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Approximate symmetry detection for reverse engineering
 Proc. 6th ACM Symp. Solid Modeling and Applications
, 2001
"... The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitab ..."
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Cited by 18 (12 self)
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The authors are developing an automated reverse engineering system for reconstructing the shape of simple mechanical parts. Brep models are created by fitting surfaces to point clouds obtained by scanning an object using a 3D laser scanner. The resulting models, although valid, are often not suitable for purposes such as redesign because expected regularities and constraints are not present. This information is lost because each face of the model is determined independently. A global approach is required, in particular one that is capable of finding symmetries originally present. This paper describes a practical algorithm for finding global symmetries in suitable Brep models built from planes, spheres, cylinders, cones and tori. It has been implemented and used to determine approximate symmetries of models with up to about 200 vertices in reasonable time. The time performance of the algorithm in the worst case is bounded by O(n^3.5 log^4 n), and a justification is given that on common engineering objects it takes about O(n^2 log^4 n), making it a practical tool for use in a reverse engineering package. Details of the algorithm are given, along with some results from a number of illustrative test runs.
Tools for Asymmetry Rectification in Shape Design
 Journal of Systems Engineering
, 1996
"... This paper considers the task of asymmetry rectification. We start by giving various reasons why the possession of symmetry may be beneficial for designed shapes, and mention how various construction methods may produce shapes which are less symmetric than desired. ..."
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Cited by 6 (3 self)
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This paper considers the task of asymmetry rectification. We start by giving various reasons why the possession of symmetry may be beneficial for designed shapes, and mention how various construction methods may produce shapes which are less symmetric than desired.
Curved GlideReflection Symmetry Detection,” Transactions on Pattern Analysis and
 Machine Intelligence (TPAMI
, 2012
"... Abstract—We generalize the concept of bilateral reflection symmetry to curved glidereflection symmetry in 2D euclidean space, such that classic reflection symmetry becomes one of its six special cases. We propose a local featurebased approach for curved glidereflection symmetry detection from real ..."
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Cited by 4 (0 self)
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Abstract—We generalize the concept of bilateral reflection symmetry to curved glidereflection symmetry in 2D euclidean space, such that classic reflection symmetry becomes one of its six special cases. We propose a local featurebased approach for curved glidereflection symmetry detection from real, unsegmented 2D images. Furthermore, we apply curved glidereflection axis detection for curved reflection surface detection in 3D images. Our method discovers, groups, and connects statistically dominant local glidereflection axes in an AxisParameterSpace (APS) without preassumptions on the types of reflection symmetries. Quantitative evaluations and comparisons against stateoftheart algorithms on a diverse 64testimage set and 1,125 Swedish leafdata images show a promising average detection rate of the proposed algorithm at 80 and 40 percent, respectively, and superior performance over existing reflection symmetry detection algorithms. Potential applications in computer vision, particularly biomedical imaging, include saliency detection from unsegmented images and quantification of deviations from normality. We make our 64testimage set publicly available. Index Terms—Symmetry, glide reflection, curved axis, curved surface. Ç 1
On Invariants of Lie Group Actions and their Application to Some Equivalence Problems
"... Abstract This thesis studies the existence of joint invariants, their computation, their relation to differential invariants and their application to object recognition and symmetry detection. Our main tool is the moving frame method as developed by M. Fels and P. J. Olver. We start by studying prol ..."
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Cited by 2 (0 self)
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Abstract This thesis studies the existence of joint invariants, their computation, their relation to differential invariants and their application to object recognition and symmetry detection. Our main tool is the moving frame method as developed by M. Fels and P. J. Olver. We start by studying prolonged Lie group actions on the Cartesian product of n copies of a manifold. We show that the orbit dimensions of such actions do not pseudostabilize when n increases and obtain a bound on the stabilization order. We also obtain a discrete analogue to a famous theorem by Ovsiannikov and Olver. These facts are important relative to the existence and computation of joint invariants. Interesting corollaries are presented. Based on these theoretical results, we show how joint invariants can be used to solve two equivalence problems, namely curve and polygon recognition (and symmetry detection). Our approach to curve recognition and symmetry detection is based on a paper by Calabi et al. and relies on the concept of differential invariant signature. The main idea consists in obtaining numerically invariant approximations of the differential invariants parameterizing the signature. This signature uniquely characterizes the equivalence class of a given curve under the action of a Lie group. We correct the numerically invariant approximations initially proposed by Calabi et al. for the special Euclidean and equiaffine differential invariants of a planar curve and solve the problem of spatial curve recognition modulo the action of the special Euclidean group. Our approach to polygon recognition and symmetry detection is based on moving frames and contains a general method. The cases of the special Euclidean, Euclidean, equiaffine, skewedaffine and similarity Lie groups are discussed in detail. The time complexity of our algorithms is linear in the number of vertices and they are noise resistant. Our method allows the detection of partial as well as approximate equivalences. i
A NEW ALGORITHM FOR RECOGNITION OF A SPHEROID
"... A sphere mesh, hereafter called simply a spheroid, is a rectangular array of processors with the rows wrapped around to form a ring, and the columns extended and meeting at a node at both the top and bottom. The appearance is that of a ball. The top node is the north pole and the bottom node is the ..."
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A sphere mesh, hereafter called simply a spheroid, is a rectangular array of processors with the rows wrapped around to form a ring, and the columns extended and meeting at a node at both the top and bottom. The appearance is that of a ball. The top node is the north pole and the bottom node is the south pole. A new algorithm is presented to recognize a spheroid. A program was written to determine if the new spheroid recognition algorithm is valid. The program was written in C and tested using a representation of a network's nodes and their neighbors. The program tests several spheroids of different dimensions and different spheroidlike structures. The program found the spheroids and rejected the nonspheroids on the test data. The algorithm presented here is fairly simple and straightforward. However, its true importance lies in the fact that it forms the foundation for algorithms for recognition of more complex mesh like structures, such as, torus, and 3dimensional mesh.