## Representation and Recognition of FreeForm Surfaces (1992)

Citations: | 55 - 6 self |

### BibTeX

@TECHREPORT{Hebert92representationand,

author = {M. Hebert and K. Ikeuchi and H. Delingette},

title = {Representation and Recognition of FreeForm Surfaces},

institution = {},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

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Citation Context ...t must be enforced when the mesh is built. Constructing meshes that fit input data and that satisfy some constraints is possible based on the optimization techniques originally introduced in [27] and =-=[17]-=-. We use an extension of the deformable surface algorithms introduced in [9] to compute the meshes. As in the EGI algorithms, each node of the mesh is mapped onto a regular mesh on the unit sphere, an... |

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Citation Context ...and the set of allowable shapes. To address these two problems, another class of approaches attempts to match sets of points directly without any prior surface fitting. An example is the work by Besl =-=[2]-=- in which the distance between point sets is computed and minimized to find the best transformation between model and scene. This approach has many advantages since it does not require any surface seg... |

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Citation Context ...to represent objects as a set of primitives such as faces or edges. Most early local methods handle polyhedral objects and report effective and encouraging results. Representative systems include [13]=-=[21]-=-[15]. Few systems can handle curved surfaces. Some systems include early work in which primitive surfaces enclosed by orientation discontinuity boundaries are extracted from range data [22]. Other sys... |

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Citation Context ...mpt to represent objects as a set of primitives such as faces or edges. Most early local methods handle polyhedral objects and report effective and encouraging results. Representative systems include =-=[13]-=-[21][15]. Few systems can handle curved surfaces. Some systems include early work in which primitive surfaces enclosed by orientation discontinuity boundaries are extracted from range data [22]. Other... |

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Citation Context ...lized cylinders for recognition is difficult due to the difficulty of extracting GC parameters from input images. Superquadrics (SQ) representation also belongs to the class of global representations =-=[23]-=-. Superquadrics are generalizations of ellipsoids. Object representations are built by fitting an implicit equation to a set of input data points. Recognition using SQs proceeds by comparing the param... |

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Citation Context ...al geometry such as [3] segment range images using Gaussian curvatures. More recent local techniques use points of interest and edges of surfaces to match observed surfaces with stored representation =-=[24]-=-. These local methods, however, are noise-sensitive and are still limited in reliably extracting primitives of curved objects from input images. The global methods assume one particular coordinate sys... |

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Citation Context ... tools can be used to compute limbs and other properties of the object. Recognition proceeds by comparing invariant properties computed from the algebraic equations of observed and reference surfaces =-=[12]-=-. Although encouraging results have been obtained in this area, more research is needed in the areas of bounding constraints, convergence of surface fitting, and recognition before this approach becom... |

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Citation Context ...ion, and scale of the underlying object. In the case of two-dimensional contours, intrinsic coordinate systems are very easy to define. For example, they are the basis of geometric hashing techniques =-=[18]-=-. For three-dimensional surfaces, a general definition of intrinsic coordinate systems on curved objects is much more difficult to define. For example, the geodesics of a surface can be used to define... |

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Citation Context ...he polynomial computed from a partial view is similar to the polynomial computed from a complete model of the object. For a survey of other techniques that can be used for global surface fitting, see =-=[5]-=-. All these approaches attempt to fit some known parametric surface, either locally or globally, to the object. Consequently, these approaches tend to limit the set of shapes that can be represented a... |

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Citation Context ...on of SQs. This limitation has the undesirable effect of making the fitting process much more expensive and numerically unstable. A possible extension is to segment objects into sets of superquadrics =-=[11]-=-, although the computational complexity of the scene analysis may become prohibitive. An interesting attempt to handle a large class of natural objects in discussed in [4] in which multiple surface re... |

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Citation Context ...lt to define. For example, the geodesics of a surface can be used to define an intrinsic coordinate system. Still other efforts focus on lines of curvatures and other differential geometry invariants =-=[6]-=-. The problem with these approaches is that they are based 4on definitions and properties that are valid for continuous surfaces, whereas we typically have to handle discrete surfaces from sensor dat... |

47 |
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Citation Context ...epresentation. Recently, new approaches for modeling objects have been developed. These approaches are based on the idea of fitting a bounded algebraic surface of fixed degree to a set of data points =-=[25]-=-[26]. With this representation, recognition proceeds by comparing the polynomials describing observed and stored surfaces, although it is not yet clear how the comparison would be performed. Using alg... |

