An Algorithm to Recover Generalized Cylinders from a Single Intensity View

Understanding a scene involves the ability to recover the shape of objects in an environment. Generalized cylinders are a flexible, loosely defined class of parametric shapes capable of modeling many real-world objects. Straight homogeneous generalized cylinders are an important subclass of generalized cylinders whose cross sections are scaled versions of a reference curve. In this paper, a general method is presented for recovering straight homogeneous generalized cylinders from monocular intensity images. The algorithm is much more general in scope than any other developed to date. combining constraints derived from both contour and intensity information. We first demonstrate that contour information alone is insufficient to recover a straight homogeneous generalized cylinder uniquely. Next, we show that the sign and magnitude of the Gaussian curvature at a point varies among members of a contour-equivalent class. The image contour fails to constrain two parameters required to recover the shape of a generalized cylinder, the 3D axis location and the object tilt. Next, a method for "ruling" straight homogeneous generalized cylinder images is developed. Once the rulings of the image have been recovered, we show that all parameters derivable from contour alone can be recovered. To recover the two remaining parameters (modulo scale) not constrained by image contour requires incorporating additional information into the recovery process, e.g. intensity information. We derive a method for recovering the tilt of the object using the ruled contour image and intensity values along cross-sectional geodesics. In addition, we derive a method for recovering the location of the object's 3D axis from intensity values along meridians of the surface. Using the different methods outlined in this paper constitutes an algorithm for recovering all the shape parameters (modulo scale) of a straight homogeneous generalized cylinder

Superquadric representation of scenes from multi-view range data

Object representation denotes representing three-dimensional (3D) real-world objects with known graphic or mathematic primitives recognizable to computers. This research has numerous applications for object-related tasks in areas including computer vision, computer graphics, reverse engineering, etc. Superquadrics, as volumetric and parametric models, have been selected to be the representation primitives throughout this research. Superquadrics are able to represent a large family of solid shapes by a single equation with only a few parameters. This dissertation addresses superquadric representation of multi-part objects and multiobject scenes. Two issues motivate this research. First, superquadric representation of multipart objects or multi-object scenes has been an unsolved problem due to the complex geometry of objects. Second, superquadrics recovered from single-view range data tend to have low confidence and accuracy due to partially scanned object surfaces caused by inherent occlusions. To address these two problems, this dissertation proposes a multi-view superquadric representation algorithm. By incorporating both part decomposition and multi-view range data, the proposed algorithm is able to not only represent multi-part objects or multi-object scenes, but also achieve high confidence and accuracy of recovered superquadrics. The multi-view superquadric representation algorithm consists of (i) initial superquadric model recovery from single-view range data, (ii) pairwise view registration based on recovered superquadric models, (iii) view integration, (iv) part decomposition, and (v) final superquadric fitting for each decomposed part. Within the multi-view superquadric representation framework, this dissertation proposes a 3D part decomposition algorithm to automatically decompose multi-part objects or multiobject scenes into their constituent single parts consistent with human visual perception. Superquadrics can then be recovered for each decomposed single-part object. The proposed part decomposition algorithm is based on curvature analysis, and includes (i) Gaussian curvature estimation, (ii) boundary labeling, (iii) part growing and labeling, and (iv) post-processing. In addition, this dissertation proposes an extended view registration algorithm based on superquadrics. The proposed view registration algorithm is able to handle deformable superquadrics as well as 3D unstructured data sets. For superquadric fitting, two objective functions primarily used in the literature have been comprehensively investigated with respect to noise, viewpoints, sample resolutions, etc. The objective function proved to have better performance has been used throughout this dissertation. In summary, the three algorithms (contributions) proposed in this dissertation are generic and flexible in the sense of handling triangle meshes, which are standard surface primitives in computer vision and graphics. For each proposed algorithm, the dissertation presents both theory and experimental results. The results demonstrate the efficiency of the algorithms using both synthetic and real range data of a large variety of objects and scenes. In addition, the experimental results include comparisons with previous methods from the literature. Finally, the dissertation concludes with a summary of the contributions to the state of the art in superquadric representation, and presents possible future extensions to this research

Reconstruction of surfaces of revolution from single uncalibrated views

This paper addresses the problem of recovering the 3D shape of a surface of revolution from a single uncalibrated perspective view. The algorithm introduced here makes use of the invariant properties of a surface of revolution and its silhouette to locate the image of the revolution axis, and to calibrate the focal length of the camera. The image is then normalized and rectified such that the resulting silhouette exhibits bilateral symmetry. Such a rectification leads to a simpler differential analysis of the silhouette, and yields a simple equation for depth recovery. It is shown that under a general camera configuration, there will be a 2-parameter family of solutions for the reconstruction. The first parameter corresponds to an unknown scale, whereas the second one corresponds to an unknown attitude of the object. By identifying the image of a latitude circle, the ambiguity due to the unknown attitude can be resolved. Experimental results on real images are presented, which demonstrate the quality of the reconstruction. © 2004 Elsevier B.V. All rights reserved.postprin

