## A survey of shape similarity assessment algorithms for product design and manufacturing applications (2003)

Venue: | Journal of Computing and Information Science in Engineering |

Citations: | 48 - 12 self |

### BibTeX

@ARTICLE{Cardone03asurvey,

author = {Antonio Cardone and Ra K. Gupta and Mukul Karnik},

title = {A survey of shape similarity assessment algorithms for product design and manufacturing applications},

journal = {Journal of Computing and Information Science in Engineering},

year = {2003},

volume = {3},

pages = {109--118}

}

### OpenURL

### Abstract

This document contains the draft version of the following paper: A. Cardone, S.K. Gupta, and M. Karnik. A survey of shape similarity assessment algorithms for product design and manufacturing applications. ASME Journal of

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Citation Context ...simple objects may have the same Model Signature Graph. Once a Model Signature Graph is constructed, the solid models are compared using spectral graph theory. The eigenvalues of the Laplacian matrix =-=[45]-=- are used in the comparison. The eigenvalues of the Laplacian are strongly related to other graph properties such as the graph diameter. The graph diameter is the largest number of vertices, which mus... |

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Citation Context ...pect to small deformations on the surface. It is necessary to choose both a robust and efficiently computable function, which is not a trivial task. Finally, from the experimental results reported in =-=[50]-=- it can be observed that this method is not invariant to Euclidean transformations (e.g., rotation, translation, scaling). Thus a given model when compared with its scaled, translated or rotated versi... |

224 | Shock graphs and shape matching
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Citation Context ...g is one such domain. This paper primarily focuses on algorithms that are suitable for product design and manufacturing applications 2 . Specialized algorithms for medical [7,12], and computer vision =-=[13,14,15,16,17,18,19]-=- applications have also been developed. However, these algorithms will not be covered in this paper. This paper is organized in the following manner. Section 2 describes the basic terminology needed t... |

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Citation Context ...cludes shape signatures based on Fourier descriptor [5], turning functions [6], bending functions [7], and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in =-=[9,10,11]-=-. 2D geometry and 3D geometry have several fundamental differences and unfortunately methods for computing and matching signatures of 2D shapes cannot be easily extended to 3D shapes, in most cases. T... |

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Citation Context ...es: (1) similarity assessment of 2D shapes, and (2) similarity assessment of 3D shapes. Representative work in 2D category includes shape signatures based on Fourier descriptor [5], turning functions =-=[6]-=-, bending functions [7], and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in [9,10,11]. 2D geometry and 3D geometry have several fundamental differences an... |

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Citation Context ..., but it could be applied to this domain. However, this technique is restricted to convex polyhedra. Hence, it is limited in scope. 6 Shape Histogram Based Shape Signatures The technique described in =-=[33]-=- computes shape distributions of solid models using shape functions and then compares these shape distributions to assess similarity. Once a set of random points is obtained on the surface of the soli... |

129 | Discrete Geometric Shapes; Matching, Interpolation and Approximation. A survey. Manuscript
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Citation Context ...cludes shape signatures based on Fourier descriptor [5], turning functions [6], bending functions [7], and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in =-=[9,10,11]-=-. 2D geometry and 3D geometry have several fundamental differences and unfortunately methods for computing and matching signatures of 2D shapes cannot be easily extended to 3D shapes, in most cases. T... |

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Neurocomputing: Foundations of Research
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Citation Context ...t and activation function fs. The algorithm for determining the output is described in [39]. The maximum number of neurons that can be used in any given layer is defined using Kolmogorov’s 11stheorem =-=[40]-=-. The vector element of Oi with the highest value represents the group to which the part belongs. The output in this case is an Opitz code used to classify rotational parts based on characteristics su... |

97 |
Theory of Backpropagation Neural Networks
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Citation Context ...g image. A back-propagation neural network system has been proposed to classify the 3D parts into a number of predetermined part families. The theory of backpropagation neural network is explained in =-=[42]-=-. Also some concepts related to the neural network such as learning rate, number of neurons in the hidden layer and number of hidden layers are discussed in [41]. The modified technique described in [... |

