This Article 
 Bibliographic References 
 Add to: 
Pictorial Recognition of Objects Employing Affine Invariance in the Frequency Domain
June 1998 (vol. 20 no. 6)
pp. 604-618

Abstract—This paper describes an efficient approach to pose invariant pictorial object recognition employing spectral signatures of image patches that correspond to object surfaces which are roughly planar. Based on Singular Value Decomposition (SVD), the affine transform is decomposed into slant, tilt, swing, scale, and 2D translation. Unlike previous log-polar representations which were not invariant to slant (i.e., foreshortening only in one direction), our log-log sampling configuration in the frequency domain yields complete affine invariance. The images are preprocessed by a novel model-based segmentation scheme that detects and segments objects that are affine-similar to members of a model set of basic geometric shapes. The segmented objects are then recognized by their signatures using multidimensional indexing in a pictorial dataset represented in the frequency domain. Experimental results with a dataset of 26 models show 100 percent recognition rates in a wide range of 3D pose parameters and imaging degradations: 0-360° swing and tilt, 0-82° of slant (more than 1:7 foreshortening), more than three octaves in scale change, window-limited translation, high noise levels (0 dB), and significantly reduced resolution (1:5).

[1] 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.
[2] Z. Wang and J. Ben-Arie, "SVD and Log-Log Frequency Sampling With Gabor Kernels for Invariant Pictorial Recognition," Proc. 1997 IEEE Int'l Conf. Image Processing (ICIP '97), vol. III, pp. 162-165,Santa Barbara, Calif., Oct.26-29 1997.
[3] J. Ben-Arie and Z. Wang, “Pictorial Recognition Using Affine-Invariant Spectral Signatures,” Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, pp. 34-39, San Juan, P.R., June 1997.
[4] J. Ben-Arie, Z. Wang, and K.R. Rao, "Affine Invariant Shape Representation and Recognition using Gaussian Kernels and Multi-dimensional Indexing," Proc. 1996 IEEE Int'l Conf. Speech, Acoustics, and Signal Processing (ICASSP '96), vol. 6, pp. 3,470-3,473,Atlanta, May 1996.
[5] J. Ben-Arie, Z. Wang, and K.R. Rao, "Iconic Recognition With Affine-Invariant Spectral Signatures," Proc. 1996 IAPR/IEEE Int'l Conf. Pattern Recognition (ICPR '96), vol. 1, pp. 672-676,Vienna, Austria, Aug. 1996.
[6] J. Ben-Arie, Z. Wang, and K.R. Rao, "Iconic Representation and Recognition Using Affine-Invariant Spectral Signatures," Proc. ARPA Image Understanding Workshop 1996, pp. 1,277-1,286,Palm Springs, Calif., Feb. 1996.
[7] J. Buhmann, J. Lange, C. von der Malsburg, J.C. Vorbruggen, and R.P. Wurtz, "Object Recognition With Gabor Functions in the Dynamic Link Architecture: Parallel Implementation on a Transputer Network," B. Kosko, ed., Neural Networks for Signal Processing, pp. 121-159.Englewood Cliffs, NJ: Prentice Hall, 1992.
[8] A. Califano and R. Mohan, "Multidimensional Indexing for Recognizing Visual Shapes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 4, pp. 373-392, 1994.
[9] D. Casasent and D. Psaltis, "Position, Rotation, and Scale Invariant Optical Correlation," Applied Optics, vol. 15, no. 7, pp. 1,795-1,799, July 1976.
[10] R. Cipolla and A. Blake, "Surface Shape From the Deformation of Apparent Contours," Int'l J. Computer Vision, vol. 9, no. 2, pp. 83-112, 1992.
[11] J. Flusser and T. Suk, "Pattern Recognition by Affine Moment Invariants," Pattern Recognition, vol. 26, no. 1, pp. 167-174, 1993.
[12] J. Flusser and T. Suk, "Affine Moment Invariants: A New Tool for Character Recognition," Pattern Recognition Letters, vol. 15, pp. 433-436, Apr. 1994.
[13] J.G. Daugman, “Complete Discrete 2D Gabor Transforms by Neural Networks for Image Analysis and Compression,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 36, no. 7, 1988.
[14] R. Hecht-Nielsen, "Fast K-NN Search for Robust ATR Object Matching," Proc. ARPA Image Understanding Workshop 1994, pp. 889-894,Monterey, Calif., Nov. 1994.
[15] M. Seibert and A.M. Waxman, "Adaptive 3-D Object Recognition From Multiple Views," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, Feb. 1992.
[16] R.P.N. Rao and D.H. Ballard, "Object Indexing Using an Iconic Sparse Distributed Memory," Proc. Fifth Int'l Conf. Computer Vision, pp. 24-31,Cambridge, Mass., June 1995.
[17] Q.M. Tieng and W.W. Boles, "Wavelet-Based Affine Invariant Representation: A Tool for Recognizing Planar Objects in 3D Space," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 846-857, Aug. 1997.
[18] X. Wu and B. Bhanu, "Target Recognition Using Multi-Scale Gabor Filters," Proc. ARPA Image Understanding Workshop 1994, pp. 505-509,Monterey, Calif., Nov. 1994.
[19] H. Wechsler, Computational Vision.New York, NY: Academic Press, 1990.
[20] Y. Lamdan, J. Schwartz, and H. Wolfson, "Object Recognition by Affine Invariant Matching," Proc. IEEE Computer Vision and Pattern Recognition Conf., IEEE Computer Society, 1988, pp. 335-344.
[21] B. Moghaddam and A. Pentland, "Probabilistic Visual Learning for Object Detection," Int'l Conf. Computer Vision, 1995, pp. 786-793.
[22] P.N. Belhumeur, J. Hespanda, and D. Kriegeman, Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 7, pp. 711-720, July 1997.
[23] H. Murase and S.K. Nayar, "Visual Learning and Recognition of 3D Objects From Appearance," Int'l J. Computer Vision, vol. 14, no. 1, pp. 5-24, 1995.
[24] R.P.N. Rao and D. Ballard, "An Active Vision Architecture Based on Iconic Representations," Artificial Intelligence, vol. 78, pp. 461-505, 1995.
[25] M.J. Black and A.D. Jepson, "Eigentracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation," Proc. ECCV, pp. 329-342, 1996.
[26] J. Edwards and H. Murase, "Appearance Matching of Occluded Objects Using Coarse-to-Fine Adaptive Masks," Proc. CVPR, pp. 533-539, 1997.
[27] R.P.N. Rao, "Dynamic Appearance-Based Recognition," Proc. CVPR, pp. 540-546, 1997.
[28] I. Biederman, "Aspects and Extensions of a Theory of Human Image Understanding," Computational Process in Human Vision: An Interdisciplinary Perspective. Z. Pylyshyn, ed., New York, NY: Ablex, 1987.

Index Terms:
Affine invariant recognition, model-based segmentation, affine invariant spectral signatures (AISS), multidimensional indexing, Gabor kernels.
Jezekiel Ben-Arie, Zhiqian Wang, "Pictorial Recognition of Objects Employing Affine Invariance in the Frequency Domain," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 6, pp. 604-618, June 1998, doi:10.1109/34.683774
Usage of this product signifies your acceptance of the Terms of Use.