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1

Miller, J. W. V., J. B. Farison, and Y. Shin. "Spatially invariant image sequences." IEEE Transactions on Image Processing 1, no. 2 (1992): 148–61. http://dx.doi.org/10.1109/83.136592.

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2

El Mir, Ghina, Karim Youssef, and Chady El Mir. "Conformal Image Viewpoint Invariant." Mathematics 12, no. 16 (2024): 2551. http://dx.doi.org/10.3390/math12162551.

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In this paper, we introduce an invariant by image viewpoint changes by applying an important theorem in conformal geometry stating that every surface of the Minkowski space R3,1 leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ∐αHα of R3,1 by means of the powerful tools of the conformal Clifford algebras. We explain that every viewpoint change is given by a planar similarity and a perspective distortion encoded by the latitude angle of the camera. We model the perspective distortion by the point at infinity of
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3

Kejia Wang, Kejia Wang, Ziliang Ping Ziliang Ping, and and Yunlong Sheng and Yunlong Sheng. "Development of image invariant moments—a short overview." Chinese Optics Letters 14, no. 9 (2016): 091001–91011. http://dx.doi.org/10.3788/col201614.091001.

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4

Wang, Mei, E. Ye Wang, and Guo Hua Pan. "Image Quality Assessment Based on Invariant Moments Similarity." Advanced Materials Research 546-547 (July 2012): 565–69. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.565.

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To resolve the problems of the image quality assessment issue and the algorithm adaptability for different image size and deformation, this paper proposes a image quality assessment algorithm based on Invariant Moments Similarity. Firstly, Hu invariant moments values of original image and evaluated image are computed. Secondly the invariant moments distance is completed between original image and evaluated image. At last, the method assess the restoration image quality depend on the invariant moment distance. The experimental result shows that the algorithm result is better than MSE, PSNR, SSI
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5

Levkovitz, J., E. Oron, and M. Tur. "Position-invariant, rotation-invariant, and scale-invariant process for binary image recognition." Applied Optics 36, no. 14 (1997): 3035. http://dx.doi.org/10.1364/ao.36.003035.

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6

Zhang, Li, Gong-bin Qian, Wei-wei Xiao, and Zhen Ji. "Geometric invariant blind image watermarking by invariant Tchebichef moments." Optics Express 15, no. 5 (2007): 2251. http://dx.doi.org/10.1364/oe.15.002251.

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7

Rodríguez, Mariano, Julie Delon, and Jean-Michel Morel. "Fast Affine Invariant Image Matching." Image Processing On Line 8 (September 24, 2018): 251–81. http://dx.doi.org/10.5201/ipol.2018.225.

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8

Dinggang Shen and H. H. S. Ip. "Generalized affine invariant image normalization." IEEE Transactions on Pattern Analysis and Machine Intelligence 19, no. 5 (1997): 431–40. http://dx.doi.org/10.1109/34.589203.

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9

Xie, Lingxi, Jingdong Wang, Weiyao Lin, Bo Zhang, and Qi Tian. "Towards Reversal-Invariant Image Representation." International Journal of Computer Vision 123, no. 2 (2016): 226–50. http://dx.doi.org/10.1007/s11263-016-0970-x.

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10

Singh, Chandan, and Sukhjeet K. Ranade. "Rotation invariant moments and transforms for geometrically invariant image watermarking." Journal of Electronic Imaging 22, no. 1 (2013): 013034. http://dx.doi.org/10.1117/1.jei.22.1.013034.

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11

Pham, Nam, Jong-Weon Lee, Goo-Rak Kwon, and Chun-Su Park. "Hybrid Image-Retrieval Method for Image-Splicing Validation." Symmetry 11, no. 1 (2019): 83. http://dx.doi.org/10.3390/sym11010083.

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Recently, the task of validating the authenticity of images and the localization of tampered regions has been actively studied. In this paper, we go one step further by providing solid evidence for image manipulation. If a certain image is proved to be the spliced image, we try to retrieve the original authentic images that were used to generate the spliced image. Especially for the image retrieval of spliced images, we propose a hybrid image-retrieval method exploiting Zernike moment and Scale Invariant Feature Transform (SIFT) features. Due to the symmetry and antisymmetry properties of the
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12

Liu, Ruoyu, Yao Zhao, Shikui Wei, Liang Zheng, and Yi Yang. "Modality-Invariant Image-Text Embedding for Image-Sentence Matching." ACM Transactions on Multimedia Computing, Communications, and Applications 15, no. 1 (2019): 1–19. http://dx.doi.org/10.1145/3300939.