81 | Application of affine-invariant Fourier descriptors to recognition of 3-D objects
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Citation Context ... two different categories: (1) similarity assessment of 2D shapes, and (2) similarity assessment of 3D shapes. Representative work in 2D category includes shape signatures based on Fourier descriptor =-=[5]-=-, turning functions [6], bending functions [7], and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in [9,10,11]. 2D geometry and 3D geometry have several fun... |

77 | Shape contexts enable efficient retrieval of similar shapes
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Citation Context ...g is one such domain. This paper primarily focuses on algorithms that are suitable for product design and manufacturing applications 2 . Specialized algorithms for medical [7,12], and computer vision =-=[13,14,15,16,17,18,19]-=- applications have also been developed. However, these algorithms will not be covered in this paper. This paper is organized in the following manner. Section 2 describes the basic terminology needed t... |

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Citation Context ...g is one such domain. This paper primarily focuses on algorithms that are suitable for product design and manufacturing applications 2 . Specialized algorithms for medical [7,12], and computer vision =-=[13,14,15,16,17,18,19]-=- applications have also been developed. However, these algorithms will not be covered in this paper. This paper is organized in the following manner. Section 2 describes the basic terminology needed t... |

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Citation Context ...neuron is the dot product of these two vectors. The output of the neuron is a vector Oi corresponding to the input and activation function fs. The algorithm for determining the output is described in =-=[39]-=-. The maximum number of neurons that can be used in any given layer is defined using Kolmogorov’s 11stheorem [40]. The vector element of Oi with the highest value represents the group to which the par... |

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Citation Context ...e Signatures 8.1 Model Signature Graphs In [43] Model Signature Graphs have been proposed for topological comparison of solid models. They are an extension of Attribute Adjacency Graphs, mentioned in =-=[44]-=-, and are introduced in order to consider curved surfaces. Model Signature Graphs are constructed from boundary representation of the solid. Each node in the model signature graph represents a face of... |

53 | A Spherical Representation for Recognition of free-form surfaces
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Citation Context ...tures 5.1 Local Curvature Distributions Over Mesh Representations In this technique, a spherical representation that stores the curvature distribution of 3D surfaces of an object is used as signature =-=[25]-=-. The solids to be compared must have a genus of zero. To generate the representation, a tessellated sphere is deformed such that it closely approximates the shape of the object. Each node of the tess... |

48 |
Level set diagrams of polyhedral objects
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Citation Context ...ure of the 3D model is defined by Multiresolutional Reeb Graphs [47], which are used to compare the 3D objects. Reeb graphs have already been used in technical applications such as modeling 3D shapes =-=[48,49]-=-. First, the Reeb Graph is defined on the input object, which is a triangulated solid. It is obtained by defining a suitable function over the 3D object considered. An example of a suitable function i... |

45 | On 3D shape similarity
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Citation Context ...sed to define the local curvature function k. As the distance is computed using Lp norm, it obeys the positivity property. It also satisfies the identity, symmetry, and triangle inequality properties =-=[27]-=-. The distance between the two shapes can be computed in time O(n 2 ) where n is the number of nodes on the sphere. However, this technique is restricted to solids having zero genus (i.e. solids witho... |

44 |
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Citation Context ...s5.2 Slope Diagram Representations The technique described in [29] uses the slope diagram representation [30] of a convex polyhedra [31] and uses mixed volumes and volumes based on Minkowski addition =-=[32]-=- to define the similarity measure. The definition and mathematical representation of mixed volume can be found in [29]. A slope diagram representation (SDR) is one where a face is represented on the u... |

41 | Feature-Based Similarity Assessment Of Solid Models
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Citation Context ...roblem to all existing feature-based similarity assessment methods. This technique considers only feature interaction and does not account for feature size and orientation. The technique described in =-=[22]-=- is based on a graph representation of the input 3D models. This graph representation is used as the shape signature for the model. Let us consider two objects, m and m′. Then, c(m) and c(m′) will be ... |

