Model-Based Object Recognition Using Geometric Invariants of Points and Lines

Song, Bong Seop; Lee, Kyoung Mu; Lee, Sang Uk

doi:10.1006/cviu.2001.0954

Cited by 15 publications

(4 citation statements)

References 16 publications

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“…Now the presented 3D structure with perspective invariance mainly involves five kinds of constrained structures. They are six points on two adjacent planes, six points on two arbitrary planes, six lines on three planes, five lines on two adjacent planes and six lines on four planes [6][7][8][9].…”

Section: B 3d Structure With Perspective Invariancementioning

confidence: 99%

Aspect and Perspective Invariance Based Three-Dimension Object Representation

Chen¹,

Chen²,

Duan³

et al. 2011

2011 3rd International Workshop on Intelligent Systems and Applications

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In this paper a representation method based on aspect of 3D object and geometrical invariant is presented. The method makes use of constrained 3D structures with the property of perspective invariance to represent aspects of 3D object. By using this representation, the machine vision system could avoid the computing of object pose, camera calibration and feature correspondence in the indexing phase of recognizing 3D object from a single view, therefore, realizing the strategy of indexing before matching and resulting in high real-time recognition efficiency. Firstly, the basic concepts of perspective invariance and constrained structure are discussed. And then, a general way to use such constrained structures to represent 3D object is given and also an application of it. At last, the weakness of this representation method is pointed out as well as further research work.

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Section: B 3d Structure With Perspective Invariancementioning

confidence: 99%

Aspect and Perspective Invariance Based Three-Dimension Object Representation

Chen¹,

Chen²,

Duan³

et al. 2011

2011 3rd International Workshop on Intelligent Systems and Applications

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“…Roh et al got a kind of invariant relation between the 3D object points and the 2D plane points by using this structure, and constructed the model base index by using this invariant relation. However, the invariant relation need to deal with more combination relation than the invariant when retrieving models, so the efficiency of the structure is not very high, but this structure is more universal than the structure proposed by Rothwell et al and Zhu et al In addition to the point structures mentioned above, Sugimoto and Song et al also proposed the perspective invariants possessed by some line structures in space respectively [28], [29]. Sugimoto derived a perspective invariant from six lines in three planes by using the method of calculating the ratio of determinants (its structure is shown in Figure 3).…”

Section: Introductionmentioning

confidence: 99%

Invariants of Space Line Element Structure Based on Projective Geometric Algebra

Zhang

Mui²

2020

IEEE Access

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Based on the theory of Conformal Geometric Algebra, this paper presents a geometric constraint structure consisting of seven straight lines on three adjacent planes and its projective invariants, which can be obtained from a single frame image. Comparing with the use of multi-frame images to calculate invariants, our method is more convenient. First, this paper uses the projective property of points as an index to introduce the projective transformation properties of geometric structure of three lines on two adjacent planes. Then using it as an index, the invariant of the geometric structure of seven lines on three adjacent planes is proposed, and the invariant of the geometric structure of five lines on three adjacent planes is obtained by using the algorithm in this paper. Finally, the accuracy and stability of the invariant geometry are verified by experiments. INDEX TERMS Geometric invariant, space line element structure, projective geometric algebra.

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“…3,4 Although it has been shown that there is no general invariant from 3-D space to a 2-D plane in a single image, 5 invariants from some special geometric configurations are available. 6,7 Some simplifications and assumptions are employed for deriving invariants; 8 however, the generality of these simplifications and assumptions are limited. For real 3-D objects, most proposed methods establish correspondences of points among images and then compute the fundamental matrix and reconstruct the objects, 9,10 in which case, the geometric invariants are actually derived from the reconstructed 3-D geometric structures, 11 and the accuracy of these invariants mainly depends on precise estimation of the fundamental matrix.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional projective invariants of points from multiple images

Xiao

Zhu³

2008

Opt. Eng

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Invariance is widely used in 3-D object recognition due to its good performance on change of viewpoint. A method of computing 3-D invariants of seven points from two images is presented, which can be used to achieve reliable recognition of a 3-D object and scene. Based on the matrix representation of the projective transformation between 3-D and 2-D points, geometric invariants are derived by the determinant ratios. First, the general ratiocination about invariants is represented. Second, the general method of deriving 3-D invariants from images is proposed. Simulation results on real images show that the derived invariants remain stable and are quite robust and accurate.

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Model-Based Object Recognition Using Geometric Invariants of Points and Lines

Cited by 15 publications

References 16 publications

Aspect and Perspective Invariance Based Three-Dimension Object Representation

Aspect and Perspective Invariance Based Three-Dimension Object Representation

Invariants of Space Line Element Structure Based on Projective Geometric Algebra

Three-dimensional projective invariants of points from multiple images

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