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13

Prasad K, Durga, Manjunathachari K, and Giri Prasad M.N. "Orientation Feature Transform Model for Image Retrieval in Sketch Based Image Retrieval System." International Journal of Engineering & Technology 7, no. 2.24 (2018): 159. http://dx.doi.org/10.14419/ijet.v7i2.24.12022.

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This paper focus on Image retrieval using Sketch based image retrieval system. The low complexity model for image representation has given the sketch based image retrieval (SBIR) a optimal selection for next generation application in low resource environment. The SBIR approach uses the geometrical region representation to describe the feature and utilize for recognition. In the SBIR model, the features represented define the image. Towards the improvement of SBIR recognition performance, in this paper a new invariant modeling using “orientation feature transformed modeling” is proposed. The ap
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14

Zatserkovnyi, R. H. "Scale-invariant image feature transformation technology." Book Qualilogy 1, no. 37 (2020): 74–78. http://dx.doi.org/10.32403/2411-3611-2020-1-37-74-78.

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15

CAI, Guo-Rong, Shao-Zi LI, Yun-Dong WU, Song-Zhi SU, and Shui-Li CHEN. "A Perspective Invariant Image Matching Algorithm." Acta Automatica Sinica 39, no. 7 (2014): 1053–61. http://dx.doi.org/10.3724/sp.j.1004.2013.01053.

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16

Kofoed, Bart, Eric Janssen, and Peter H. N. de With. "Multi-Image Sparse Motion-Invariant Photography." Electronic Imaging 2016, no. 18 (2016): 1–6. http://dx.doi.org/10.2352/issn.2470-1173.2016.18.dpmi-030.

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17

Shyam, Pranjay, Kuk-Jin Yoon, and Kyung-Soo Kim. "Towards Domain Invariant Single Image Dehazing." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (2021): 9657–65. http://dx.doi.org/10.1609/aaai.v35i11.17162.

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Presence of haze in images obscures underlying information, which is undesirable in applications requiring accurate environment information. To recover such an image, a dehazing algorithm should localize and recover affected regions while ensuring consistency between recovered and its neighboring regions. However owing to fixed receptive field of convolutional kernels and non uniform haze distribution, assuring consistency between regions is difficult. In this paper, we utilize an encoder-decoder based network architecture to perform the task of dehazing and integrate an spatially aware channe
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18

Hyung Shin Kim and Heung-Kyu Lee. "Invariant image watermark using zernike moments." IEEE Transactions on Circuits and Systems for Video Technology 13, no. 8 (2003): 766–75. http://dx.doi.org/10.1109/tcsvt.2003.815955.

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19

Li, Meng, and Subhashis Ghosal. "Fast Translation Invariant Multiscale Image Denoising." IEEE Transactions on Image Processing 24, no. 12 (2015): 4876–87. http://dx.doi.org/10.1109/tip.2015.2470601.

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20

Rister, Blaine, Mark A. Horowitz, and Daniel L. Rubin. "Volumetric Image Registration From Invariant Keypoints." IEEE Transactions on Image Processing 26, no. 10 (2017): 4900–4910. http://dx.doi.org/10.1109/tip.2017.2722689.

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21

Khotanzad, A., and Y. H. Hong. "Invariant image recognition by Zernike moments." IEEE Transactions on Pattern Analysis and Machine Intelligence 12, no. 5 (1990): 489–97. http://dx.doi.org/10.1109/34.55109.

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22

Flusser, J., and T. Suk. "Degraded image analysis: an invariant approach." IEEE Transactions on Pattern Analysis and Machine Intelligence 20, no. 6 (1998): 590–603. http://dx.doi.org/10.1109/34.683773.

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23

Fienup, J. R. "Invariant error metrics for image reconstruction." Applied Optics 36, no. 32 (1997): 8352. http://dx.doi.org/10.1364/ao.36.008352.

