## Shape Distributions (2002)

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Venue: | ACM Transactions on Graphics |

Citations: | 194 - 0 self |

### BibTeX

@ARTICLE{Osada02shapedistributions,

author = {Robert Osada and Thomas Funkhouser and Bernard Chazelle and David Dobkin},

title = {Shape Distributions},

journal = {ACM Transactions on Graphics},

year = {2002},

volume = {21},

pages = {807--832}

}

### Years of Citing Articles

### OpenURL

### Abstract

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

### Citations

1161 | Information Theory and Statistics
- Kullback
- 1968
(Show Context)
Citation Context ...paring two functions f and g representing probability distributions [Puzicha et al. 1999]. Examples include the Minkowski LN norms, Kolmogorov-Smirnov distance, Kullback-Leibler divergence distances [=-=Kullback 1968],-=- Match distances [Shen and Wong 1983; Werman et al. 1985], Earth Mover’s distance [Rubner et al. 1998], and Bhattacharyya distance [Bhattacharyya 1943]. Other methods, perhaps based on 2D curve matc... |

883 |
Query by image and video content: The qbic system
- Flickner, Sawhney, et al.
- 1995
(Show Context)
Citation Context ...surfaces, 3D volumes, structural models, or statistics. The vast majority of work in shape matching has focused on characterizing similarity between objects in 2D images (e.g., [Chang and Smith 1995; =-=Flickner et al. 1995-=-; Jacobs et al. 1995; Ogle and Stonebraker 1995]). Unfortunately, most 2D methods do not extend directly to 3D model matching. The main problem is boundary parameterization. Although the 1D boundary c... |

371 | Teddy: a sketching interface for 3D freeform design
- Igarashi, Matsuoka, et al.
- 1999
(Show Context)
Citation Context ... a tool with which users can retrieve models from a 3D database based on their shape attributes. In the early prototype system [Chen 2001], the user draws a 3D query model using a Java applet (Teddy [=-=Igarashi et al. 1999-=-]) running in any web browser. The resulting set of polygons is sent to a web server, which computes its D2 shape distribution and a dissimilarity measure for all models in a 3D database using the met... |

350 |
Dynamic 3d models with local and global deformations: deformable superquadrics
- Terzopoulos, Metaxas
- 1991
(Show Context)
Citation Context ...es, and fitting model parameters more expensive. As a result, methods that match shapes using deformations [Amit et al. 1991; Jain et al. 1996; Pentland and Sclaroff 1991; Sclaroff and Pentland 1995; =-=Terzopoulos and Metaxas 1991-=-] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian Images [Horn ... |

327 |
Geometric hashing: A general and efficient model-based recognition scheme
- Lamdan, Wolfson
- 1988
(Show Context)
Citation Context ...99] or Earth Mover’s Distance [Rubner et al. 1998] usually rely upon a priori registration of objects’ coordinate systems, which is difficult to achieve automatically and robustly. Geometric hashi=-=ng [Lamdam and Wolfson 1988-=-] is a potential solution, but it requires a large amount of storage for complex models. Another popular approach to shape analysis and matching is based on comparing high-level representations of sha... |

309 | A Metric for Distributions with Applications to Image Databases
- Rubner, Tomasi, et al.
- 1998
(Show Context)
Citation Context ...topologically valid surface mesh or an explicit volume is available for every object. In addition, volumetric dissimilarity measures based on wavelets [Gain and Scott 1999] or Earth Mover’s Distance=-= [Rubner et al. 1998] -=-usually rely upon a priori registration of objects’ coordinate systems, which is difficult to achieve automatically and robustly. Geometric hashing [Lamdam and Wolfson 1988] is a potential solution,... |

271 | Fast Multiresolution Image Querying
- Jacobs, Finkelstein, et al.
- 1995
(Show Context)
Citation Context ...structural models, or statistics. The vast majority of work in shape matching has focused on characterizing similarity between objects in 2D images (e.g., [Chang and Smith 1995; Flickner et al. 1995; =-=Jacobs et al. 1995-=-; Ogle and Stonebraker 1995]). Unfortunately, most 2D methods do not extend directly to 3D model matching. The main problem is boundary parameterization. Although the 1D boundary contours of 2D shapes... |

