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An algorithm was proposed to generate automatically embedded image. With the use of outline matching and shape deformation, the proposed method can insert an interior object with partial deformation into an outer object image, having better results by considering the cavity of the outer object. The embedded object is easily observed because its color is opposite to the outer object while the outer object’s cavity can be part of the interior object. By designing method which is applied to express object’s edge strength, the matching result of the algorithm can be optimized.

This paper presents a method for estimating the bounding volume for image-based 3D object reconstruction. The bounding volume of an object is a three-dimensional space where the object is expectedto exist, and the size of the bounding volume strongly affects the resolution of the reconstructed geometry. Therefore, the size of a bounding volume should be as small as possible while it encloses an actual object. To this end, the proposed method uses a set of silhouettes of an object and generates a point cloud using a point filter. A bounding volume is then determined as the minimum sphere that encloses the point cloud. The experimental results show that the proposed method generates a bounding volume that encloses an actual object as small as possible.

Coordinate axes have been used extensively in three-dimensional (3D) GIS processing to help visualize the location of points directly. Meanwhile, AxSceneControl is a visual control provided by ESRI®ArcGIS®Engine, which is suited to generating perspective scenes that allow user to navigate and interact with 3D feature and raster data. However, there is no direct solution given by ArcGIS Engine to set Coordinate axes in 3D scenes. In this paper, we proposed and implemented an approach to generate and customize coordinate axis in AxSceneControl. By this method, up to five coordinate axes, named as x axis, y axis, z axis, top axis and right axis, can be drawn based on the layer that is loaded to the AxSceneControl. Furthermore, users can modify the properties of coordinate axes such as changing the style of degree scale, determining which axis will be shown and resizing the degree density to achieve simple coordinate axis.

International audience; — This paper deals with the geometrical properties of an ellipsoidal object (aspect ratio, volume, orientation) estimation with an underwater sensor inspired by the uncommon sense of the electric fish. The proposed method first locates the object independently of its geometrical properties thanks to the MUSIC (MUltiple SIgnal Classification) algorithm and then, estimates the geometrical properties using an optimization method and the object's electrical response model. The simulation results show the relevance of the method.

There are various factors for determining object shape, such as size, slope and its direction, curvature, length, surface, angles between lines or planes, distribution of the model key points, and so on. Most of the object description and recognition methods are for the 2D space not for the 3D object space where the objects actually exist. In this study, 3D chain code operator, which is basically extension of 2D chain code, was proposed for object description and analysis in 3D space. Results show that the sequence of the 3D chain codes could be basis of a top-down approach for object recognition and modeling. In addition, the proposed method could be applicable to segment point cloud data such as LiDAR data.

This article describes how to construct a wide range of geometry objects (called GeographicGeometry objects) in the coordinate system of an ellipsoid such as the Geographic coordinate system. Each construction process is formulated analytically and algorithmically using a combination of a set of fairly well-known mathematical methods such as ellipsoid geodesic construction functions, spherical trigonometry and iterative refinement methods. Each such geometry object may efficiently be converted to a corresponding Cartesian geometry object in any map projection coordinate system using an approximation algorithm. This property makes them particularly useful as a coordinate-system-independent geometry representation. A geographic geometry object is normally topologically equivalent to its Cartesian geometry counterpart except for some discontinuity and singularity cases.

This paper discusses a method for controlling a hyper-redundant arm to manipulate an object on a plane. The hyper-redundant arm can perform simple whole-arm manipulation by coiling or wrapping around the object and then pulling the object toward the goal position. The process of object manipulation can be separated into two steps: encircling the object and transporting the object. In the process of encircling the object, the arm is controlled by a set of virtual constraints that guide the arm to reach around the object and encircle it, keeping the arm within a specified bound to ensure the circular shape around the object. In the process of transporting the object, a simplified desired shape is generated from a Bezier curve according to a given goal position and the arm geometry. Then, the gradient descent method is used to update the joint angles of the arm at each step to move the arm toward the desired shape until the object reaches its target position. The proposed method has been tested in both simul...