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24

ZENG, FANPING, KESONG YAN, and GENGRONG ZHANG. "Pre-image pressure and invariant measures." Ergodic Theory and Dynamical Systems 27, no. 03 (2007): 1037. http://dx.doi.org/10.1017/s0143385706000812.

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25

Patra, Prashant Kumar. "Neural Network for Invariant Image Classification." IETE Journal of Research 42, no. 4-5 (1996): 281–90. http://dx.doi.org/10.1080/03772063.1996.11415934.

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26

Drew, Mark S., Chao Chen, Steven D. Hordley, and Graham D. Finlayson. "Sensor Transforms for Invariant Image Enhancement." Color and Imaging Conference 10, no. 1 (2002): 325–30. http://dx.doi.org/10.2352/cic.2002.10.1.art00060.

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27

Han, Ju, and Kai-Kuang Ma. "Rotation-invariant and scale-invariant Gabor features for texture image retrieval." Image and Vision Computing 25, no. 9 (2007): 1474–81. http://dx.doi.org/10.1016/j.imavis.2006.12.015.

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28

Xu, Guang Zhu, Bang Jun Lei, Jing Jing Zhao, and Chun Lin Li. "Using LBP to Improve PCNN Performance for Texture Image Retrieval." Applied Mechanics and Materials 530-531 (February 2014): 480–88. http://dx.doi.org/10.4028/www.scientific.net/amm.530-531.480.

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Local binary pattern (LBP) spectrum is a powerful feature for texture image, which is invariant to local illumination changes. Pulse coupled neural network (PCNN) is a biologically inspired algorithm, which is well suited for image processing and can generate rotation, scale, translation invariant image signature. This paper proposed an image retrieval tool named LBP-PCNN which combined the advantages of LBP and PCNN. First, images are mapped into local structural domain with rotation invariant LBP. Then, the simplified PCNN was adapted to extract the image signature in structural domain. At l
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29

Su, Ching-Liang. "Object Identification by Signal Gain and Correlation." International Journal of Mathematical Models and Methods in Applied Sciences 16 (January 12, 2022): 12–22. http://dx.doi.org/10.46300/9101.2022.16.3.

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In this study, “ring rotation invariant transform” techniques are used to add more salient feature to the original images. The “ring rotation invariant transform” can solve image rotation problem, which transfers a ring signal to several signal vectors in the complex domain, whereby to generate invariant magnitude. Matrix correlation is employed to combine these magnitudes to generate the various discriminators, by which to identify objects. For managing image-shifting problem, one pixel in sample image is compared with surrounding pixels of unknown image. The comparison approaching in this st
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30

Wang, ZM, M. Li, C. Gao, and XM Jin. "LCS-based Visual Recognition for AGV Guide Paths under Complex Illumination Conditions." Journal of Physics: Conference Series 2476, no. 1 (2023): 012069. http://dx.doi.org/10.1088/1742-6596/2476/1/012069.

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Abstract Complex lighting is one of the most challenging problems in automatic guided vehicle (AGV) vision recognition system. In order to overcome the influence of uneven illumination on the accuracy and robustness of path recognition, this paper proposes the LCS based visual recognition for AGV guide paths under complex illumination conditions method, which converts the collected image into an invariant image through logarithmic chromaticity space (LCS) to eliminate the influence of illumination, and the minimum average entropy angle is used as the projection angle to generate the invariant
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31

Tzimiropoulos, G., V. Argyriou, S. Zafeiriou, and T. Stathaki. "Robust FFT-Based Scale-Invariant Image Registration with Image Gradients." IEEE Transactions on Pattern Analysis and Machine Intelligence 32, no. 10 (2010): 1899–906. http://dx.doi.org/10.1109/tpami.2010.107.

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32

Shao, Yuanjie, Nong Sang, Juncai Peng, and Changxin Gao. "Joint Image Deblurring and Matching with Blurred Invariant-Based Sparse Representation Prior." Complexity 2019 (October 31, 2019): 1–12. http://dx.doi.org/10.1155/2019/3829263.