270 | Chabot: retrieval from a relational database of images
- Ogle, Stonebraker
- 1995
(Show Context)
Citation Context ...r statistics. The vast majority of work in shape matching has focused on characterizing similarity between objects in 2D images (e.g., [Chang and Smith 1995; Flickner et al. 1995; Jacobs et al. 1995; =-=Ogle and Stonebraker 1995-=-]). Unfortunately, most 2D methods do not extend directly to 3D model matching. The main problem is boundary parameterization. Although the 1D boundary contours of 2D shapes have a natural arc length ... |

222 |
Three-dimensional object recognition
- Besl, Jain
- 1985
(Show Context)
Citation Context ... of two shapes has been well-studied in several fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [Alt and Guibas 1996; Arman and Aggarwal 1993; =-=Besl and Jain 1985;-=- Loncaric 1998; Pope 1994; Veltkamp and Hagedoorn 1999]. To briefly review, prior matching methods can be classified according to ACM Transactions on Graphics, Vol. V, No. N, 10 202002.s4 · Robert Os... |

200 | A survey of shape analysis techniques
- Loncaric
- 1998
(Show Context)
Citation Context ...een well-studied in several fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [Alt and Guibas 1996; Arman and Aggarwal 1993; Besl and Jain 1985; =-=Loncaric 1998;-=- Pope 1994; Veltkamp and Hagedoorn 1999]. To briefly review, prior matching methods can be classified according to ACM Transactions on Graphics, Vol. V, No. N, 10 202002.s4 · Robert Osada et al. thei... |

193 |
B.: An efficiently computable metric for comparing polygonal shapes
- ARKIN, CHEW, et al.
- 1991
(Show Context)
Citation Context ...th parameterization, 3D surfaces of arbitrary genus do not. As a result, common representations of 2D contours for shape matching, such as Fourier descriptors [Arbter et al. 1990], turning functions [=-=Arkin et al. 1991-=-], bending energy functions [Young et al. 1974], arch height functions [Lin et al. 1992], size functions [Uras and Verri 1994; 1997], and order structures [Carlsson 1999] have no direct analogs for 3D... |

192 |
On a measure of divergence between two statistical populations defined by probability distributions
- Bhattacharyya
- 1943
(Show Context)
Citation Context ...nov distance, Kullback-Leibler divergence distances [Kullback 1968], Match distances [Shen and Wong 1983; Werman et al. 1985], Earth Mover’s distance [Rubner et al. 1998], and Bhattacharyya distance=-= [Bhattacharyya 1943-=-]. Other methods, perhaps based on 2D curve matching [Alt and Guibas 1996; Veltkamp and Hagedoorn 1999], could also be used. In our implementation, we have experimented with eight simple dissimilarity... |

192 | Empirical evaluation of dissimilarity measures for color and texture
- Puzicha, Rubner, et al.
- 1999
(Show Context)
Citation Context ... two 3D models, we are left with the task of comparing them to produce a dissimilarity measure. There are many standard ways of comparing two functions f and g representing probability distributions [=-=Puzicha et al. 1999].-=- Examples include the Minkowski LN norms, Kolmogorov-Smirnov distance, Kullback-Leibler divergence distances [Kullback 1968], Match distances [Shen and Wong 1983; Werman et al. 1985], Earth Mover’s ... |

189 | Recovery of parametric models from range images: the case for superquadrics with global deformations
- Solina, Bajcsy
- 1990
(Show Context)
Citation Context ...e between objects based on the differences between their features and/or their spatial relationships. Example representations of this type include generalized cylinders [Binford 1971], superquadrics [=-=Solina and Bajcsy 1990-=-], geons [Wu and Levine 1994], deformable regions [Basri et al. 1998], shock graphs [Siddiqi et al. 1998], medial axes [Bardinet et al. 2000], and skeletons [Bloomenthal and Lim 1999; Storti et al. 19... |

182 | Modal Matching for Correspondence and Recognition
- Sclaroff, Pentland
- 1995
(Show Context)
Citation Context ...inding feature correspondences, and fitting model parameters more expensive. As a result, methods that match shapes using deformations [Amit et al. 1991; Jain et al. 1996; Pentland and Sclaroff 1991; =-=Sclaroff and Pentland 1995-=-; Terzopoulos and Metaxas 1991] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include E... |

175 |
Visual perception by computer
- Binford
- 1971
(Show Context)
Citation Context ... compute a dissimilarity measure between objects based on the differences between their features and/or their spatial relationships. Example representations of this type include generalized cylinders =-=[18]-=-, superquadrics [61], geons [72], deformable regions [13], shock graphs [59], medial axes [11], and skeletons [19, 62]. These methods work best when 3D models can be segmented into a canonical set of ... |