41 |
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Citation Context ... object and a given resolution up to a rotation of the representation space. Detailed presentations of the basic results on semi-regular tessellations, triangulations, and duality can be found in [20]=-=[28]-=-[29]. 2.1 Intrinsic Representation of 2-D Curves A standard approach to representing and recognizing contours is to approximate contours by polygons, and to compute a quantity that is related to the c... |

34 | Object Recognition Using Three-Dimensional Information - M, Shirai - 1983 |

28 | Recognition of 3-D Objects Using the Extended Gaussian Image
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Citation Context ...ized cylinders, are used. The type of representation is selected based on the level of detail available from the range image. EGI and CEGI map surface orientation distributions to the Gaussian sphere =-=[14]-=-[19][16]. Since the Gauss map is independent on translation, the representation is quite suitable to handle convex curved objects. In this case, recognition proceeds by finding the rotation 2that max... |

22 |
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Citation Context ... into sets of superquadrics [11], although the computational complexity of the scene analysis may become prohibitive. An interesting attempt to handle a large class of natural objects in discussed in =-=[4]-=- in which multiple surface representations, ranging from quadrics to superquadrics to generalized cylinders, are used. The type of representation is selected based on the level of detail available fro... |

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Citation Context ...inders, are used. The type of representation is selected based on the level of detail available from the range image. EGI and CEGI map surface orientation distributions to the Gaussian sphere [14][19]=-=[16]-=-. Since the Gauss map is independent on translation, the representation is quite suitable to handle convex curved objects. In this case, recognition proceeds by finding the rotation 2that maximizes t... |

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Citation Context ...scontinuity boundaries are extracted from range data [22]. Other systems determine primitive surfaces which satisfy planar or quadric equations [10]. Techniques based on differential geometry such as =-=[3]-=- segment range images using Gaussian curvatures. More recent local techniques use points of interest and edges of surfaces to match observed surfaces with stored representation [24]. These local metho... |

11 |
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Citation Context ...epresent objects as a set of primitives such as faces or edges. Most early local methods handle polyhedral objects and report effective and encouraging results. Representative systems include [13][21]=-=[15]-=-. Few systems can handle curved surfaces. Some systems include early work in which primitive surfaces enclosed by orientation discontinuity boundaries are extracted from range data [22]. Other systems... |

8 | The Representation, Recognition, and Locating of 3-D - Faugeras, Hebert - 1986 |

6 | J.J.,"Determining Object Attitude from Extended Gaussian Image
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Citation Context ... cylinders, are used. The type of representation is selected based on the level of detail available from the range image. EGI and CEGI map surface orientation distributions to the Gaussian sphere [14]=-=[19]-=-[16]. Since the Gauss map is independent on translation, the representation is quite suitable to handle convex curved objects. In this case, recognition proceeds by finding the rotation 2that maximiz... |

6 |
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Citation Context ...sentation. Recently, new approaches for modeling objects have been developed. These approaches are based on the idea of fitting a bounded algebraic surface of fixed degree to a set of data points [25]=-=[26]-=-. With this representation, recognition proceeds by comparing the polynomials describing observed and stored surfaces, although it is not yet clear how the comparison would be performed. Using algebra... |

5 |
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Citation Context ...aints that must be enforced when the mesh is built. Constructing meshes that fit input data and that satisfy some constraints is possible based on the optimization techniques originally introduced in =-=[27]-=- and [17]. We use an extension of the deformable surface algorithms introduced in [9] to compute the meshes. As in the EGI algorithms, each node of the mesh is mapped onto a regular mesh on the unit s... |

3 | Space Structures - Loeb - 1976 |

2 |
Parameterizing and Fitting Bounded Algebraic
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Citation Context ...sentation. Recently, new approaches for modeling objects have been developed. These approaches are based on the idea of fitting a bounded algebraic surface of fixed degree to a set of data points [25]=-=[26]-=-. With this representation, recognition proceeds by comparing the polynomials describing observed and stored surfaces, although it is not yet clear how the comparison would be performed. Using algebra... |

1 | Intrinsic Geometry of Surfaces", Translation - Aleksandrov, Zalgaller - 1967 |

1 | Intrinsic Geometry of Surfaces”, Translation - Aleksandrov, Zalgaller - 1967 |