The ability to extract spatial features from 3D objects is essential for applications such as shape matching and object classification. However, designing an effective feature vector which is invariant with respect to rotation, translation and scaling is a challenging task and is often solved by normalization techniques such as PCA, which can give rise to poor object alignment. In this paper, we introduce a novel method to extract robust and invariant 3D features based on rotational symmetry. By applying a rotation-variant similarity function on two instances of the same 3D object, we can define an autocorrelation on the object in the space of rotations. We use a special representation of the SO(3) and determine significant rotation axes for an object by means of optimization techniques. By sampling the similarity function via rotations around these axes, we obtain robust and invariant features, which are descriptive for the underlying geometry. The resulting feature vector cannot only be used to characterize an object with respect to rotational symmetry but also to define a distance between 3D models. Because the features are compact and pre-computable, our method is suitable to perform similarity searches in large 3D databases.

A novel pose normalization method based on 3D object reflective symmetry is presented. It is a general purpose global pose normalization method; in this paper it is used to enhance the performance of a 3D object retrieval pipeline. Initially, the axis-aligned minimum bounding box of a rigid 3D object is modified by requiring that the 3D object is also in minimum angular difference with respect to the normals to the faces of its bounding box. To estimate the modified axis-aligned bounding box, a set of predefined planes of symmetry are used and a combined spatial and angular distance, between the 3D object and its symmetric object, is calculated. By minimizing the combined distance, the 3D object fits inside its modified axis-aligned bounding box and alignment with the coordinate system is achieved. The proposed method is incorporated in a hybrid scheme, that serves as the alignment method in a 3D object retrieval system. The effectiveness of the 3D object retrieval system, using the hybrid pose normalization scheme, is evaluated in terms of retrieval accuracy and demonstrated using both quantitative and qualitative measures via an extensive consistent evaluation on standard benchmarks. The results clearly show performance boost against current approaches.

In today's fast-moving life many a pathological labs still use probabilistic approach to count the number of microscopic cells in a sample slide, which is a tedious job and not accurate all the time. The problem of finding the position of objects in an image as well as to count the occurrence of that object in the image is a hitch for the researcher. We have restricted our problem only to completely circular disk shaped objects. Our aim is to accurately calculate the geometrical position of the objects and the object count. Boundaries of the object patches have been extracted using morphological operation and with the help of classical geometry we locate the exact boundary coordinate of the objects. In this paper we propose a new, simple framework for visual object detection and object counting for the image of circular objects, whether these are partially occluded to each other or not.

In this paper, we describe a shape space based approach for invariant object representation and recognition. In this approach, an object and all its similarity transformed versions are identified with a single point in a high-dimensional manifold called the shape space. Object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space. This approach produced promising results in 2D object recognition experiments: it is invariant to similarity transformations and is relatively insensitive to noise and occlusion. Potentially, it can also be used for 3D object recognition.

Identifying a three-dimensional (3D) object in an image is traditionally dealt with by referencing to a 3D model of the object. In the last few years there has been a growing interest of using not a 3D shape but multiple views of the object as the reference. This paper attempts a further step in the direction, using not multiple views but a single clean view as the reference model. The key issue is how to establish correspondences from the model view where the boundary of the object is explicitly available, to the scene view where the object can be surrounded by various distracting entities and its boundary disturbed by noise. We propose a solution to the problem, which is based upon a mechanism of predicting correspondences from just four particular initial point correspondences. The object is required to be polyhedral or near-polyhedral. The correspondence mechanism has a computational complexity linear with respect to the total number of visible corners of the object in the model view. The limitation of the mechanism is also analyzed thoroughly in this paper. Experimental results over real images are presented to illustrate the performance of the proposed solution.

We present a novel approach of shape matching and recognition of 3D objects using artificial potential fields. The potential model assumes that boundary of every 3D template object of identical volume is uniformly charged. An initially small input object placed inside a template object will experience repulsive force and torque arising from the potential field. A better match in shape between the template object and the input object can be obtained if the input object translates and reorients itself to reduce the potential while growing in size. The template object which allows the maximum growth of the input object corresponds to the best match and thus represents the shape of the input object. The above repulsive force and torque are analytically tractable for an input object represented by its boundary samples, which makes the shape matching efficient. The proposed approach is intrinsically invariant under translation, rotation and size changes of the input object.

L. Richard Hitt received his B.S., M.S., and Ph.D. from Florida State University. He is a professor of mathematics at the University of South Alabama where he has been on the faculty since 1977. His research interests include geometric topology, especially knot theory, as well as elementary and differential geometry. His teaching interests also include mathematical modeling and the use of computing technology in mathematics.