171 | Simplification envelopes
- Cohen
- 1996
(Show Context)
Citation Context ...dels. We further investigated the robustness of our method by testing it with different polygon tessellations of two 3D shapes. We used the Simplification Envelopes software provided by Cohen et al. [=-=Cohen et al. 1996-=-] to produce 8 versions of the Stanford Bunny [Laboratory 1996] ranging from 70,000 down to 600 triangles, and 6 versions of a sphere ranging from 200 down to 28 triangles. Then, we constructed D2 sha... |

171 |
S.: Object Matching Using Deformable Templates
- Jain, Zhong, et al.
- 1996
(Show Context)
Citation Context ...3D data is higher, which makes registration, finding feature correspondences, and fitting model parameters more expensive. As a result, methods that match shapes using deformations [Amit et al. 1991; =-=Jain et al. 1996-=-; Pentland and Sclaroff 1991; Sclaroff and Pentland 1995; Terzopoulos and Metaxas 1991] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For instance, representa... |

170 |
Closed-form solutions for physically based shape modeling and recognition
- Pentland, Sclaroff
- 1991
(Show Context)
Citation Context ... which makes registration, finding feature correspondences, and fitting model parameters more expensive. As a result, methods that match shapes using deformations [Amit et al. 1991; Jain et al. 1996; =-=Pentland and Sclaroff 1991-=-; Sclaroff and Pentland 1995; Terzopoulos and Metaxas 1991] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For instance, representations for registering and ma... |

149 | Extended Gaussian Image
- Horn
- 1984
(Show Context)
Citation Context ... 1991] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian Images [=-=Horn 1984-=-], Spherical Attribute Images [Delingette et al. 1992; 1993], Harmonic Shape Images [Zhang and Hebert 1999], and Spin Images [Johnson and Hebert 1999]. Unfortunately, these previous methods usually as... |

147 | Matching shapes
- Belongie, Malik, et al.
(Show Context)
Citation Context ...l. [Huet and Hancock 1996], and Ikeuchi et al. [Ikeuchi et al. 1996] have all represented shapes in 2D images by histograms of angles and distances between pairs of 2D line segments. Belongie et al. [=-=Belongie et al. 2001-=-] and Mori et al. [Mori et al. 2001] have represented 2D shapes by the distributions of points on their boundaries with respect to multiple reference frames. For 3D shapes, Ankerst et al. [Ankerst et ... |

127 |
Pattern classification, second edition
- Duda, Hart, et al.
(Show Context)
Citation Context ...nd/or large storage requirements. Finally, shapes have been compared on the basis of their statistical properties. The simplest approach of this type is to evaluate distances between feature vectors [=-=Duda et al. 2001-=-] in a multidimensional space where the axes encode global geometric properties, such as circularity, eccentricity, or algebraic moments [Prokop and Reeves 1992; Taubin and Cooper 1992]. Other methods... |

126 |
Structural image restoration through deformable templates
- Amit, Grenander, et al.
- 1991
(Show Context)
Citation Context ...dimensionality of 3D data is higher, which makes registration, finding feature correspondences, and fitting model parameters more expensive. As a result, methods that match shapes using deformations [=-=Amit et al. 1991-=-; Jain et al. 1996; Pentland and Sclaroff 1991; Sclaroff and Pentland 1995; Terzopoulos and Metaxas 1991] are far more difficult in 3D. Shape matching has also been well-studied for 3D objects. For in... |

126 | Touring protein fold space with Dali/FSSP
- Holm, Sander
- 1998
(Show Context)
Citation Context ... improved modeling tools and scanning devices are making acquisition of 3D models easier and less expensive, creating a large supply of publically available 3D data sets (e.g., the Protein Data Bank [=-=Holm and Sander 1998-=-]). Second, the World Wide Web is enabling access to 3D models constructed by people all over the world, providing a mechanism for wide-spread distribution of high quality 3D models (e.g., avalon.view... |

125 | Discrete geometric shapes: matching, interpolation, and approximation: a survey
- Alt, Guibas
- 1996
(Show Context)
Citation Context ...WORK The problem of determining the similarity of two shapes has been well-studied in several fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [=-=Alt and Guibas 1996-=-; Arman and Aggarwal 1993; Besl and Jain 1985; Loncaric 1998; Pope 1994; Veltkamp and Hagedoorn 1999]. To briefly review, prior matching methods can be classified according to ACM Transactions on Grap... |

