Abstract
In this paper we propose a reconstruction based recognition scheme for objects with repeated components, using a single image of such a configuration, in which one of the repeated components may be partially occluded. In our strategy we reconstruct each of the components with respect to the same frame and use these to compute invariants.We propose a new mathematical framework for the projective reconstruction of affinely repeated objects. This uses the repetition explicitly and hence is able to handle substantial occlusion of one of the components. We then apply this framework to the reconstruction of a pair of repeated quadrics. The image information required for the reconstruction are the outline conic of one of the quadrics and correspondence between any four points which are images of points in general position on the quadric and its repetition. Projective invariants computed using the reconstructed quadrics have been used for recognition. The recognition strategy has been applied to images of monuments with multi-dome architecture. Experiments have established the discriminatory ability of the invariants.
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References
F. Bookstein, “Fitting conic sections to scattered data,” Computer Vision Graphics and Image Processing, Vol. 9, pp. 56–71, 1979.
J.B. Burns, R.S. Weiss, and E.M. Riseman, “The non-existance of general-case view-invariants,” in Geometric Invariance in ComputerVision,A. Zisserman and J. Mundy (Eds. ),MIT Press: Cambridge, MA, 1992.
R. Choudhury, J.B. Srivastava, and S. Chaudhury, “A reconstruction based recognition scheme for translationally repeated quadrics,” in First Indian Conference on Computer Vision, Graphics and Image Processing, S. Chaudhury and S.K. Nayar (Eds. ), 1998, pp. 101–108.
G. Cross and A. Zisserman, “Quadric reconstruction from dual space geometry,” in Proceedings of Sixth International Conference of Computer Vision, Narosa, India, 1998, pp. 25–31.
P.A. Devijver and J. Kittler, Pattern Recognition: A Statistical Approach, Prentice-Hall International: Englewood Cliffs, NJ, 1981.
O. Faugeras, “What can be seen in three dimensions with an uncalibrated stereo rig?” in Lecture Notes in Computer Science, Vol. 588: Proceedings of European Conference on Computer Vision, G. Sandini (Ed. ), Springer-Verlag: Berlin, 1992.
P. Gros and L. Quan, “Projective invariants for computer vision,” Technical Report RT 90 IMAG—15 LIFIA, INRIA, France, 1992.
R.I. Hartley, “In defense of the eight-point algorithm,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 8, pp. 580–593, 1997.
D. Heisterkamp and P. Bhattacharya, “Invariants of families of coplanar conics and their applications to object recognition,” Journal of Mathematical Imaging and Vision, Vol. 7, pp. 253–267, 1997.
J. Liu, E. Walker, and J. Mundy, “Characterizing the stability of 3D invariants derived from 3D translational symmetry,” in Proceedings of ACCV'95, 1995.
H.C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature,Vol. 293, pp. 133–135, 1981.
Q.T. Luong and T. Vieville, “Canonic representations for the geometries of multiple projective views,” Computer Vision and Image Understanding, Vol. 64, No. 2, pp. 193–229, 1996.
T. Moons, L. Van Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object—Camera translation in between,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 18, No. 1, pp. 77–83, 1996.
J.L. Mundy and A. Zisserman, “Repeated structures: Image correspondence and 3D structure recovery,” in Lecture Series in Computer Science, Vol. 825: Applications of Invariance in Computer Vision, J.L. Mundy, A. Zisserman, and D. Forsyth (Eds.), Springer-Verlag: Berlin, 1994, pp. 89–106.
L. Quan and F. Veillon, “Joint invariants of a triplet of coplanar conics: Stability and discriminatory power for object recognition,” ComputerVision and Image Understanding,Vol. 70, No. 1, pp. 111–119, 1998.
C.A. Rothwell, “Recognition using projective invariance,” Ph.D. Thesis, University of Oxford, 1993.
C. Rothwell, O. Faugeras, and G. Csurka, “A comparison of projective reconstruction methods for pairs of views,” Computer Vision and Image Understanding, Vol. 68, No. 1, pp. 37–58, 1997.
A. Shashua, “Projective structure from two uncalibrated images: Structure from motion and recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 16, No. 8, pp. 778–790, 1994.
A. Shashua and N. Navab, “Relative affine structure: Canonical model for 3D from 2D geometry and applications,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 18, No. 9, pp. 873–883, 1996.
A. Shashua and S. Toelg, “The quadric reference surface: Theory and application,” International Journal of Computer Vision, Vol. 23, No. 2, pp. 185–198, 1996.
A. Zisserman, D.A. Forsyth, J.L. Mundy, C.A. Rothwell, J. Liu, and N. Pillow, “3D object recognition using invariance,” Artifi-cial Intelligence, Vol. 78, pp. 239–288, 1995.
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Choudhury, R., Chaudhury, S. & Srivastava, J. A Framework for Reconstruction based Recognition of Partially Occluded Repeated Objects. Journal of Mathematical Imaging and Vision 14, 5–20 (2001). https://doi.org/10.1023/A:1008373429426
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DOI: https://doi.org/10.1023/A:1008373429426