In object segmentation field, while the non-predefined object segmentation distinguishes arbitrary self-assumed object from background, predefined object segmentation pre-specifies object evidently. This paper presents a new method to segment predefined objects by globally optimizing an orientation-based objective function that measures the fitness of object boundary in a discretized parameter space. A specific object is explicitly described by normalized discrete sets of boundary points and corresponding normal vectors with respect to its plane shapes in a certain aspect. The orientation factor provides robust distinctness for target objects. By considering the order relation of transformation elements, and their dependency on derived over-segmentation outcome, the domain of translations and scales is discretized efficiently. The appropriate transformation parameters of a shape model corresponding to a target object in an image are determined using the global optimization algorithm branch-bound. Discrete boundary points of the consequent transformed model are chained together to produce the final contour of the target object. The results tested on PASCAL dataset show a considerable achievement in solving complex background and unclear boundary images.

We have developed a method of recognising 3-D objects and determining their orientation from single 2-D images. These images may be noisy and contain partially occluded shapes. The method combines both analytical and structural type techniques to build a description of the viewed object. This description is then compared to a database of 2-D model descriptions for various object orientations using 2-D pose-clustering techniques. Features derived from the local geometry of the object boundary are used in the matching process. This enables the object to be recognised and its orientation determined to within an average uncertainty of less than six degrees of arc, in both the major and minor axes of the object.

In this paper a new algorithm is proposed for extracting medial axes of object. This algorithm is based on minimum exterior rectangle and edge detection. First, edge detection algorithm is used to each image to obtain all the boundary points exactly, and the center of each object is evaluated. Then, the directions of major and minor axes of the object be obtained using the center-point and boundary-points. The four vertexes of the bounding rectangle are computed by pair wise solving the four straight lines. At last, using FMABR's short axes to scan the object boundary points, all the middle point of the line which made by the scan line and boundary points buildup the medial axes of the object's body. The algorithm has both simplicity and accuracy properties.

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.

This paper proposes a new method to describe and identify a 3-D curved object for the purpose of validating a fabricated object to the design specification. Curved 3-D objects are, in general, difficult to represent and identify because they lack distinct properties such as edges, planes, or cylindrical surfaces which are the building blocks in representing objects. In this paper, the authors propose to use principal axes of a 3-D object to establish a reference for the representation. A method of obtaining an inertia matrix from a 3-D range image is developed. The unique set of principal axes is obtained from the inertia matrix of an object with an arbitrary 3-D position and orientation, and the object can be described uniquely on these principal axes. On the principal axes, an object is described by a set of features describing the shape of the object such as spine, section size, section orientation, and section contraction. The features are used for comparing two objects for the validation purpose. The authors also propose a direct measure of similarity between two objects as a mean-squared difference of radii. As an experiment, two 3-D object models are designed through a CAD package, and fabricated objects are compared with the designed models for validation purposes. >

Recovering the 3-D shape of an object from its 2-D image contour is an important problem in computer vision. In this correspondence, the author motivates and develops two object-based heuristics. The structured nature of objects is the motivation for the nonaccidental alignment criterion: parallel coordinate axes within the object's bounding contour correspond to object-centered coordinate axes. The regularity and symmetry inherent in many man-made objects is the motivation for the orthogonal basis constraint. An oblique set of coordinate axes in the image is presumed to be the projection of an orthogonal set of 3-D coordinate axes in the scene. These object-based heuristics are used to recover shape in both real and synthetic images. >

This paper describes a computer vision method for reconstruction of three-dimensional object, this method can reconstruct the object real time and has high precision. In this approach the structured light is used and the light beam is projected to the surface of object. This work is composed of three parts: the first is the introduction of the light-section method and the experimental platform based on it. The information of the three-dimensional object surface can be acquired by the platform. In the second part a coordinate transformation algorithm is introduced, including camera calibration and calibration of the central axis of a turntable. And then the space information about object surface can be restored from the two-dimensional plane coordinate of the surface. Finally, a method for plotting the contour of the three-dimensional object surface using OpenGL is described in detail. In this paper, an experiment on a small flowerpot has been carried out and the three-dimensional contour of the flowerpot has been obtained. The result shows a high precision of the three-dimensional reconstruction.