123 |
The Radon Transform
- Helgason
- 1980
(Show Context)
Citation Context ...e number of non-congruent homometric discrete point sets in arbitrary dimensions. Properties have also been proven for the Radon transform for a convex region C in the plane [Rann and Katsevich 1996; =-=Helgason 1999-=-]. This transform maps any oriented line to the length of its intersection with C. It completely specifies the region C, and it can be inverted fairly efficiently. The Radon transform has found many u... |

107 | A survey of moment-based techniques for unoccluded object representation and recognition
- Prokop, Reeves
- 1992
(Show Context)
Citation Context ...o evaluate distances between feature vectors [Duda et al. 2001] in a multidimensional space where the axes encode global geometric properties, such as circularity, eccentricity, or algebraic moments [=-=Prokop and Reeves 1992-=-; Taubin and Cooper 1992]. Other methods have compared discrete histograms of geometric statistics. For example, Thacker et al [Aherne et al. 1997; A.P.Ashbrook et al. 1995; Ashbrook et al. 1995; Ashb... |

105 | Determining the similarity of deformable shapes
- Basri, Costa, et al.
- 1998
(Show Context)
Citation Context ...their spatial relationships. Example representations of this type include generalized cylinders [Binford 1971], superquadrics [Solina and Bajcsy 1990], geons [Wu and Levine 1994], deformable regions [=-=Basri et al. 1998-=-], shock graphs [Siddiqi et al. 1998], medial axes [Bardinet et al. 2000], and skeletons [Bloomenthal and Lim 1999; Storti et al. 1997]. These methods work best when 3D models can be segmented into a ... |

77 | State-of-the-art in shape matching
- Hagedoorn, Veltkamp
- 2001
(Show Context)
Citation Context ...l fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [Alt and Guibas 1996; Arman and Aggarwal 1993; Besl and Jain 1985; Loncaric 1998; Pope 1994; =-=Veltkamp and Hagedoorn 1999]-=-. To briefly review, prior matching methods can be classified according to ACM Transactions on Graphics, Vol. V, No. N, 10 202002.s4 · Robert Osada et al. their representations of shape: 2D contours,... |

75 |
Shape representation and image segmentation using deformable surfaces
- Delingette, Hebert, et al.
- 1992
(Show Context)
Citation Context ...pe matching has also been well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian Images [Horn 1984], Spherical Attribute Images [=-=Delingette et al. 1992-=-; 1993], Harmonic Shape Images [Zhang and Hebert 1999], and Spin Images [Johnson and Hebert 1999]. Unfortunately, these previous methods usually assume that a topologically valid surface mesh or an ex... |

74 | Application of affineinvariant fourier descriptors to recognition of 3-d objects
- Arbter, Snyder, et al.
- 1990
(Show Context)
Citation Context ...urs of 2D shapes have a natural arc length parameterization, 3D surfaces of arbitrary genus do not. As a result, common representations of 2D contours for shape matching, such as Fourier descriptors [=-=Arbter et al. 1990-=-], turning functions [Arkin et al. 1991], bending energy functions [Young et al. 1974], arch height functions [Lin et al. 1992], size functions [Uras and Verri 1994; 1997], and order structures [Carls... |

72 |
Model-based object recognition in dense-range images { a review
- Arman, Aggarwal
- 1993
(Show Context)
Citation Context ...etermining the similarity of two shapes has been well-studied in several fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [Alt and Guibas 1996; =-=Arman and Aggarwal 1993-=-; Besl and Jain 1985; Loncaric 1998; Pope 1994; Veltkamp and Hagedoorn 1999]. To briefly review, prior matching methods can be classified according to ACM Transactions on Graphics, Vol. V, No. N, 10 2... |

70 | Shape contexts enable efficient retrieval of similar shapes
- Mori, Belongie, et al.
(Show Context)
Citation Context ... et al. [Ikeuchi et al. 1996] have all represented shapes in 2D images by histograms of angles and distances between pairs of 2D line segments. Belongie et al. [Belongie et al. 2001] and Mori et al. [=-=Mori et al. 2001-=-] have represented 2D shapes by the distributions of points on their boundaries with respect to multiple reference frames. For 3D shapes, Ankerst et al. [Ankerst et al. 1999] has used shape histograms... |

