentation. We conjecture that this dissociation between the effects of size consistency on naming and old-new shape may reflect the differential functioning of 2 independent systems subserving object memory: 1 for representing object shape and the other for representing its size, position, and orientation (metric attributes). Allowing for response selection, object naming RTs may provide a relatively pure measure of the functioning of the shape system. Both the shape and metric systems may affect the feelings of familiarity that govern old-new episodic shape judgments. A comparison of speeded naming and episodic judgments may provide a behavioral, noninvasive technique for determining the neural loci of these 2 systems. The recognition latency of a shape originally viewed at one size is lengthened when that shape is presented at a different size (Jolicoeur, 1987). This result, and a number of others demonstrating time costs for comparing two simultaneously (or immediately sequential) presented shapes that differ in size (Besner, 1983; Bundesen & Larsen, 1975; Ellis, Allport, Humphreys, & Collis, 1989; Jolicoeur & Besner, 1987; Larsen, 1985; Larsen & Bundesen, 1978) have led to the belief that shapes are stored at a specified scale (Kosslyn, 1987; Ullman, 1989).' To achieve matching of the representation of that shape when it is presented at a different size, according to this view, scaling transformations are necessary (e.g., Ullman, 1989). Presumably, the additional time to perform these transformations is the reason why the match of a different-size shape requires more time. Recognition was placed in quotes in the previous paragraph because, curiously, the effects of size consistency on a relatively direct measure of object classification, basic-level naming, have never been assessed. Jolicoeur's (1987) measure of was old-new discrimination. Jolicoeur himself cautioned that it was possible that the effects of size inconsistency in his experiment were not reflecting the perceptual representation used for pattern of the object but rather the processes for episodic discrimination. We report here that Jolicoeur's disquiet was well founded: Size consistency does not affect basic-level naming reaction times (RTs). We used a picture-primin g task where it has been well documented that an object viewed on one occasion

Recovery of parametric models from range images: the case for superquadrics with global deformations

A method for recovery of compact volumetric models for shape representation of single-part objects in computer vision is introduced. The models are superquadrics with parametric deformations (bending, tapering, and cavity deformation). The input for the model recovery is three-dimensional range points. Model recovery is formulated as a least-squares minimization of a cost function for all range points belonging to a single part. During an iterative gradient descent minimization process, all model parameters are adjusted simultaneously, recovery position, orientation, size, and shape of the model, such that most of the given range points lie close to the model's surface. A specific solution among several acceptable solutions, where are all minima in the parameter space, can be reached by constraining the search to a part of the parameter space. The many shallow local minima in the parameter space are avoided as a solution by using a stochastic technique during minimization. Results using real range data show that the recovered models are stable and that the recovery procedure is fast.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>