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Image matching is important for vision-based navigation. However, most image matching approaches do not consider the degradation of the real world, such as image blur; thus, the performance of image matching often decreases greatly. Recent methods try to deal with this problem by utilizing a two-stage framework—first resorting to image deblurring and then performing image matching, which is effective but depends heavily on the quality of image deblurring. An emerging way to resolve this dilemma is to perform image deblurring and matching jointly, which utilize sparse representation prior to ex
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33

Honarvar Shakibaei, Barmak, and Peyman Jahanshahi. "Image Deconvolution by Means of Frequency Blur Invariant Concept." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/951842.

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Different blur invariant descriptors have been proposed so far, which are either in the spatial domain or based on the properties available in the moment domain. In this paper, a frequency framework is proposed to develop blur invariant features that are used to deconvolve a degraded image caused by a Gaussian blur. These descriptors are obtained by establishing an equivalent relationship between the normalized Fourier transforms of the blurred and original images, both normalized by their respective fixed frequencies set to one. Advantage of using the proposed invariant descriptors is that it
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34

Bez, H. E. "The invariant functions and invariant-image conditions of the rational Bézier triangles." Applicable Algebra in Engineering, Communication and Computing 23, no. 3-4 (2012): 195–205. http://dx.doi.org/10.1007/s00200-012-0174-8.

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35

Lata, Hem, та P. K. Sharma. "On the translational invariant intuitionistic fuzzy subset of a Γ-ring". Notes on Intuitionistic Fuzzy Sets 28, № 1 (2022): 11–22. http://dx.doi.org/10.7546/nifs.2022.28.1.11-22.

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In this paper, we introduce the notion of translational invariant intuitionistic fuzzy subset of a Γ-ring and generalize some notions of a ring to a Γ-ring. Also, we define ideals of a Γ-ring generated by an intuitionistic fuzzy subset with an element of Γ-ring and study their properties. The notion of units, associate, prime element, irreducible element are also generalized with respect to the intuitionistic fuzzy subset of a Γ-ring. Further, we study the properties of homomorphic image and pre-image of translational invariant intuitionistic fuzzy subset under the Γ-ring homomorphism and we p
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36

Chen, Xiu Xin, Ke Bin Jia, Chong Chong Yu, and Shiang Wei. "A New Image Affine-Invariant Region Detector and Descriptor." Applied Mechanics and Materials 130-134 (October 2011): 2911–14. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2911.

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To solve the problems that exist in present affine-invariant region detection and description methods, a new affine-invariant region detector and descriptor are proposed in this paper. First, affine-invariant regions in an image are detected using a connected-region based method. And then a vector composed of a group of affine invariant moments is adopted to descript the regions. Experiments show the effectiveness and robustness of the method. It is also very fast.
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37

LI, QIAOLIANG, HUISHENG ZHANG, and TIANFU WANG. "SCALE INVARIANT FEATURE MATCHING USING ROTATION-INVARIANT DISTANCE FOR REMOTE SENSING IMAGE REGISTRATION." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 02 (2013): 1354004. http://dx.doi.org/10.1142/s0218001413540049.

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Scale invariant feature transform (SIFT) has been widely used in image matching. But when SIFT is introduced in the registration of remote sensing images, the keypoint pairs which are expected to be matched are often assigned two different value of main orientation owing to the significant difference in the image intensity between remote sensing image pairs, and therefore a lot of incorrect matches of keypoints will appear. This paper presents a method using rotation-invariant distance instead of Euclid distance to match the scale invariant feature vectors associated with the keypoints. In the
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38

Pawlak, Mirosław, Gurmukh Singh Panesar, and Marcin Korytkowski. "A Novel Method for Invariant Image Reconstruction." Journal of Artificial Intelligence and Soft Computing Research 11, no. 1 (2021): 69–80. http://dx.doi.org/10.2478/jaiscr-2021-0005.

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AbstractIn this paper we propose a novel method for invariant image reconstruction with the properly selected degree of symmetry. We make use of Zernike radial moments to represent an image due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image. The regularized ridge regression estimation strategy under symmetry constraints for estimating Zernike moments is proposed. This extended regularization problem allows us to enforces the bilateral symmetry in the reconstructed object. This is achieved by the proper choice o
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39

FENG, Deying, Jie YANG, Cheng YANG, and Congxin LIU. "Image Retrieval with Scale Invariant Visual Phrases." IEICE Transactions on Information and Systems E96.D, no. 5 (2013): 1063–67. http://dx.doi.org/10.1587/transinf.e96.d.1063.