66 |
Harmonic maps and their applications in surface matching
- Zhang, Hebert
- 1999
(Show Context)
Citation Context ...n well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian Images [35], Spherical Attribute Images [24, 25], Harmonic Shape Images =-=[74]-=-, and Spin Images [41]. Unfortunately, these previous methods usually assume that a topologically valid surface mesh or an explicit volume is available for every object. In addition, volumetric dissim... |

64 |
The Radon Transform and Local Tomography
- Ramm, Katsevich
- 1996
(Show Context)
Citation Context ...er and lower bounds on the number of non-congruent homometric discrete point sets in arbitrary dimensions. Properties have also been proven for the Radon transform for a convex region C in the plane [=-=Rann and Katsevich 1996-=-; Helgason 1999]. This transform maps any oriented line to the length of its intersection with C. It completely specifies the region C, and it can be inverted fairly efficiently. The Radon transform h... |

63 |
Using spin-images for efficient multiple model recognition in cluttered3-d scenes
- Johnson, Hebert
- 1999
(Show Context)
Citation Context ...ering and matching 3D surfaces include Extended Gaussian Images [Horn 1984], Spherical Attribute Images [Delingette et al. 1992; 1993], Harmonic Shape Images [Zhang and Hebert 1999], and Spin Images [=-=Johnson and Hebert 1999-=-]. Unfortunately, these previous methods usually assume that a topologically valid surface mesh or an explicit volume is available for every object. In addition, volumetric dissimilarity measures base... |

56 | Model-based object recognition. a survey of recent research
- Pope
- 1994
(Show Context)
Citation Context ...d in several fields. For a broad introduction to shape matching methods, please refer to any of several survey papers [Alt and Guibas 1996; Arman and Aggarwal 1993; Besl and Jain 1985; Loncaric 1998; =-=Pope 1994;-=- Veltkamp and Hagedoorn 1999]. To briefly review, prior matching methods can be classified according to ACM Transactions on Graphics, Vol. V, No. N, 10 202002.s4 · Robert Osada et al. their represent... |

51 | A.: Consistent solid and boundary representations from arbitrary polygonal data
- MURALI, FUNKHOUSER
- 1997
(Show Context)
Citation Context ...pot with no bottom?). Meanwhile, fixing the degeneracies in such 3D models to form a consistent solid region and manifold surface is a difficult problem [Barequet and Kumar 1997; Gueziec et al. 1998; =-=Murali and Funkhouser 1997-=-], often requiring human intervention to resolve ambiguities. In this paper, we describe and analyze a method for computing 3D shape signatures and dissimilarity measures for arbitrary objects describ... |

46 | Recovering Parametric Geons from Multiview Range Data
- Wu, Levine
- 1994
(Show Context)
Citation Context ...ifferences between their features and/or their spatial relationships. Example representations of this type include generalized cylinders [Binford 1971], superquadrics [Solina and Bajcsy 1990], geons [=-=Wu and Levine 1994-=-], deformable regions [Basri et al. 1998], shock graphs [Siddiqi et al. 1998], medial axes [Bardinet et al. 2000], and skeletons [Bloomenthal and Lim 1999; Storti et al. 1997]. These methods work best... |

43 | Nearest neighbor classification in 3d protein databases. ISMB
- Ankerst, Kastenmuller, et al.
- 1999
(Show Context)
Citation Context ...et al. 2001] and Mori et al. [Mori et al. 2001] have represented 2D shapes by the distributions of points on their boundaries with respect to multiple reference frames. For 3D shapes, Ankerst et al. [=-=Ankerst et al. 1999] ha-=-s used shape histograms decomposing shells and sectors around a model’s centroid. Besl [Besl 1995] has considered histograms of the crease angle for all edges in a 3D triangular mesh. Besl’s metho... |

42 |
Cursive script recognition by elastic matching
- Tappert
- 1982
(Show Context)
Citation Context ...ize functions [Uras and Verri 1994; 1997], and order structures [Carlsson 1999] have no direct analogs for 3D models. Similarly, computationally efficient methods based on dynamic programming (e.g., [=-=Tappert 1982-=-] and [Tsai and Yu 1985]) cannot be applied to 3D objects. Another problem is that the dimensionality of 3D data is higher, which makes registration, finding feature correspondences, and fitting model... |

40 | Extracting Multi-Dimensional Signal Features for ContentBased Visual Query
- Chang, Smith
- 1995
(Show Context)
Citation Context ...hape: 2D contours, 3D surfaces, 3D volumes, structural models, or statistics. The vast majority of work in shape matching has focused on characterizing similarity between objects in 2D images (e.g., [=-=Chang and Smith 1995-=-; Flickner et al. 1995; Jacobs et al. 1995; Ogle and Stonebraker 1995]). Unfortunately, most 2D methods do not extend directly to 3D model matching. The main problem is boundary parameterization. Alth... |

