On the reconstruction of an image from its moments

Las Vegas: International Conference on Imaging …, 2003

Several pattern recognition applications use orthogonal moments to capture independent shape characteristics of an image, with minimum amount of information redundancy in a feature set. Legendre, Zernike, and Pseudo-Zernike moments are examples of such orthogonal feature descriptors. An image can also be reconstructed from a sufficiently large number of orthogonal moments. Discrete orthogonal moments provide a more accurate description of image features by evaluating the moment components directly in the image coordinate space. This paper examines some of the problems associated with the computation of large order Tchebichef moments, and proposes an orthonormal version to improve the quality of reconstructed images.

2002 International Joint Conference on Neural Networks (IJCNN '02)

Krawtchouk polynomials [1] can be used to form the basis of a set of discrete orthogonal moments. In this paper, Krawtchouk moments are used to analytically reconstruct binary images. Their performance is compared to that of Zernike, Legendre (continuous) [2, 3, 4, 5] and Chebyshev (discrete) [6, 7, 8] moments. www.researchgate.net/publication/224722898_Krawtchouk_moments_as_a_new_set_of_discrete_orthogonal_moments_forimage_reconstruction/file/9fcfd5134b6f5389f5.pdf

2007

This paper proposes a new set of orthogonal moments based on continuous Pollaczek polynomials. In order to ensure numerical stability, Pollaczek polynomials are weighted using a weight function and a squared norm term associated with these polynomials. Weighted polynomials thus obtained are used to define continuous Pollaczek moments. In order to apply these moments for digital image reconstruction problem, a discrete representation of the continuous moments is considered for both binary as well as multilevel images. Further, it is observed that Legendre moments are a special case of Pollaczek moments. Hence the results are compared with Legendre moments only. It is also noted from the simulation results (peak signal to noise ratio, reconstruction error and universal image quality index) that Pollaczek moments are better than Legendre moments as par as image reconstruction problem is considered. Index Terms — Pollaczek polynomials, weighted Pollaczek polynomials, Pollaczek moments.

Information Sciences, 2009

A novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments. The computation scheme is mainly based on a new image representation method, the ISR (Image Slice Representation) method, according to which an image can be expressed as the outcome of an appropriate combination of several nonoverlapped intensity slices. This image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities, black or any other graylevel value. Therefore the image block representation can be effectively applied to describe the image in a more compact way. Once the image is partitioned into intensity blocks, the computation of the image moments can be accelerated, as the moments can be computed by using decoupled computation forms. The proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results, as has been concluded through a detailed experimental investigation.

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.

The discrete orthogonal moments have been recently introduced in the field of image analysis. It has been shown to have a better ability to represent the image than the continuous orthogonal moments. A problem concerning the use of moments as descriptors is the highest cost of calculation, which may limit their application to the problems in which the calculation online is necessary. In this paper, we present an approach for the rapid calculation of two-dimensional Tchebichef moments by using image block representation for binary images and the slice representation of intensity to gray-scale images. A theoretical analysis shows that the computational complexity of the proposed method is based on the number of blocks of the image, thus, it can accelerate the computational efficiency since the number of blocks is less than the size of the image. Finally, the performances of Tchebichef moments in describing images were measured in terms of the image reconstruction error.

International Joint Conference on Neural Networks (IJCNN'01), 2001

Chebyshev (sometimes referred to as Tchebichef) moments, introduced recently in [1], belong to a class of discrete orthogonal moments. In this paper, Chebyshev moments are used to analytically reconstruct grey level images. Their capability to reconstruct images with and without noise is compared to that of Zernike and Legendre moments, which are well known classes of continuous moments. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=938829

2012 Colloquium in Information Science and Technology, 2012

The discrete orthogonal moments have been recently introduced in the field of image analysis. It has been shown to have a better ability to represent the image than the continuous orthogonal moments. A problem concerning the use of moments as descriptors is the highest cost of calculation, which may limit their application to the problems in which the calculation online is necessary. In this paper, we present an approach for the rapid calculation of two-dimensional Tchebichef moments by using image block representation for binary images and the slice representation of intensity to gray-scale images. A theoretical analysis shows that the computational complexity of the proposed method is based on the number of blocks of the image, thus, it can accelerate the computational efficiency since the number of blocks is less than the size of the image. Finally, the performances of Tchebichef moments in describing images were measured in terms of the image reconstruction error.

Pattern Recognition Letters, 2006

Various types of moments have been used to recognize image patterns in a number of applications. However, only few works have paid attention to the completeness property of the invariant descriptor set, which is of fundamental importance from the theoretical as well as the practical points of views. This paper proposes a systematic method to extract a complete set of similarity invariants (translation, rotation and scale), by means of some linear combinations of complex moments. The problem of image reconstruction from a finite set of its moment invariants is then examined by exploiting the link between the discrete Fourier transform of an image and its complex moments. Experimental results are presented that confirm theoretical properties as well as numerical effectiveness of the method.

Wireless Communications and Mobile Computing

Accurate image moment computation is critical because they are used in a variety of fields, including image reconstruction and object recognition. Orthogonal polynomials are frequently used to compute moments due to their numerous intersecting and important theoretical properties. In polar coordinate systems, orthogonal polynomials such as the Polar Harmonic Fourier Transform (PHFT) and Polar Harmonic Transformation (PHT) are defined. However, the images are defined by a Cartesian coordinate system. To obtain image moments, a double integration over a unit circle over the product of the PHFT or PHT and the image function must be performed. The choice of double integration techniques and domain for the double integral has a significant effect on the precision of the computed moments. We have proposed a method for using the entire unit circle as an integration domain in this study, for image reconstruction. We used the PHFT and PHT to apply this technique to computing moments for the ...