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Image reconstruction from a complete set of geometric and complex moments

Barmak Honarvar, Raveendran Paramesran, Chern-Loon Lim
2014 Signal Processing  
Then, by using the invertibility property of the Stirling transform, the original image can be reconstructed from its complete set of either geometric or complex moments.  ...  An image can be reconstructed from the finite set of its orthogonal moments.  ...  Conclusion In this paper, a new approach has been proposed for image reconstruction from geometric and complex moments.  ... 
doi:10.1016/j.sigpro.2013.11.037 fatcat:opfkdqrgnvckflc7xxhx4f4h4y

Image reconstruction from a complete set of similarity invariants extracted from complex moments

F. Ghorbel, S. Derrode, R. Mezhoud, T. Bannour, S. Dhahbi
2006 Pattern Recognition Letters  
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.  ...  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.  ...  Image reconstruction from complex moments In Section 2, we have seen that it is possible to recover the complex moments of an image from the complete set of invariants by mean of Eq. (7).  ... 
doi:10.1016/j.patrec.2006.01.001 fatcat:xu6wwpslpzfjfpn4quj6xpienq

2D and 3D Image Analysis by Gaussian-Hermite Moments [chapter]
English

Bo Yang, Tomas Suk, Mo Dai, Jan Flusser
2014 Gate to Computer Science and Research  
Thanks to their numerical stability, GaussianHermite moments provide better reconstruction and recognition power than the geometric and most of other orthogonal moments while keeping the simplicity of  ...  This chapter introduces 2D and 3D GaussianHermite moments and rotation invariants constructed from them.  ...  Thanks to the above Theorems and a direct link between geometric and complex moments [5] we just follow that way and propose a design of a complete set of GaussianHermite invariants.  ... 
doi:10.15579/gcsr.vol1.ch7 fatcat:b5n34ayi5jecrk74lj4jamasgy

Image analysis by Tchebichef moments

R. Mukundan, S.H. Ong, P.A. Lee
2001 IEEE Transactions on Image Processing  
redundancy in a moment set.  ...  The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.  ...  ACKNOWLEDGMENT The authors are thankful to the reviewers and the editor for their valuable comments and suggestions, which have greatly helped in improving the content of this paper.  ... 
doi:10.1109/83.941859 pmid:18255550 fatcat:zs6hd4w64jb4bpe4xo6odcyjo4

Fast Legendre Moments in Securing Digital Image

2019 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE  
rather as a 2D function of a digital image and the results of reconstruction in case of tampering is also shown  ...  and geometric error when applied to digital images.  ...  -----> 6 where is the qth order moment of row i 7 The image can be reconstructed without any loss of information since legendre moments are free from approximation errors and geometric errors.  ... 
doi:10.35940/ijitee.k1278.10812s19 fatcat:f3vpcjuxtrf6blrh5tm5rty264

Design of high-order rotation invariants from Gaussian–Hermite moments

Bo Yang, Jan Flusser, Tomáš Suk
2015 Signal Processing  
from geometric moments are available.  ...  In this paper we proposed a method to design and numerically calculate high-order rotation invariants from Gaussian-Hermite moments.  ...  The question now isgiven a set of invariants up to certain order r, what image can be reconstructed from them and what is its difference from the original?  ... 
doi:10.1016/j.sigpro.2015.01.005 fatcat:z5yb7wetzjaillaitkc3mhdya4

Application of a hybrid orthogonal function system on trademark image retrieval

Xiaochun WANG, Yena WANG, Honglei SUN, Ruixia SONG
2014 Journal of Advanced Mechanical Design, Systems, and Manufacturing  
can be precisely reconstructed by finite number of the W-moments, due to the orthogonality of the basis functions on a discrete data set.  ...  Region-based orthogonal moments, such as Zernike moments and Legendre moments, allow for accurate reconstruction of the described shape by expanding an image into a series of orthogonal moment bases and  ...  to reconstruct an image from the geometric moments.  ... 
doi:10.1299/jamdsm.2014jamdsm0077 fatcat:mfupg6ujozdklcxlps4ft3ranq

A look at . .

