A Unifying Approach to Moment-Based Shape Orientation and Symmetry Classification (original) (raw)
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We give a general framework of statistical aspects of the problem of understanding and a description of image symmetries, by utilizing the theory of moment invariants. In particular, we examine the issues of joint symmetry estimation and detection. These questions are formulated as the statistical decision and estimation problems since we cope with images observed in the presence of noise. The estimation/detection procedures are based on the minimum L 2-distance between the reconstructed image function and the reconstruction of its hypothesized symmetrical version. Our reconstruction algorithms are relying on a class of radial orthogonal moments. The proposed symmetry estimation and detection techniques reveal some statistical optimality properties. Our technical developments are based on the statistical theory of nonparametric testing and semi-parametric inference.
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The analytical Fourier-Mellin transform is used in order to assess motion parameters between gray-level objects having the same shape with distinct scale and orientation. From results on commutative harmonic analysis, a functional is constructed in which the location of the minimum gives an estimation of the size and orientation parameters. Furthermore, when the set of geometrical transformations is restricted to the compact rotation group, we show that this minimum is exactly the Hausdor distance between shapes represented in the Fourier-Mellin domain. This result is used for the detection and the estimation of both all rotation and re ection symmetries in objects. ?
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2011 8th International Conference on Information, Communications & Signal Processing, 2011
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Fast computation of geometric moments using a symmetric kernel
Pattern Recognition, 2008
This paper presents a novel set of geometric moments with symmetric kernel (SGM) obtained using an appropriate transformation of image coordinates. By using this image transformation, the computational complexity of geometric moments (GM) is reduced significantly through the embedded symmetry and separability properties. In addition, it minimizes the numerical instability problem that occurs in high order GM computation. The novelty of the method proposed in this paper lies in the transformation of GM kernel from interval [0, ∞] to interval [−1, 1]. The transformed GM monomials are symmetry at the origin of principal Cartesian coordinate axes and hence possess symmetrical property. The computational complexity of SGM is reduced significantly from order O(N 4 ) using the original form of computation to order O(N 3 ) for the proposed symmetry-separable approach. Experimental results show that the percentage of reduction in computation time of the proposed SGM over the original GM is very significant at about 75.0% and 50.0% for square and non-square images, respectively. Furthermore, the invariant properties of translation, scaling and rotation in Hu's moment invariants are maintained. The advantages of applying SGM over GM in Zernike moments computation in terms of efficient representation and computation have been shown through experimental results. ᭧ About the Author-CHONG-YAW WEE received his B.Eng., M.Eng.Sc., and Ph.D. degrees in electrical engineering from University of Malaya, Malaysia, in 2001. He is currently a post-doctoral research fellow in Centre for Signal and Image Processing (CISIP), Department of Electrical Engineering at University of Malaya. His research interests lie in the field of image and signal analysis, statistical pattern recognition, and evolutionary computation. His present work includes developing novel degraded image recognition system, image/video quality assessment system using the orthogonal moment functions and statistical pattern recognition concepts. . His primary research interests are in the areas of moment-based feature descriptors and their applications in computer vision, computer graphics algorithms, and image-based rendering.
Orthogonal Fourier-Mellin moments for invariant pattern recognition
Journal of The Optical Society of America A-optics Image Science and Vision, 1994
We propose orthogonal Fourier-Mellin moments, which are more suitable than Zernike moments, for scaleand rotation-invariant pattern recognition. The new orthogonal radial polynomials have more zeros than do the Zernike radial polynomials in the region of small radial distance. The orthogonal Fourier-Mellin moments may be thought of as generalized Zernike moments and orthogonalized complex moments. For small images, the description by the orthogonal Fourier-Mellin moments is better than that by the Zernike moments in terms of image-reconstruction errors and signal-to-noise ratio. Experimental results are shown.
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