Describes a method of recognizing objects whose contours can be represented in smoothly varying polar coordinate form. Both low- and high-level information about the object (contour smoothness and edge sharpness at the low level and contour shape at the high level) are incorporated into a single energy function that defines a 1D, cyclic, Markov random field (1DCMRF). This 1DCMRF is based on a polar coordinate object representation whose center can be initialized at any location within the object. The recognition process is based on energy function minimization, which is implemented by simulated annealing. >

Describing shapes is an important task in graphics and vision. A simple, concise descriptor that captures the essential shape properties of an object would greatly facilitate computer-based understanding of the object and applications such as matching and segmentation. For this reason, medial axes (MA) has become a popular shape descriptor since its introduction by Blum [Blum 1967]. The MA of an N-D object is an (N -- 1)-D geometry centered within the object. For example, the MA of a 2D object consists of medial curves at elongated parts, whereas the MA of a 3D object consists of medial surfaces describing the protrusions on the object.

Recovering the three-dimensional (3D) object shape remains an unresolved area of research on the cross-section of computer vision, photogrammetry and bioinformatics. Although various techniques have been developed, the computational complexity and the constraints introduced to overcome the problems have limited their applicability in the real world scenarios. In this paper, we propose a method that is based on the projective geometry between the object space and the silhouette-images taken from multiple view-points. The approach eliminates the problems related to dense feature point matching and camera calibration that are generally adopted by many state of the art shape reconstruction methods. The object shape is reconstructed by establishing a set of hypothetical planes slicing the object volume and estimating the projective geometric relations between the images of these planes. The experimental results show that the 3D object shape can be recovered by applying minimal constraints.

In this paper, a novel and simple approach for tracking the object pose, position and orientation, using two object points when the object is rotated about one of the axes of the reference coordinate system is presented. The object rotation angle can be tracked up to a range of 180? for object rotations around each axis of the reference coordinate system from an initial object situation. The considered two object points are arbitrary points of the object which can be uniquely identified in stereo images. Since the approach requires only two object points, it is advantageous for the robotic applications where very few feature points can be obtained because of lack of pattern information on the objects. The paper also presents the results for the pose estimation of a meal tray in a rehabilitation robotics environment.

The following paper explores possibilities of using geodesic distance-based description of two-dimensional image objects. The main idea of the proposed representation is to create a set of equally-spaced contours composed of image points that are equidistant, in terms of geodesic distance, from the object's boundary. Due to geodesic distance properties, the proposed representation is expected to be robust against several types of nonlinear object deformations, thus being attractive for object recognition purposes.

People often recognize 3D objects by their boundary shape. Designing an algorithm for such a task is interesting and useful for retrieving objects from a shape database. In this paper, we present a fast 2-stage algorithm for recognizing 3D objects using a new feature space, built from curvature scale space images, as a shape representation that is scale, translation, rotation and reflection invariant. As well, the new shape representation removes the inherent ambiguity of the zero position of arc length for a scale space image. The 2-stage matching algorithm, conducted in the eigenspaces of the feature space, is analogous to the way people recognize an object: first identifying the type of object, and then determining the actual object. We test the new algorithm on a 3D database comprising 209 colour objects in 2926 different view poses, and achieve a 97% recognition rate for the object type and 95% for the object pose.

This paper describes the dynamic modeling of linear object deformation considering geometrical constraints and contact with obstacles. Deformable linear objects such as cables and strings are widely used in our daily life, some industries, and medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have formulated the static deformation of a linear object using the differential geometry coordinates. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we consider dynamic deformation of the linear object when forces/moments and geometrical constraints are imposed on the object. Third, we model contact of a linear object with a circular obstacle. It can be applied to self-contact of the linear object. Finally, we show simulation results using the proposed modeling technique.

This paper describes a new approach that generates a higher resolution curved surface of an object from fewer three-dimensional(3-D) measurement points compared with conventional approaches. In Computer Graphics (CG) field, an object is often expressed as the cluster of the polygons, which are converted from the 3-D position data. However, if the 3-D position data of an object is small in number, it is difficult to accurately reconstruct the object. In this paper, we propose a new approach of reconstruction of an object using both the position data and the orientation data. The advantage of this approach is to accurately reconstruct with a small number of the 3-D position data compared with the conventional approach. The main idea of this approach is both to introduce the orientation data of an object and to use Hermite interpolation for accurate reconstruction of the object.

We present a method for coding the information of a 3D object into a representation on a unit sphere. The coding is based on mapping the phase Fourier transform of the range images of the object onto the sphere. This procedure creates a unique object signature that we call three-dimensional object orientation map (3DOOM). The correlation between 3DOOM of different objects is discussed and defined. The maps permit to obtain detection as well as the orientation of an object from a range image, using only partial object information.

