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Representation and Recognition of FreeForm Surfaces
, 1992
"... We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ..."
Abstract

Cited by 53 (6 self)
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We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. We define local regularity constraints that the mesh must satisfy. We then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is poseinvariant is stored at every node of the mesh. We use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. We show how the similarity between reference model and observed data can be evaluated and we show how the pose of the reference object in the observed scene can be easily computed using this representation. We present results on real range images which show that this approach to modelling and recognizing threedimensional objects has three main advantages: First, it is applicable to complex curved surfaces that cannot be handled by conventional techniques. Second, it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search. Finally, even though it is based on a spherical mapping, the approach can handle occlusions and partial views.
A Hybrid Hyperquadric Model for 2D and 3D Data Fitting
 COMPUTER VISION AND IMAGE UNDERSTANDING
, 1994
"... We present in this paper a new curve and surface implicit model. This implicit model based on hyperquadrics allows a local and global control of the shape and a wide variety of allowable shapes. We define a hybrid hyperquadric model by introducing implicitly some local properties on a global shape m ..."
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Cited by 26 (2 self)
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We present in this paper a new curve and surface implicit model. This implicit model based on hyperquadrics allows a local and global control of the shape and a wide variety of allowable shapes. We define a hybrid hyperquadric model by introducing implicitly some local properties on a global shape model. The advantage of our model is that it describes global and local properties through a unique implicit equation yielding a representation of the shape by means of its parameters, independently of the chosen numerical resolution. The data fitting is obtained through the minimization of an energy, modelling the attraction to data independently of the implicit description of the shape. After studying the geometry of hyperquadrics and how the shape deforms when we modify slightly its implicit equation, we are able to define an algorithm for automatic refining of the fit by adding an adequate term to the implicit representation. This geometric approach allows an efficient description of th...
Approximate conversion of parametric to implicit surfaces
 in Implicit Surfaces’95
, 1996
"... ..."
Reconstruction of HOT Curves from Image Sequences
, 1993
"... Recently, a novel shape representation of general curved objects, which is suitable for object recognition, has been proposed; it is based on a set of surface curves, named HOT curves, de ned bythelocus of points where a line has high order tangency with the surface [16]. These curves determine the ..."
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Cited by 5 (2 self)
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Recently, a novel shape representation of general curved objects, which is suitable for object recognition, has been proposed; it is based on a set of surface curves, named HOT curves, de ned bythelocus of points where a line has high order tangency with the surface [16]. These curves determine the structure of an object's image contours and their catastrophic changes. A natural correspondence between a point in an intensity image and some of these curves can be directly established. This correspondence can be used for pose estimation and indexing in recognition. It also permits their 3D reconstruction from feature points on the edges detected in a sequence of images under known observer motion. This paper presents an implemented reconstruction method and experimental results.
Simultaneous surface approximation and segmentation of complex objects
 Comput. Vis. Image Understanding
, 1999
"... Deformable models represent a useful approach to approximate objects from collected data points. We propose to augment the basic approaches designed to handle mostly compact objects or objects of known topology. Our approach can fit simultaneously more than one curve or surface to approximate multip ..."
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Cited by 2 (0 self)
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Deformable models represent a useful approach to approximate objects from collected data points. We propose to augment the basic approaches designed to handle mostly compact objects or objects of known topology. Our approach can fit simultaneously more than one curve or surface to approximate multiple topologically complex objects by using (1) the residual data points, (2) the badly fitting parts of the approximating surface, and (3) appropriate Boolean operations. In 2D, Bsnakes [3] are used to approximate each object (pattern). In 3D, an analytical surface representation, based on the elements detected, is presented. The global representation of a 3D object, in terms of elements and their connection, takes the form of Bspline and Bézier surfaces. A Bézier surface is used to connect different elements, and the connecting surface itself conforms to the data points nearby through energy minimization. This way, a G1 continuity surface is achieved for the underlying 3D object. We present experiments on synthetic and real data in 2D and 3D. In these experiments, multiple complex patterns and objects with through holes are segmented. The system proceeds automatically without human interaction or any prior knowledge of the topology of the underlying object. c ○ 1999 Academic Press Key Words: snakes; deformable model; Bspline; segmentation; energy minimization.
Surface Approximation of Complex 3D Objects
, 1994
"... Our goal is to generate a surface description of complex objects with parts and holes. We start by fitting a surface, assuming the object is of Genus 0, then analyze the result to further segment the description. In the first part of our algorithm, the system provides an initial estimated surface wh ..."
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Our goal is to generate a surface description of complex objects with parts and holes. We start by fitting a surface, assuming the object is of Genus 0, then analyze the result to further segment the description. In the first part of our algorithm, the system provides an initial estimated surface which is subject to internal forces (describing implicit continuity properties such as smoothness) and external forces which attract it toward the data points. The problem is cast in terms of energy minimization. We solve this nonconvex optimization problem by using the well known Powell algorithm which guarantees convergence and does not require gradient information. The variables are the positions of the control points. The number of control points processed by Powell at one time is controlled. The process is controlled by two parameters only, which are constant for all our experiments. The above approach is not sufficient for complex objects with cavities, or for more than one object. We therefore propose an approach that can apply simultaneously more than one curve or surface to approximate multiple objects. Using (1) the residual data points, (2) the bad parts of the fitting surface, and (3) appropriate Boolean operations, our approach is able to handle objects more complicated than Genus 0 or with deep cavities, and can perform segmentation if there is more than one underlying object. 1