3-D object recognition using a new invariant relationship by single-view
We propose a new method for recognizing three-dimensional objects using a three-dimensional invariant relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an invariant...
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| Published in: | Pattern recognition Vol. 33; no. 5; pp. 741 - 754 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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2000
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| ISSN: | 0031-3203, 1873-5142 |
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| Abstract | We propose a new method for recognizing three-dimensional objects using a three-dimensional invariant relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an invariant relationship for the structure, which is represented by a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the plane, thereby satisfying the invariant relationship, are mapped into a set of points intersecting the plane and the unit sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. (Oxford University TR-OUEL 1927/92, 1992) and Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731), it gives enough many voting to generate hypotheses. We also show that from the proposed invariant relationship, an invariant for the structure by two-view and an invariant for a structure proposed by Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731) can also be derived. Experiments using three-dimensional polyhedral objects are carried out to demonstrate the feasibility of our method for three-dimensional objects. |
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| AbstractList | We propose a new method for recognizing three-dimensional objects using a three-dimensional invariant relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an invariant relationship for the structure, which is represented by a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the plane, thereby satisfying the invariant relationship, are mapped into a set of points intersecting the plane and the unit sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. and Zhu et al., it gives enough many voting to generate hypotheses. We also show that from the proposed invariant relationship, an invariant for the structure by two-view and an invariant for a structure proposed by Zhu et al. can also be derived. Experiments using three-dimensional polyhedral objects are carried out to demonstrate the feasibility of our method for three-dimensional objects. We propose a new method for recognizing three-dimensional objects using a three-dimensional invariant relationship and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two non-planar points with respect to the plane. We derive an invariant relationship for the structure, which is represented by a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the plane, thereby satisfying the invariant relationship, are mapped into a set of points intersecting the plane and the unit sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. (Oxford University TR-OUEL 1927/92, 1992) and Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731), it gives enough many voting to generate hypotheses. We also show that from the proposed invariant relationship, an invariant for the structure by two-view and an invariant for a structure proposed by Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731) can also be derived. Experiments using three-dimensional polyhedral objects are carried out to demonstrate the feasibility of our method for three-dimensional objects. |
| Author | Roh, Kyoung Sig Kweon, In So |
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| Keywords | One-viewed invariant relationship Geometric hashing 3-D object recognition |
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| References_xml | – volume: 23 start-page: 92 year: 1983 end-page: 98 ident: BIB1 article-title: Closed-form extension of the an-harmonic ratio to N-Space publication-title: Comput. Vision Graphics Image Process. – volume: 13 start-page: 971 year: 1991 end-page: 991 ident: BIB2 article-title: Invariant descriptors for 3-D object recognition and pose publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – reference: J.G. Semple, G.T. Kneebone, Algebraic Projective Geometry, Oxford Science Publication, Oxford, 1952. – reference: L. Quan, Invariants of six points from 3 uncalibrated images, Proceedings of the fourth European Conference on Computer Vision, Stocholm, Sweden, 1994, pp. 459–470. – reference: A. Zisserman, S.J. Maybank, A case against epipolar geometry, in: J.L. Mundy, A. Zisserman, D. Forsyth (Eds.), Applications of Invariance in Computer Vision, Springer, Berlin, 1993, pp. 69–88. – reference: C.A. Rothwell, D.A. Forsyth, A. Zisserman, J.L. Mundy, Extracting projective invariant from single views of 3D point sets, Oxford University TR-OUEL 1927/92, April, 1992. – reference: J.L. Mundy, A. Zisserman (Eds.), Geometric Invariance in Computer Vision, MIT Press, Cambridge, MA, USA, 1992. – reference: E.B. Barrett, G. Gheen, P. Payton, Representation of three-dimensional object structure as cross-ratios of determinants of stereo image points, in: J.L. Mundy, A. Zisserman, D. Forsyth (Eds.), Applications of Invariance in Computer Vision, Springer, Berlin, 1993, pp. 47–68. – reference: J.B. Buns, R.S. Weiss, E.M. Riseman, The non-existence of general-case view invariants, in: J.L. Mundy, A. Zisserman (Eds.), Geometric Invariance in Computer Vision, MIT Press, Cambridge, MA, USA, 1992. – reference: Y. Zhu, L.D. Seneviratne, S.W.E. Earles, A new structure of invariant for 3D point sets from a single view, Proceedings 12th International Conference on Robotics and Automation, Nagoya, Japan, 1995, pp. 1726–1731. – volume: 17 start-page: 34 year: 1995 end-page: 46 ident: BIB9 article-title: Invariants of six points and projective reconstruction from three uncalibated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – volume: 27 start-page: 377 year: 1994 end-page: 389 ident: BIB14 article-title: Geometric hashing with line features publication-title: Pattern Recognition – reference: O. Fauseras, What can be seen in three dimensions with an uncalibrated stereo rig?, in: G. Sandini (Ed.), Proceedings of the Second European Conference on Computer Vision, Santa Margherita, Italy, Springer, Berlin, 1992, pp. 563–578. – volume: 15 start-page: 531 year: 1993 end-page: 544 ident: BIB10 article-title: The automatic construction of a view-independent relational model for 3-D object recognition publication-title: IEEE Trans. Pattern Anal. Mach. Intell. – ident: 10.1016/S0031-3203(99)00092-8_BIB6 doi: 10.1007/3-540-55426-2_61 – ident: 10.1016/S0031-3203(99)00092-8_BIB8 doi: 10.1007/BFb0028377 – volume: 15 start-page: 531 issue: 6 year: 1993 ident: 10.1016/S0031-3203(99)00092-8_BIB10 article-title: The automatic construction of a view-independent relational model for 3-D object recognition publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.216723 – ident: 10.1016/S0031-3203(99)00092-8_BIB7 doi: 10.1007/3-540-58240-1_4 – ident: 10.1016/S0031-3203(99)00092-8_BIB11 doi: 10.1109/ROBOT.1995.525521 – volume: 13 start-page: 971 issue: 10 year: 1991 ident: 10.1016/S0031-3203(99)00092-8_BIB2 article-title: Invariant descriptors for 3-D object recognition and pose publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.99233 – ident: 10.1016/S0031-3203(99)00092-8_BIB5 doi: 10.1007/3-540-58240-1_3 – ident: 10.1016/S0031-3203(99)00092-8_BIB3 – ident: 10.1016/S0031-3203(99)00092-8_BIB4 – volume: 17 start-page: 34 issue: 1 year: 1995 ident: 10.1016/S0031-3203(99)00092-8_BIB9 article-title: Invariants of six points and projective reconstruction from three uncalibated images publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.368154 – ident: 10.1016/S0031-3203(99)00092-8_BIB13 – ident: 10.1016/S0031-3203(99)00092-8_BIB12 – volume: 23 start-page: 92 year: 1983 ident: 10.1016/S0031-3203(99)00092-8_BIB1 article-title: Closed-form extension of the an-harmonic ratio to N-Space publication-title: Comput. Vision Graphics Image Process. doi: 10.1016/0734-189X(83)90055-5 – volume: 27 start-page: 377 issue: 3 year: 1994 ident: 10.1016/S0031-3203(99)00092-8_BIB14 article-title: Geometric hashing with line features publication-title: Pattern Recognition doi: 10.1016/0031-3203(94)90115-5 |
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| Title | 3-D object recognition using a new invariant relationship by single-view |
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