Abstract

We describe an optomechanical technique using a knife-edge, which is scanned spatially across a beam of light to identify shape-based irradiance. Symmetry groups are identified through linear and rotational scanning signatures of illuminated shapes. The scanning signature is used to classify the shape into a symmetry group. To demonstrate the shape analysis technique, we have classified basic geometric shapes, which belong to the orthogonal and dihedral symmetry groups O2, D2, D3, and D6.

© 2010 Optical Society of America

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  1. Z. He, X. You, and Y. Yuan, “Texture image retrieval based on non-tensor product wavelet filter banks,” Signal Process. 89, 1501–1510 (2009).
    [CrossRef]
  2. R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
    [CrossRef]
  3. H. Kawasaki and R. Furukawa, “Shape reconstruction and camera self-calibration using cast shadows and scene geometries,” Int. J. Comput. Vision 83, 135–148 (2009).
    [CrossRef]
  4. G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vision 85, 35–37 (2009).
    [CrossRef]
  5. W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
    [CrossRef]
  6. A. Ecker and S. Ullman, “A hierarchical non-parametric method for capturing non-rigid deformations,” Image Vision Comput. 27, 87–98 (2009).
    [CrossRef]
  7. D. Levi and S. Ullman, “Learning to classify by ongoing feature selection,” Image Vision Comput. 28, 715–723(2010).
    [CrossRef]
  8. E. Borenstein and S. Ullman, “Combined top-down/bottom-up segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 2109–2125 (2008).
    [CrossRef] [PubMed]
  9. S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
    [CrossRef]
  10. F. de Vieilleville and J.-O. Lachaud, “Comparison and improvement of tangent estimators on digital curves,” Pattern Recogn. 42, 1693–1707 (2009).
    [CrossRef]
  11. I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
    [CrossRef]
  12. T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
    [CrossRef]
  13. R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
    [CrossRef]
  14. T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
    [CrossRef] [PubMed]
  15. S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
    [CrossRef]
  16. J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
    [CrossRef] [PubMed]
  17. D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
    [CrossRef]
  18. J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.
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  21. O. Wolfgang, “Application of optical shape measurement for the nondestructive evaluation of complex objects,” Opt. Eng. 39, 232–243 (2000).
    [CrossRef]

2010 (1)

D. Levi and S. Ullman, “Learning to classify by ongoing feature selection,” Image Vision Comput. 28, 715–723(2010).
[CrossRef]

2009 (9)

Z. He, X. You, and Y. Yuan, “Texture image retrieval based on non-tensor product wavelet filter banks,” Signal Process. 89, 1501–1510 (2009).
[CrossRef]

R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
[CrossRef]

H. Kawasaki and R. Furukawa, “Shape reconstruction and camera self-calibration using cast shadows and scene geometries,” Int. J. Comput. Vision 83, 135–148 (2009).
[CrossRef]

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vision 85, 35–37 (2009).
[CrossRef]

W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
[CrossRef]

A. Ecker and S. Ullman, “A hierarchical non-parametric method for capturing non-rigid deformations,” Image Vision Comput. 27, 87–98 (2009).
[CrossRef]

F. de Vieilleville and J.-O. Lachaud, “Comparison and improvement of tangent estimators on digital curves,” Pattern Recogn. 42, 1693–1707 (2009).
[CrossRef]

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
[CrossRef]

2008 (2)

E. Borenstein and S. Ullman, “Combined top-down/bottom-up segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 2109–2125 (2008).
[CrossRef] [PubMed]

D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
[CrossRef]

2007 (1)

2000 (1)

O. Wolfgang, “Application of optical shape measurement for the nondestructive evaluation of complex objects,” Opt. Eng. 39, 232–243 (2000).
[CrossRef]

1997 (2)

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

1994 (1)

T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

Baumung, R.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Bergevin, R.

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Biederman, I.

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Bolle, R. M.

R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
[CrossRef]

Borenstein, E.

E. Borenstein and S. Ullman, “Combined top-down/bottom-up segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 2109–2125 (2008).
[CrossRef] [PubMed]

Bültoff, H. H.

T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

Burt, D.

D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
[CrossRef]

J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
[CrossRef] [PubMed]

Cadenasso, M. L.

W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
[CrossRef]

Carmona-Poyato, A.

R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
[CrossRef]

Cervantes, I.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Cohen, E.

T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
[CrossRef]

Connell, J. H.