41 |
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Citation Context ...ions are generated the distance between the two solid models is computed using LN norm. Usually L2 norm is used for comparison. Other distances such as Earth Mover’s distance [15], or Match distances =-=[34,35]-=- can also be used. This technique is robust and efficient. Also there is no restriction on the type of solid models that can be compared. However, as this method involves generating random points on t... |

40 |
Foundations of Neural Networks
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Citation Context ...e part drawings. The neural network consists of number of layers of neurons, which include an input layer, some hidden layers and an output layer. The theory of neural network systems is described in =-=[38]-=-. The input to the neural network system is a vector I containing bit data that represents the image of a part drawing. For every input i, there is a neuron with a weight vector W i attached to it. Th... |

39 | Regli: Using shape distributions to compare solid models
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Citation Context ...m it can be seen that heat_exchanger1 is more similar to a grip than heat_exchanger2. Thus this technique has limited discrimination capability. An extension of the previous technique is described in =-=[36]-=-. The procedure for generating random points on the surface as well as the shape function used is the same. However, instead of computing a single shape distribution for each solid model, this method ... |

35 | Similarity matching
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Citation Context ...T code, that is assigned to that part. However, as the classification is done manually, it is subject to individual interpretation. It has been shown that human perception of similarity is subjective =-=[4]-=-. Thus there are possibilities of errors in such classifications. Direct assessment of similarity between 3D models via Boolean operations is computationally very slow due to difficulty in aligning th... |

34 | Machining Feature-based Comparisons of Mechanical Parts
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Citation Context .... Objects where the cylindrical features intersect other faces non-orthogonally are also ruled out. This technique also does not account for local feature interactions. Another technique described in =-=[21]-=-, involves feature extraction and comparison to determine similarity between mechanical parts. It defines a Model Dependency Graph for each of the two objects being compared and determines the largest... |

31 |
Efficient Geometry-based Similarity Search of 3D Spatial Databases
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Citation Context ...duct design and manufacturing is one such domain. This paper primarily focuses on algorithms that are suitable for product design and manufacturing applications 2 . Specialized algorithms for medical =-=[7,12]-=-, and computer vision [13,14,15,16,17,18,19] applications have also been developed. However, these algorithms will not be covered in this paper. This paper is organized in the following manner. Sectio... |

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R.B.Yates. Assessing the completeness properties of pairwise geometric histograms
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On Computing The Minimum Hausdorff Distance For Point Sets Under Translation
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Citation Context ...e of the two objects is rotated such that it aligns with the other. The distance between the two objects computed using Lp norm. Alternatively Hausdorff distance may be used to compute the difference =-=[26]-=-. The shape similarity assessment in this case is invariant under translation, rotation and scaling as the curvature depends only on the relative locations of the four nodes that are used to define th... |

29 |
Attributed string matching with merging for shape recognition
- Tsai, Yu
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Citation Context ...exists a one-to-one mapping, the objects are rotated so that the unit vectors v2 match. Additional pair of faces, which do not have normal along v2 are matched by attributed string matching algorithm =-=[52]-=-, to completely align the two models. After rotating the layer faces to the correct orientation, initial matched sub-graphs of the layer faces are obtained. The nodes in the graph represent faces whil... |

27 |
An analysis technique for biological shape
- Young, Calvert
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Citation Context ...ssment of 2D shapes, and (2) similarity assessment of 3D shapes. Representative work in 2D category includes shape signatures based on Fourier descriptor [5], turning functions [6], bending functions =-=[7]-=-, and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in [9,10,11]. 2D geometry and 3D geometry have several fundamental differences and unfortunately methods... |

22 |
A Feature-Based Approach for Smooth Surfaces
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Citation Context ...ure of the 3D model is defined by Multiresolutional Reeb Graphs [47], which are used to compare the 3D objects. Reeb graphs have already been used in technical applications such as modeling 3D shapes =-=[48,49]-=-. First, the Reeb Graph is defined on the input object, which is a triangulated solid. It is obtained by defining a suitable function over the 3D object considered. An example of a suitable function i... |