A new polar-exponential grid technique for object recognition is proposed in this paper. An object in the rectangular coordinate is mapped into the polar-log coordinate, and the closed profile of the object is transformed a one dimension curve. The structure of the curve has rotate, scale, translate invariance, which can be used in object recognition. Better recognition result using the structure invariant is got.

A survey and critique of previous work is given, and two object-based heuristics are developed. The structured nature of objects is the motivation for the nonaccidental alignment criterion; parallel lines within the object's bounding contour are related to the object-centered coordinate system. The regularity and symmetry inherent in many man-made objects is the motivation for the orthogonal basis constraint, an oblique set of coordinate axes in the image is presumed to be the projection of an orthogonal set of 3D coordinate axes in the scene. These heuristics are demonstrated on real and synthetic image contours. >

This paper describes a new approach to invariant object recognition. In this approach, an object is represented by a set of key points called landmarks. All possible translation, scaling, and rotation of the object are placed into an equivalent class and associated to a single point in a complex projective space called the shape space. Object recognition is then achieved by distance calculations in this shape space. This approach is invariant to object translation, scaling, and rotation, and is computationally simple. Our experimental results also indicate that it is insensitive to noise and moderate occlusions.

This is paper describe a new method to built up a 3D geometrical model of objects from a single image. This method is based on a new concept, namely cylindrical projective geometry. This geometry enables one to compute automatically the shape of objects with axial symmetry using only one image of the object without any knowledge about the camera used. The mathematics of the concept are shown as well as their use in the modeling process. Some results are presented to show the efficiency and accuracy of our method.

International audience; This paper presents an application of some recent results in computer vision, in particular the use of geometric properties. The problem we examine here is the accurate positioning of an object with respect to another, say a tool. Such applications could be used in complex and hazardous environments like nuclear plants. Because high accuracy in positioning is our goal here, we suppose that the objects have planar faces on which targets can be put. Without loss of generality, we have used only two objects in our experiments. Throughout this paper, we have called them the reference object and the unknown object respectively. The positions of the targets of the reference object with their associated projective invariants are computed in an off-line stage. Hence, given at least two images of the two objects, we can automatically identify the reference object points in the images and reconstruct the points of the unknown object relative to the reference object. The experiments show that a precision of 0.1 mm in relative positioning can be reached for an object observed at a distance of 2 m.

Two objects with homologous landmarks are said to be of the same shape if the configurations of landmarks of one object can be exactly matched with that of the other by translation, rotation/reflection, and scaling. The observations on an object are coordinates of its landmarks with reference to a set of orthogonal coordinate axes in an appropriate dimensional space. The origin, choice of units, and orientation of the coordinate axes with respect to an object may be different from object to object. In such a case, how do we quantify the shape of an object, find the mean and variation of shape in a population of objects, compare the mean shapes in two or more different populations, and discriminate between objects belonging to two or more different shape distributions. We develop some methods that are invariant to translation, rotation, and scaling of the observations on each object and thereby provide generalizations of multivariate methods for shape analysis.

A novel geometric approach for 3D object segmentation and representation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is equivalent to the computation of surfaces of minimal area, better known as ‘minimal surfaces,’ in a Riemannian space. This space is defined by a metric induced from the 3D image (volumetric data) in which the objects are to be detected. The model shows the relation between classical deformable surfaces obtained via energy minimization, and geometric ones derived from curvature based flows. The new approach is stable, robust, and automatically handles changes in the surface topology during the deformation. Based on an efficient numerical algorithm for surface evolution, we present examples of object detection in real and synthetic images.

In this paper, we describe a computationally efficient 3D object surface matching algorithm. In the proposed method, object and model surfaces are scaled to be in a unit cube in the 3D space. They are then sliced along the magnitude axis and the resultant object and model surface cross sections are represented in binary image format. The cross sections' centroids of an unknown object and the models of different shapes are computed in their respective binary images. The resultant cross-sections are translated to the origin of the spatial plane using the centroids. Major and minor axes of the plane cross sections are aligned with the coordinate axes of the spatial plane. Matching of the aligned cross sections is done in the direction of the gradient of the cross section distance between the object boundary points and the corresponding points in the model cross section boundary. The shape deformation distances measured in different cross sections are averaged and the minimum average shape deformation distance is used to identify the model best matching to the object of unknown classification.