40 |
A distance metric for multidimensional histograms
- Werman, Peleg, et al.
- 1985
(Show Context)
Citation Context ... distributions [Puzicha et al. 1999]. Examples include the Minkowski LN norms, Kolmogorov-Smirnov distance, Kullback-Leibler divergence distances [Kullback 1968], Match distances [Shen and Wong 1983; =-=Werman et al. 1985],-=- Earth Mover’s distance [Rubner et al. 1998], and Bhattacharyya distance [Bhattacharyya 1943]. Other methods, perhaps based on 2D curve matching [Alt and Guibas 1996; Veltkamp and Hagedoorn 1999], c... |

38 |
Converting sets of polygons to manifold surfaces by cutting and stitching
- Guéziec, Taubin, et al.
(Show Context)
Citation Context ... ill-defined (e.g., what is the volume of a teapot with no bottom?). Meanwhile, fixing the degeneracies in such 3D models to form a consistent solid region and manifold surface is a difficult problem =-=[12, 32, 48]-=-, often requiring human intervention to resolve ambiguities. In this paper, we describe and analyze a method for computing 3D shape signatures and dissimilarity measures for arbitrary objects describe... |

38 |
A sketching interface for 3D freeform design
- Teddy
- 1999
(Show Context)
Citation Context ... plots comparing retrieval results achieved with shape distributions versus moments of different orders. In the early prototype system [22], the user draws a 3D query model using a Java applet (Teddy =-=[37]-=-) running in any web browser. The resulting set of polygons is sent to a web server, which computes its D2 shape distribution and a dissimilarity measure for all models in a 3D database using the meth... |

35 | S.: Repairing CAD models
- BAREQUET, KUMAR
- 1997
(Show Context)
Citation Context ... ill-defined (e.g., what is the volume of a teapot with no bottom?). Meanwhile, fixing the degeneracies in such 3D models to form a consistent solid region and manifold surface is a difficult problem =-=[12, 32, 48]-=-, often requiring human intervention to resolve ambiguities. In this paper, we describe and analyze a method for computing 3D shape signatures and dissimilarity measures for arbitrary objects describe... |

31 |
A spherical representation for the recognition of curved objects
- Delingette, Hebert, et al.
- 1993
(Show Context)
Citation Context ... 3D. Shape matching has also been well-studied for 3D objects. For instance, representations for registering and matching 3D surfaces include Extended Gaussian Images [35], Spherical Attribute Images =-=[24, 25]-=-, Harmonic Shape Images [74], and Spin Images [41]. Unfortunately, these previous methods usually assume that a topologically valid surface mesh or an explicit volume is available for every object. In... |

30 |
Skeletonbased modeling operations on solids
- Storti, Turkiyyah, et al.
- 1997
(Show Context)
Citation Context ...ial relationships. Example representations of this type include generalized cylinders [18], superquadrics [61], geons [72], deformable regions [13], shock graphs [59], medial axes [11], and skeletons =-=[19, 62]-=-. These methods work best when 3D models can be segmented into a canonical set of features naturally and correspondences can be found between features robustly. Unfortunately, these tasks are difficul... |

29 | and J.E.W.Mayhew, The Use of Geometric Histograms for Model-Based Object Recognition
- Evans
- 1993
(Show Context)
Citation Context ...code global geometric properties, such as circularity, eccentricity, or algebraic moments [52, 64]. Other methods have compared discrete histograms of geometric statistics. For example, Thacker et al =-=[1, 5, 9, 10, 28, 29, 55, 66]-=-, Huet et al. [36], and Ikeuchi et al. [38] have all represented shapes in 2D images by histograms of angles and distances between pairs of 2D line segments. Belongie et al. [14] and Mori et al. [47] ... |

28 |
Reconstructing sets from interpoint distances
- Skiena, Smith, et al.
- 1990
(Show Context)
Citation Context ...are investigating provable properties for the D2 shape function. Uniqueness properties for homometric discrete point sets (ones with the same distance distribution) have been proven by Skiena et al. [=-=Skiena et al. 1990-=-]. They developed upper and lower bounds on the number of non-congruent homometric discrete point sets in arbitrary dimensions. Properties have also been proven for the Radon transform for a convex re... |