R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
[CrossRef]

David, T.

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

de Vieilleville, F.

F. de Vieilleville and J.-O. Lachaud, “Comparison and improvement of tangent estimators on digital curves,” Pattern Recogn. 42, 1693–1707 (2009).
[CrossRef]

Dickinson, S. J.

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Drew, M. S.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vision 85, 35–37 (2009).
[CrossRef]

Druml, T.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Ecker, A.

A. Ecker and S. Ullman, “A hierarchical non-parametric method for capturing non-rigid deformations,” Image Vision Comput. 27, 87–98 (2009).
[CrossRef]

Eklundh, J.

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Eklundh, J.-O.

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Finlayson, G. D.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vision 85, 35–37 (2009).
[CrossRef]

Furukawa, R.

H. Kawasaki and R. Furukawa, “Shape reconstruction and camera self-calibration using cast shadows and scene geometries,” Int. J. Comput. Vision 83, 135–148 (2009).
[CrossRef]

Garetz, B. A.

Gutiérrez, J. P.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Haas, N.

R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
[CrossRef]

Hartke, J.

D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
[CrossRef]

J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
[CrossRef] [PubMed]

He, Z.

Z. He, X. You, and Y. Yuan, “Texture image retrieval based on non-tensor product wavelet filter banks,” Signal Process. 89, 1501–1510 (2009).
[CrossRef]

Huang, G.

W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
[CrossRef]

Jain, A. K.

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Kawasaki, H.

H. Kawasaki and R. Furukawa, “Shape reconstruction and camera self-calibration using cast shadows and scene geometries,” Int. J. Comput. Vision 83, 135–148 (2009).
[CrossRef]

Khakurel, R.

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

Khosrofian, J. M.

Kinneberg, M.

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

Kirby, R. M.

T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
[CrossRef]

Lachaud, J.-O.

F. de Vieilleville and J.-O. Lachaud, “Comparison and improvement of tangent estimators on digital curves,” Pattern Recogn. 42, 1693–1707 (2009).
[CrossRef]

Levi, D.

D. Levi and S. Ullman, “Learning to classify by ongoing feature selection,” Image Vision Comput. 28, 715–723(2010).
[CrossRef]

Lu, C.

G. D. Finlayson, M. S. Drew, and C. Lu, “Entropy minimization for shadow removal,” Int. J. Comput. Vision 85, 35–37 (2009).
[CrossRef]

Madrid-Cuevas, F. J.

R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
[CrossRef]

Magnes, J.

D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
[CrossRef]

J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
[CrossRef] [PubMed]

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

Martin, T.

T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
[CrossRef]

McCally, R. L.

Medina-Carnicer, R.

R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
[CrossRef]

Melikechi, N.

J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
[CrossRef] [PubMed]

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

Mohan, R.

R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
[CrossRef]

Molina, A.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Munck-Fairwood, R.

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Munk-Fairwood, R.

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Muñoz-Salinas, R.

R. Medina-Carnicer, F. J. Madrid-Cuevas, A. Carmona-Poyato, and R. Muñoz-Salinas, “On candidates selection for hysteresis thresholds in edge detection,” Pattern Recogn. 42, 1284–1296(2009).
[CrossRef]

Olson, D.

J. Magnes, T. David, R. Khakurel, M. Kinneberg, D. Olson, and N. Melikechi, “Shape recognition through opto-mechanical scanning,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper FMJ5.

Pentland, A.

S. J. Dickinson, R. Bergevin, I. Biederman, J. Eklundh, R. Munk-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

Poggio, T.

T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

Schwarz, G.

D. Burt, J. Magnes, G. Schwarz, and J. Hartke, “Teaching integration through a physical phenomenon,” Primus 18, 283 (2008).
[CrossRef]

J. Magnes, G. Schwarz, J. Hartke, D. Burt, and N. Melikechi, “Optomechanical integration method for finite integrals,” Appl. Opt. 46, 6918–6922 (2007).
[CrossRef] [PubMed]

Sölkner, J.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Taubin, G.

R. M. Bolle, J. H. Connell, N. Haas, R. Mohan, and G. Taubin, “VeggieVision: a produce recognition system,” in Proceedings of the 3rd IEEE Workshop on Applications of Computer Vision (IEEE, 1996), pp. 244–251.
[CrossRef]

Troy, A.

W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
[CrossRef]

Ullman, S.