This paper describes a computationally efficient 3D object surface matching algorithm. In the proposed method, object and model surfaces are scaled to be in a unit cube in the 3D space. They are then sliced along the magnitude axis and the resultant object and model surface cross sections are represented in binary image format. The cross- sections' centroids of an unknown object and the models of different shapes are computed in their respective binary images. The resultant cross-sections are translated to the origin of the spatial plane using the centroids. Major and minor axes of the plane cross sections are aligned with the coordinate axes of the spatial plane. Matching of the aligned cross sections is done in the direction of the gradient of the cross section boundary by computing the shape deformation as the Euclidean distance between the object boundary points and the corresponding points in the model cross section boundary. The shape deformation distances measured in different cross sections are average and the minimum average shape deformation distance is used to identify the model best matching to the object of unknown classification.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Research with humans and with nonhuman species has suggested a special role of room geometry in spatial memory functioning. In two experiments, participants learned the configuration of a room with four corners, along with the configuration of four objects within the room, while standing in a fixed position at the room’s periphery. The configurations were either rectangular (Experiment 1) or irregular (Experiment 2). Room geometry was not recalled better than object layout geometry, and memories for both configurations were orientation dependent. These results suggest that room geometry and object layout geometry are represented similarly in human memory, at least in situations that promote long-term learning of object locations. There were also some differences between corners and objects in orientation dependence, suggesting that the two sources of information are represented in similar but separate spatial reference systems.

Recovering the 3D shape of an object from its 2D image contour is an important problem in computer vision. This paper begins with a survey and critique of some of the previous shape from contour methods that have been proposed. The author then develops two object-based heuristics and uses them to recover shape constraints from contour. The basic assumption guiding these object-based heuristics is that objects tend to be highly structured and can be parametrized with respect to an object-centered, orthogonal coordinate system. The structured nature of objects is the motivation for the non-accidental alignment criterion: parallel lines within the object's bounding contour are significant and are related to the 3D object-centered coordinate system. The regularity and symmetry inherent in many man-made objects, coupled with a human preference for an orthogonal perceptual space, is the motivation for the orthogonal basis constraint: an oblique set of coordinate axes in the image is presumed to be the projection of an orthogonal set of coordinate axes in the scene. These object-based heuristic methods are demonstrated on both real and synthetic image contours.

Most current object recognition systems are based on a 3D model which is used to describe the image projection of an object over all viewpoints. We introduce a new technique which can predict the geometry of an object under projective transformation. The object geometry is represented by a set of corresponding features taken from two views. The projected geometry can be constructed in any third view, using a viewpoint invariant derived from the correspondences.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Scattering of plane electromagnetic waves from a cylindrical object of arbitrary cross-section which is buried in a geometry with parallel plane interfaces is studied. Far-zone scattered field expression is derived in a general form which contain two terms. Each term of this general form contains two factors. One factor depends only on geometry of the problem while other factor depends upon shape of the object, primary excitation and geometry of the problem. Shape dependent factor becomes independent of the geometry if it assumed that the object is deeply buried and in this situation this factor is termed as shape function. Field expression in a particular geometry for one object can be utilized for other object by inserting the shape function of desired object. Shape functions involved in field expression can be identified analytically for objects with simple shapes. It is observed that field expressions becomes quite simple for the case of a circular cylinder.

In Chapter 1 we introduced configuration space as a space in which the robot maps to a point. The mathematical structure of this space, however, is not completely straightforward, and deserves some specific consideration. The purpose of this chapter and the next one is to provide the reader with a general understanding of this structure when the robot is a rigid object not constrained by any kinematic or dynamic constraint. This chapter mainly focuses on topological and differential properties of the configuration space. More detailed algebraic and geometric properties related to the mapping of the obstacles into configuration space will be investigated in Chapter 3.

An algorithm is presented in which a computer is visually shown a sequence of views of a solid planar object as the object is rotated in space. The computer automatically forms a three-dimensional description of the object. The description consists of a deterministic description of the object's surfaces and how they are interconnected to form the object, along with a measure of each surface's shape which is invariant to three-dimensional rotation. From this self-learned model of the object, the object can later be recognized from any viewing angle. The basis of the algorithm is the ability of the program to determine in a specific visual view: "What do I see now that I have seen before?" This is accomplished by generating two sets of mappings of one object description to another object description.