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40

Liang, Zhuoqian, Bingwen Feng, Xuba Xu, Xiaotian Wu, and Tao Yang. "Geometrically Invariant Image Watermarking Using Histogram Adjustment." International Journal of Digital Crime and Forensics 10, no. 1 (2018): 54–66. http://dx.doi.org/10.4018/ijdcf.2018010105.

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In this article, a blind image watermarking scheme, which is a robust against common image processing and geometric attacks is proposed by adopting the concept of histogram-based embedding. The average filter is employed to low-pass pre-filter the host image. The watermark bits are embedded into the histogram of the low-frequency component and the template bits are embedded in the high-frequency residual. The embedding is performed by adjusting the value of two consecutive histogram bins. Furthermore, a post-quantization is employed after the embedding round to improve robustness. All pixel mo
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41

Yang, Yi, and Shawn Newsam. "Geographic Image Retrieval Using Local Invariant Features." IEEE Transactions on Geoscience and Remote Sensing 51, no. 2 (2013): 818–32. http://dx.doi.org/10.1109/tgrs.2012.2205158.

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42

Zhang, Hua, Li Jia Wang, Zhen Jie Wang, and Wei Yi Yuan. "View-Invariant Face Detection for Colorful Image." Advanced Materials Research 945-949 (June 2014): 1880–84. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.1880.

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To overcome illumination changes and pose variations, a pose-invariant face detection method is presented. First, an illumination compensation method based on reference white is presented to overcome the lighting variations. The reference white is obtained according to the component Y from YCbCr color space. Then, a mixture face model is constructed by the Cb and Cr from YCbCr color space and H from the HSV color space to extract faces from colorful image. At last, an eyes model is designed to locate eyes in the obtained face images, which can distinguish face from neck and arms ultimately. Th
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43

Ismail. "Invariant Image Watermarking Using Accurate Zernike Moments." Journal of Computer Science 6, no. 1 (2010): 52–59. http://dx.doi.org/10.3844/jcssp.2010.52.59.

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44

Kim, Hyungshin. "Robust image watermarking using local invariant features." Optical Engineering 45, no. 3 (2006): 037002. http://dx.doi.org/10.1117/1.2181887.

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45

Moiseenko, G. A., S. V. Pronin, and Yu E. Shelepin. "Investigation of scale-invariant image classification mechanisms." Journal of Optical Technology 86, no. 11 (2019): 729. http://dx.doi.org/10.1364/jot.86.000729.

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46

Al-Temeemy, Ali A., and Joseph W. Spencer. "Laser radar invariant spatial chromatic image descriptor." Optical Engineering 53, no. 12 (2014): 123109. http://dx.doi.org/10.1117/1.oe.53.12.123109.

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47

Vonesch, Cédric, Frédéric Stauber, and Michael Unser. "Steerable PCA for Rotation-Invariant Image Recognition." SIAM Journal on Imaging Sciences 8, no. 3 (2015): 1857–73. http://dx.doi.org/10.1137/15m1014930.

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48

Shen, Lixin. "Noncentral image moments for invariant pattern recognition." Optical Engineering 34, no. 11 (1995): 3181. http://dx.doi.org/10.1117/12.213614.

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49

Li, Qiaoliang, Huisheng Zhang, and Tianfu Wang. "Multispectral Image Matching Using Rotation-Invariant Distance." IEEE Geoscience and Remote Sensing Letters 8, no. 3 (2011): 406–10. http://dx.doi.org/10.1109/lgrs.2010.2080351.

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50

Hameed, Vazeerudeen Abdul. "Orthogonal Moment Invariant Function for Image Processing." Journal of Computational and Theoretical Nanoscience 16, no. 8 (2019): 3400–3403. http://dx.doi.org/10.1166/jctn.2019.8299.

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Orthogonal moments are of great importance in image processing due to their high discriminatory capability. Orthogonal moment invariant functions like Legendre moments and Complex Zernike moments are known for high computational complexity and/or they are complex valued. This paper presents a new orthogonal moment function that is real valued. The formulation is appraised to prove that it is computationally less complex when compared to the existing moment functions. The proposed orthogonal moment functions are appraised over their reversible nature to obtain the original data. The new moment
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