D. Levi and S. Ullman, “Learning to classify by ongoing feature selection,” Image Vision Comput. 28, 715–723(2010).
[CrossRef]

A. Ecker and S. Ullman, “A hierarchical non-parametric method for capturing non-rigid deformations,” Image Vision Comput. 27, 87–98 (2009).
[CrossRef]

E. Borenstein and S. Ullman, “Combined top-down/bottom-up segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 2109–2125 (2008).
[CrossRef] [PubMed]

Valera, M.

I. Cervantes, R. Baumung, A. Molina, T. Druml, J. P. Gutiérrez, J. Sölkner, and M. Valera, “Size and shape analysis of morphofunctional traits in the Spanish Arab horse,” Livest. Sci. 125, 43–49 (2009).
[CrossRef]

Vetter, T.

T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

Wolfgang, O.

O. Wolfgang, “Application of optical shape measurement for the nondestructive evaluation of complex objects,” Opt. Eng. 39, 232–243 (2000).
[CrossRef]

You, X.

Z. He, X. You, and Y. Yuan, “Texture image retrieval based on non-tensor product wavelet filter banks,” Signal Process. 89, 1501–1510 (2009).
[CrossRef]

Yuan, Y.

Z. He, X. You, and Y. Yuan, “Texture image retrieval based on non-tensor product wavelet filter banks,” Signal Process. 89, 1501–1510 (2009).
[CrossRef]

Zhou, W.

W. Zhou, G. Huang, A. Troy, and M. L. Cadenasso, “Object-based land cover classification of shaded areas in high spatial resolution imagery of urban areas: a comparison study,” Remote Sens. Environ. 113, 1769–1777 (2009).
[CrossRef]

Appl. Opt. (3)

Comput. Aided Geom. Des. (1)

T. Martin, E. Cohen, and R. M. Kirby, “Volumetric parameterization and trivariate B-spline fitting using harmonic functions,” Comput. Aided Geom. Des. 26, 648–664 (2009).
[CrossRef]

Curr. Biol. (1)

T. Vetter, T. Poggio, and H. H. Bültoff, “The importance of symmetry and virtual views in three-dimensional object recognition,” Curr. Biol. 4, 18–23 (1994).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

E. Borenstein and S. Ullman, “Combined top-down/bottom-up segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 30, 2109–2125 (2008).
[CrossRef] [PubMed]

Image Vision Comput. (4)

S. J. Dickinson, R. Bergevin, I. Biederman, J.-O. Eklundh, R. Munck-Fairwood, A. K. Jain, and A. Pentland, “Panel report: the potential of geons for generic 3-D object recognition,” Image Vision Comput. 15, 277–292 (1997).
[CrossRef]

A. Ecker and S. Ullman, “A hierarchical non-parametric method for capturing non-rigid deformations,” Image Vision Comput. 27, 87–98 (2009).
[CrossRef]

D. Levi and S. Ullman, “Learning to classify by ongoing feature selection,” Image Vision Comput. 28, 715–723(2010).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) A laser was used in this optomechanical scanning setup. The laser light is expanded using a diffuser so that the laser light envelops the object. The knife-edge is used to scan across the shadow. The light is then collected using a lens and directed onto a photodetector. (b) A knife-edge is displaced linearly. (c) The object is rotated about different points for rotational scanning.

Fig. 2
Fig. 2

(a) Raw data: area as a function of knife-edge translation for two different orientations. (b) Differentiated area for two different orientations.

Fig. 3
Fig. 3

Experimental and simulated data for a tilted house show good agreement.

Fig. 4
Fig. 4

Shapes represented by a non-single-valued function can be reproduced in sections using optomechanical scanning, as long as the exposed part represents a function.

Fig. 5
Fig. 5

Rotational scanning reveals k-fold rotational symmetry through the optomechanical signature. Each peak represents a symmetry axis.

Tables (1)

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Table 1 Group Multiplication Table for Dihedral Group D 3

Equations (4)

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A = σ ^ y A = = ( 1 0 0 1 ) ( x x peak y ) = ( ( x x peak ) y ) ,
γ = n ( n 1 ) ( n 2 ) ( x i x ¯ σ ) 3 ,
γ = n ( n 1 ) ( n 2 ) j = 1 m f ( x j ) ( x j x ¯ σ ) 3 ,
C ^ k ( Z ) = ( cos 2 π k sin 2 π k 0 sin 2 π k cos 2 π k 0 0 0 1 ) .

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