22 |
Shape Similarity Assessment Of Mechanical Parts Based On Solid Models
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Citation Context ...e Reeb graph is a flexible tool that can be used to assess similarity in several applications of product design and manufacturing, by choosing an appropriate function. 8.3 Graphs of Aligned Models In =-=[51]-=- a similarity assessment technique has been described based on the information provided by Brep model and CSG tree termed as T0 tree. T0 tree is a specialized linear tree whose primitives are all swee... |

19 |
The introduction of group technology
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Citation Context ...imilarities in design and manufacturing. Group Technology (GT) involves classifying similar products into groups in order to achieve economies of scale normally associated with high-volume production =-=[3]-=-. In order to implement GT, one must have a concise coding scheme for describing products and a method for grouping (or classifying) similar products, such as the popular Opitz, DCLASS, and MICLASS sc... |

19 |
Generalized Texture Representation And Metric
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Citation Context ...ions are generated the distance between the two solid models is computed using LN norm. Usually L2 norm is used for comparison. Other distances such as Earth Mover’s distance [15], or Match distances =-=[34,35]-=- can also be used. This technique is robust and efficient. Also there is no restriction on the type of solid models that can be compared. However, as this method involves generating random points on t... |

17 |
Feature-Based Shape Similarity Measurement For Retrieval Of Mechanical Parts
- Ramesh, Yip-Hoi, et al.
- 2001
(Show Context)
Citation Context ...comparison but are useful as quick and efficient filters. Section 9 describes representative techniques in this category. 4 Feature-Based Shape Signatures The first step in the technique described in =-=[20]-=- consists of extracting the features from a B-rep model. This is achieved by constructing cells that are portions of space resembling machining features. Once these cells are obtained following a seri... |

16 |
Transformation Invariant Shape Similarity Comparison Of Solid Models
- McWherter, Peabody, et al.
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Citation Context ...est number of vertices, which must be traversed, in order to travel from one vertex to another in the graph. Another technique proposed for comparing the graphs is the use of graph invariance vectors =-=[46]-=-. Graph invariance vectors are vectors whose elements are graph invariants. The vectors are then compared using L2 norm to determine similarity between the graphs and hence the solid models. The graph... |

14 | Database Techniques For Archival Of Solid Models
- McWherter, Peabody, et al.
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Citation Context ...gn and manufacturing applications. They are specifically used to classify the parts in a database to reuse design information. 8 Topological Graph Based Shape Signatures 8.1 Model Signature Graphs In =-=[43]-=- Model Signature Graphs have been proposed for topological comparison of solid models. They are an extension of Attribute Adjacency Graphs, mentioned in [44], and are introduced in order to consider c... |

13 |
Retrieval Of Similarly Shaped Parts From A CAD Database
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Citation Context ...s. It is usually an expensive task, but in this case it is made easier from the labeling of nodes and edges. In fact the labeling allows easier matching of sub graphs. 8sIn the technique described in =-=[24]-=-, different attributes of features such as feature type, machining type etc. are stored in Attribute Type table. A qualitative matrix is used to record all the feature interactions. By searching throu... |

12 |
Contour Shape Description Based On Arch Height Function
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Citation Context ...milarity assessment of 3D shapes. Representative work in 2D category includes shape signatures based on Fourier descriptor [5], turning functions [6], bending functions [7], and arch height functions =-=[8]-=-. A comprehensive discussion of 2D shape signatures can be found in [9,10,11]. 2D geometry and 3D geometry have several fundamental differences and unfortunately methods for computing and matching sig... |

11 |
Grouping Parts With A Neural Network
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Citation Context ...ethod will require manual intervention to identify the part drawing with desired orientation. The technique described above involves classification of rotational parts using neural network system. In =-=[41]-=- this classification has been extended to include 3D parts based on their binarized part drawing image. A back-propagation neural network system has been proposed to classify the 3D parts into a numbe... |

