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 pose-invariant 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 three-dimensional 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.

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...

In this paper we present a framework for the approximate conversion of parametric to implicit surfaces. It takes as input a parametric description and generates a piecewise analytic implicit representation. The conversion process consists of three steps: 1) the parametric surface is rasterized into a volumetric characteristic function. 2) this binary function is converted into a volume array corresponding to samples of a smooth implicit function. 3) this volumetric representation is converted into a multiscale B-spline model. This method is based on wavelet analysis and synthesis techniques and is very general. It can convert to implicit form any geometric object that is suitable for discretization into a characteristic function. 1. Introduction The two main forms of describing the geometry a solid object are the parametric and implicit descriptions. In the parametric description, the solid is specified through its bounding surface, usually in a piecewise manner. In the implic...

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, defined by the locus 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 nat 2 ural 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.