| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
Wavelet-Based Affine Invariant Representation: A Tool for Recognizing Planar Objects in 3D Space
August 1997 (vol. 19 no. 8)
pp. 846-857
Abstract—A technique is developed to construct a representation of planar objects undergoing a general affine transformation. The representation can be used to describe planar or nearly planar objects in a three-dimensional space, observed by a camera under arbitrary orientations. The technique is based upon object contours, parameterized by an affine invariant parameter and the dyadic wavelet transform. The role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation. A dissimilarity function is also developed and used to distinguish among different object representations. This function makes use of the extrema on the representations, thus making its computation very efficient. A study of the effect of using different wavelet functions and their order or vanishing moments is also carried out. Experimental results show that the performance of the proposed representation is better than that of other existing methods, particularly when objects are heavily corrupted with noise.
[1] 846 P.J.V. Otterloo, A Contour-Oriented Approach to Shape Analysis. Prentice Hall, 1991.[2] R.C. Gonzalez and R.E. Woods, Digital Image Processing. Addison-Wesley, 1993.[3] K. Arbter, W.E. Snyder, H. Burkhardt, and G. Hirzinger, “Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 640-647, July 1990.[4] Q. Jin and P. Yan, “A New Method of Extracting Invariants under Affine-Transform,” Proc. 11th IAPR Int'l Conf. Pattern Recognition, pp. 742-745, 1992.[5] D. Cyganski and R.F. Vaz, "A Linear Signal Decomposition Approach to Affine Invariant Contour Identification," SPIE: Intelligent Robots and Computer Vision X, vol. 1,607, pp. 98-109, 1991.[6] R.F. Vaz and D. Cyganski, "3D Object Orientation from Partial Contour Feature Data," SPIE: Applications of Digital Image Processing XIII, vol. 1,349, pp. 452-459, 1990.[7] J. Sprinzak and M. Werman, "Affine Point Matching," Pattern Recognition Letters, vol. 15, pp. 337-339, Apr. 1994.[8] J. Flusser and T. Suk, "Pattern Recognition by Affine Moment Invariants," Pattern Recognition, vol. 26, no. 1, pp. 167-174, 1993.[9] M.K. Hu, “Pattern Recognition by Moment Invariants,” Proc. IRE Trans. Information Theory, vol. 8, pp. 179-187, 1962.[10] J. Flusser and T. Suk, "Affine Moment Invariants: A New Tool for Character Recognition," Pattern Recognition Letters, vol. 15, pp. 433-436, Apr. 1994.[11] D. Cyganski and J.A. Orr, "Applications of Tensor Theory to Object Recognition and Orientation Determination," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, pp. 662-673, Nov. 1985.[12] S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.[13] H.W. Guggenheimer, Differential Geometry. McGraw Hill, 1963.[14] P. Modenov and A. Parkhomenko, Geometric Transformations, vol. 1. Academic Press, 1965.[15] M.M. Fleck, “Some Defects in Finite-Difference Edge Finders,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 3, pp. 337-345, Mar. 1992.[16] D.P. Dobkin, S.V.F. Levy, W.P. Thurston, and A.R. Wilks, "Contour Tracing by Piecewise Linear Approximations," ACM Trans. Graphics, vol. 9, pp. 389-423, Oct. 1990.[17] T.D. Haig, Y. Attikiouzel, and M.D. Alder, "Border Following: New Definition Gives Improved Borders," IEE Proc., vol. 139, no. 2, pp. 206-211, Apr. 1992.[18] B.-D. Chen and P. Siy, "Forward/Backward Contour Tracing with Feedback," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 5, pp. 438-446, May 1987.[19] I. Daubechies, Ten Lectures on Wavelets.Philadelphia: Society for Industrial and Applied Mathematics, 1992.[20] S.G. Mallat, "Zero-Crossings of a Wavelet Transform," IEEE Trans. Information Theory, vol. 37, no. 4. pp. 1,019-1,033, July 1991.[21] S. Mallat and S. Zhong, “Characterization of Signals from Multiscale Edges,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 7, pp. 710-732, July 1992.[22] M.J. Shensa, "The Discrete Wavelet Transform: Wedding theàTrous Algorithms and Mallat Algorithms," IEEE Trans. Signal Processing, vol. 40, no. 10, pp. 2,464-2,482, 1992.[23] A.H. Tewfik and P.E. Jorgensen, "On the Choice of a Wavelet for Signal Coding and Processing," Proc. ICASSP '91, vol. 4, pp. 2,015-2,028, May 1991.[24] Q.M. Tieng and W.W. Boles, "Recognition of 2D Object Contours Using the Wavelet Transform Zero-Crossing Representation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 910-916, Aug. 1997.[25] J.F. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, pp. 679-698, Nov. 1986.
Index Terms:
Affine invariant, object contour, object representation, wavelet transform.
Citation:
Quang Minh Tieng, Wageeh W. Boles, "Wavelet-Based Affine Invariant Representation: A Tool for Recognizing Planar Objects in 3D Space," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 846-857, Aug. 1997, doi:10.1109/34.608288