10 | Similarity Measures For Convex Polyhedra Based On Minkowski Addition
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Citation Context ... be used in applications where curvature plays a major role. Nevertheless the restriction to solids without holes is a major limitation. 9s5.2 Slope Diagram Representations The technique described in =-=[29]-=- uses the slope diagram representation [30] of a convex polyhedra [31] and uses mixed volumes and volumes based on Minkowski addition [32] to define the similarity measure. The definition and mathemat... |

8 |
Mathematical morphological operations of boundary-represented geometric objects
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Citation Context ...ays a major role. Nevertheless the restriction to solids without holes is a major limitation. 9s5.2 Slope Diagram Representations The technique described in [29] uses the slope diagram representation =-=[30]-=- of a convex polyhedra [31] and uses mixed volumes and volumes based on Minkowski addition [32] to define the similarity measure. The definition and mathematical representation of mixed volume can be ... |

8 |
Assessing The Effectiveness Of Filters For Shape Matching
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Citation Context ...e solid models and are stored as searchable entries in a database. To analyze the performance of the search engine, similarity matrices based on human perception of similarity have been generated. In =-=[54]-=-, four new filters for shape matching have been proposed. These are based on the coefficient of surface area and convex hull of the solid model. The convex hull based filters include hull crumpliness,... |

7 | Sheet Metal Bending: Generating Shared Setups
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Citation Context ...new part. • Part Family Formation. In many manufacturing domains such as sheet metal bending, machine tools can be setup to produce more than one type of part without requiring a setup or tool change =-=[1,2]-=-. However, parts need to be shape compatible in order for them to share common tools and setups. Therefore, in order to find common tools and setups, geometrically similar and therefore compatible par... |

7 | Part sourcing in a global market
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(Show Context)
Citation Context ...s must be polyhedral. This technique has been applied to product design and manufacturing on models that comply with the restrictions mentioned above. 14s9 Shape Statistics The technique described in =-=[53]-=-, uses global shape metrics such as surface area/volume ratio, number of holes, compactness, and crinkliness to perform similarity assessment. These metrics are orientation independent and are extract... |

5 | Automated design of sheet metal punches for bending multiple parts in a single setup. Robotics Comput Integrated Manufact 2001;17(1/2):33–47
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Citation Context ...new part. • Part Family Formation. In many manufacturing domains such as sheet metal bending, machine tools can be setup to produce more than one type of part without requiring a setup or tool change =-=[1,2]-=-. However, parts need to be shape compatible in order for them to share common tools and setups. Therefore, in order to find common tools and setups, geometrically similar and therefore compatible par... |

5 |
A Neural Network System For Shape Based Classification And Coding
- Kaparthi, Suresh
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Citation Context ...in design and manufacturing applications. 7 Section Images Based Shape Signatures Manual classification and coding of parts for group technology applications is time-consuming and prone to errors. In =-=[37]-=- a neural network system has been proposed for classifying parts based on bitmaps of the part drawings. The neural network consists of number of layers of neurons, which include an input layer, some h... |

5 |
On The Singular Points Of A Completely Integrable Pfaff Form Or Of A Numerical Function. Comptes Rendus De l’Academie De Sciences
- Reeb
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Citation Context ...ble to product design and manufacturing domain. 8.2 Multiresolutional Reeb Graphs In this technique, the skeletal and topological structure of the 3D model is defined by Multiresolutional Reeb Graphs =-=[47]-=-, which are used to compare the 3D objects. Reeb graphs have already been used in technical applications such as modeling 3D shapes [48,49]. First, the Reeb Graph is defined on the input object, which... |

4 |
Shape matching: Similarity measures and algorithms
- Veltkmap
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(Show Context)
Citation Context ...cludes shape signatures based on Fourier descriptor [5], turning functions [6], bending functions [7], and arch height functions [8]. A comprehensive discussion of 2D shape signatures can be found in =-=[9,10,11]-=-. 2D geometry and 3D geometry have several fundamental differences and unfortunately methods for computing and matching signatures of 2D shapes cannot be easily extended to 3D shapes, in most cases. T... |