Identification of parameters in amplitude equations describing coupled wakes

We study the flow behind an array of equally spaced parallel cylinders. A system of Stuart-Landau equations with complex parameters is used to model the oscillating wakes. Our purpose is to identify the 6 scalar parameters which most accurately reproduce the experimental data of Chauve and Le Gal [{Physica D {\bf 58}}, pp 407--413, (1992)]. To do so, we perform a computational search for the minimum of a distance \calj. We define \calj as the sum-square difference of the data and amplitudes reconstructed using coupled equations. The search algorithm is made more efficient through the use of a partially analytical expression for the gradient $\nabla \cal J$. Indeed $\nabla \cal J$ can be obtained by the integration of a dynamical system propagating backwards in time (a backpropagation equation for the Lagrange multipliers). Using the parameters computed via the backpropagation method, the coupled Stuart-Landau equations accurately predicted the experimental data from Chauve and Le Gal over a correlation time of the system. Our method turns out to be quite robust as evidenced by using noisy synthetic data obtained from integrations of the coupled Stuart-Landau equations. However, a difficulty remains with experimental data: in that case the several sets of identified parameters are shown to yield equivalent predictions. This is due to a strong discretization or ``round-off" error arising from the digitalization of the video images in the experiment. This ambiguity in parameter identification has been reproduced with synthetic data subjected to the same kind of discretization.Comment: 25 pages uuencoded compressed PostScript file (58K) with 13 figures (155K in separated file) Submitted to Physica

Image Understanding and Robotics Research at Columbia University

Over the past year, the research investigations of the Vision/Robotics Laboratory at Columbia University have reflected the interests of its four faculty members, two staff programmers, and 16 Ph.D. students. Several of the projects involve other faculty members in the department or the university, or researchers at AT&T, IBM, or Philips. We list below a summary of our interests and results, together with the principal researchers associated with them. Since it is difficult to separate those aspects of robotic research that are purely visual from those that are vision-like (for example, tactile sensing) or vision-related (for example, integrated vision-robotic systems), we have listed all robotic research that is not purely manipulative. The majority of our current investigations are deepenings of work reported last year; this was the second year of both our basic Image Understanding contract and our Strategic Computing contract. Therefore, the form of this year's report closely resembles last year's. Although there are a few new initiatives, mainly we report the new results we have obtained in the same five basic research areas. Much of this work is summarized on a video tape that is available on request. We also note two service contributions this past year. The Special Issue on Computer Vision of the Proceedings of the IEEE, August, 1988, was co-edited by one of us (John Kender [27]). And, the upcoming IEEE Computer Society Conference on Computer Vision and Pattem Recognition, June, 1989, is co-program chaired by one of us (John Kender [23])

Object representation and recognition

One of the primary functions of the human visual system is object recognition, an ability that allows us to relate the visual stimuli falling on our retinas to our knowledge of the world. For example, object recognition allows you to use knowledge of what an apple looks like to find it in the supermarket, to use knowledge of what a shark looks like to swim in th

Part Description and Segmentation Using Contour, Surface and Volumetric Primitives

The problem of part definition, description, and decomposition is central to the shape recognition systems. The Ultimate goal of segmenting range images into meaningful parts and objects has proved to be very difficult to realize, mainly due to the isolation of the segmentation problem from the issue of representation. We propose a paradigm for part description and segmentation by integration of contour, surface, and volumetric primitives. Unlike previous approaches, we have used geometric properties derived from both boundary-based (surface contours and occluding contours), and primitive-based (quadric patches and superquadric models) representations to define and recover part-whole relationships, without a priori knowledge about the objects or object domain. The object shape is described at three levels of complexity, each contributing to the overall shape. Our approach can be summarized as answering the following question : Given that we have all three different modules for extracting volume, surface and boundary properties, how should they be invoked, evaluated and integrated? Volume and boundary fitting, and surface description are performed in parallel to incorporate the best of the coarse to fine and fine to coarse segmentation strategy. The process involves feedback between the segmentor (the Control Module) and individual shape description modules. The control module evaluates the intermediate descriptions and formulates hypotheses about parts. Hypotheses are further tested by the segmentor and the descriptors. The descriptions thus obtained are independent of position, orientation, scale, domain and domain properties, and are based purely on geometric considerations. They are extremely useful for the high level domain dependent symbolic reasoning processes, which need not deal with tremendous amount of data, but only with a rich description of data in terms of primitives recovered at various levels of complexity