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

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

Recovery of 3-D objects with multiple curved surfaces from 2-D contours

Cataloged from PDF version of article.Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. Often, techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well. In this paper, we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously, though it is limited to objects made of zero-Gaussian curvature surfaces. Our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them, and from other boundaries. This technique uses some of the constraints developed in an earlier paper that was limited to examining a zero-Gaussian curvature surface cut by parallel planes. This restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces. Results on some complex examples are shown

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

Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models

The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models. To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions. The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation. We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision

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

Recovery of 3-D shape of curved objects from multiple views

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (p. 65-66).by Eugene S. Lin.M.Eng

3D object reconstruction from line drawings.

Cao Liangliang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 64-69).Abstracts in English and Chinese.Chapter 1 --- Introduction and Related Work --- p.1Chapter 1.1 --- Reconstruction from Single Line Drawings and the Applications --- p.1Chapter 1.2 --- Optimization-based Reconstruction --- p.2Chapter 1.3 --- Other Reconstruction Methods --- p.2Chapter 1.3.1 --- Line Labeling and Algebraic Methods --- p.2Chapter 1.3.2 --- CAD Reconstruction --- p.3Chapter 1.3.3 --- Modelling from Images --- p.3Chapter 1.4 --- Finding Faces of Line Drawings --- p.4Chapter 1.5 --- Generalized Cylinder --- p.4Chapter 1.6 --- Research Problems and Our Contribution --- p.5Chapter 1.6.1 --- A New Criteria --- p.5Chapter 1.6.2 --- Recover Objects from Line Drawings without Hidden Lines --- p.6Chapter 1.6.3 --- Reconstruction of Curved Objects --- p.6Chapter 1.6.4 --- Planar Limbs Assumption and the Derived Models --- p.6Chapter 2 --- A New Criteria for Reconstruction --- p.8Chapter 2.1 --- Introduction --- p.8Chapter 2.2 --- Human Visual Perception and the Symmetry Measure --- p.10Chapter 2.3 --- Reconstruction Based on Symmetry and Planarity --- p.11Chapter 2.3.1 --- Finding Faces --- p.11Chapter 2.3.2 --- Constraint of Planarity --- p.11Chapter 2.3.3 --- Objective Function --- p.12Chapter 2.3.4 --- Reconstruction Algorithm --- p.13Chapter 2.4 --- Experimental Results --- p.13Chapter 2.5 --- Summary --- p.18Chapter 3 --- Line Drawings without Hidden Lines: Inference and Reconstruction --- p.19Chapter 3.1 --- Introduction --- p.19Chapter 3.2 --- Terminology --- p.20Chapter 3.3 --- Theoretical Inference of the Hidden Topological Structure --- p.21Chapter 3.3.1 --- Assumptions --- p.21Chapter 3.3.2 --- Finding the Degrees and Ranks --- p.22Chapter 3.3.3 --- Constraints for the Inference --- p.23Chapter 3.4 --- An Algorithm to Recover the Hidden Topological Structure --- p.25Chapter 3.4.1 --- Outline of the Algorithm --- p.26Chapter 3.4.2 --- Constructing the Initial Hidden Structure --- p.26Chapter 3.4.3 --- Reducing Initial Hidden Structure --- p.27Chapter 3.4.4 --- Selecting the Most Plausible Structure --- p.28Chapter 3.5 --- Reconstruction of 3D Objects --- p.29Chapter 3.6 --- Experimental Results --- p.32Chapter 3.7 --- Summary --- p.32Chapter 4 --- Curved Objects Reconstruction from 2D Line Drawings --- p.35Chapter 4.1 --- Introduction --- p.35Chapter 4.2 --- Related Work --- p.36Chapter 4.2.1 --- Face Identification --- p.36Chapter 4.2.2 --- 3D Reconstruction of planar objects --- p.37Chapter 4.3 --- Reconstruction of Curved Objects --- p.37Chapter 4.3.1 --- Transformation of Line Drawings --- p.37Chapter 4.3.2 --- Finding 3D Bezier Curves --- p.39Chapter 4.3.3 --- Bezier Surface Patches and Boundaries --- p.40Chapter 4.3.4 --- Generating Bezier Surface Patches --- p.41Chapter 4.4 --- Results --- p.43Chapter 4.5 --- Summary --- p.45Chapter 5 --- Planar Limbs and Degen Generalized Cylinders --- p.47Chapter 5.1 --- Introduction --- p.47Chapter 5.2 --- Planar Limbs and View Directions --- p.49Chapter 5.3 --- DGCs in Homogeneous Coordinates --- p.53Chapter 5.3.1 --- Homogeneous Coordinates --- p.53Chapter 5.3.2 --- Degen Surfaces --- p.54Chapter 5.3.3 --- DGCs --- p.54Chapter 5.4 --- Properties of DGCs --- p.56Chapter 5.5 --- Potential Applications --- p.59Chapter 5.5.1 --- Recovery of DGC Descriptions --- p.59Chapter 5.5.2 --- Deformable DGCs --- p.60Chapter 5.6 --- Summary --- p.61Chapter 6 --- Conclusion and Future Work --- p.62Bibliography --- p.6

A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds

This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201

Recovery of 3-D objects with multiple curved surfaces from 2-D contours

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. Often, techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well. In this paper, we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously, though it is limited to objects made of zero-Gaussian curvature surfaces. Our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them, and from other boundaries. This technique uses some of the constraints developed in an earlier paper that was limited to examining a zero-Gaussian curvature surface cut by parallel planes. This restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces. Results on some complex examples are shown. © 1994