Huazhong Shu, Limin Luo, J.-L. Coatrieux
2008 IEEE Engineering in Medicine and Biology Magazine  
By establishing a relationship between the image geometric moments and projection moments, Wang and Sze [10] presented an approach to reconstruct the CT images from limited range projections.  ...  [6] presented a variational framework for the tomographic reconstruction of an image from the maximum likelihood estimates of its orthogonal moments.  ... 
doi:10.1109/memb.2008.927990 pmid:18799403 pmcid:PMC2586127 fatcat:aqfxhtuhxvbabjtsnqd3tvu4ke

Image reconstruction from limited range projections using orthogonal moments

H.Z. Shu, J. Zhou, G.N. Han, L.M. Luo, J.L. Coatrieux
2007 Pattern Recognition  
A set of orthonormal polynomials is proposed for image reconstruction from projection data.  ...  The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated.  ...  His recent work concentrates on the treatment planning optimization, medical imaging, and pattern recognition. Dr. SHU is a member of IEEE.  ... 
doi:10.1016/j.patcog.2006.05.035 fatcat:lboz3skoojfcpghzald77k33fm

Optical-digital incoherent system for image reconstruction by using Zernike moments

Alfonso Padilla-Vivanco, Fermin-Solomon Granados-Agustin, Gonzalo Urcid-Serrano, Javier Baez-Rojas, John D. Gonglewski, Karin Stein
2004 Optics in Atmospheric Propagation and Adaptive Systems VI  
On the other hand, the reconstruction of the input image can be obtained from a discrete sum of the data matrices corresponding to the Zernike images weighted by suitable coefficients.  ...  The Zernike images acquired by the optical-digital system generate a basis set for the image reconstruction, which depends on both LCD and CCD sensor spatial resolution.  ...  Figure 3 : 3 are reconstructed with the basis image set of the Figure 2. The complex Zernike moments are numerically computed by using Ec. Input binary images a) and b).  ... 
doi:10.1117/12.514382 fatcat:r45jguelp5gj7cr4fusuoacq7m

Efficient Image Recognition Technique Using Invariant Moments and Principle Component Analysis

Mohammad Arafah, Qusay Abu Moghli
2017 Journal of Data Analysis and Information Processing  
We used twelve moments for each image of gray images and Hu's seven moments for color images to decrease dimensionality of the problem to 6 PCA's for gray and 5 PCA's for color images and hence the recognition  ...  In this research, we introduced image recognition using efficient invariant moments and Principle Component Analysis (PCA) for gray and color images using different number of invariant moments.  ...  Geometric Moments for any image function with all order exists, and the finite can reconstruct an image function from the set of Moments.  ... 
doi:10.4236/jdaip.2017.51001 fatcat:hx5tzmm2pjbolo7e5xctrbclke

On the accuracy of Zernike moments for image analysis

S.X. Liao, M. Pawlak
1998 IEEE Transactions on Pattern Analysis and Machine Intelligence  
In this paper, we give a detailed analysis of the accuracy of Zernike moments in terms of their discretization errors and the reconstruction power.  ...  It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain.  ...  IMAGE RECONSTRUCTION FROM $ A pq % & ' ( ) * In order to assess the performance of a set of image descriptors, one can look at their reconstruction power.  ... 
doi:10.1109/34.735809 fatcat:kjggupgcevcqlbfro6y727kpsu

Image Deconvolution in the Moment Domain [chapter]

Barmak Honarvar Shakibaei, Jan Flusser
2014 Gate to Computer Science and Research  
We propose a novel algorithm for image deconvolution from the geometric moments (GMs) of a degraded image by a circular or elliptical Gaussian point-spread function (PSF).  ...  In the proposed scheme, to show the invertibility of the moment equation in a closed form, we establish a relationship between the moments of the degraded image and the moments of the original image and  ...  Doing so, we obtain an who proposed a new and exact image reconstruction algorithms from a complete set of geometric moments based on the Stirling transform.  ... 
doi:10.15579/gcsr.vol1.ch5 fatcat:uixeeeypxvb2tg6247b3mkerma

Orthogonal Fourier–Mellin moments for invariant pattern recognition

Yunlong Sheng, Lixin Shen
1994 Optical Society of America. Journal A: Optics, Image Science, and Vision  
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.  ...  The orthogonal Fourier-Mellin moments may be thought of as generalized Zernike moments and orthogonalized complex moments.  ...  They are sensitive to noise and suffer from information suppression, loss, and redundancy. 2 From the uniqueness theorem of moments, an image is uniquely determined by its geometrical moments of all  ... 
doi:10.1364/josaa.11.001748 fatcat:jo3oickil5fhrfqppjnbcbtjdq

The RST invariant digital image watermarking using Radon transforms and complex moments

Hongqing Zhu, Min Liu, Yu Li
2010 Digital signal processing (Print)  
This approach achieves a set of completely invariant descriptors from the complex moments of the original image's Radon projection.  ...  The watermarking detection is as simple as computing a set of the proposed invariant features to illuminate the robustness problem under geometric image manipulations.  ...  This work has been supported by National Natural Science Foundation of China under Grant No. 60975004.  ... 
doi:10.1016/j.dsp.2010.01.010 fatcat:64l3dq3h7jfcldi2g47popj5lu
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