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In this research, we have proposed the central-symmetrical property of image reconstructions
from Zernike moments and pseudo-Zernike moments. We conducted the image reconstructions from the odd, even, and complete sets of
Zernike moments and pseudo-Zernike moments, and verified the proposed central-symmetrical property.
We have concluded that if th...
Contexts in source publication
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... V R pq (x, y) and V I pq (x, y) are the real and imaginary parts of V pq (x, y), respectively. Figure 1 shows an image divided into four quadrants, where the centre of the image is taken as the origin. Since the values of R pq (ρ) in each of the quadrants are symmetrical to either the x− or y−axis, we can calculate the values of V pq (ρ) in one quadrant, then obtain the values of the other three quadrants with conjugate transformation and sign changes. ...
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... columns highlighted by gold represent the even order sets of pseudo-Zernike moments, while the blue columns represent the odd order sets. Figure 10 shows some reconstructed Figure 4 (a) from the pseudo-Zernike moments with odd orders, even orders, and the complete orders, respectively. The corresponding PSNRs are illustrated in Table 4. ...
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... have also reconstructed Figure 4 (b) from the even and complete order sets and shown some results in Figure 11 and the corresponding PSNR values in Table 5. Figure 12 illustrates some reconstructed Figure 4 (c), which is centrally symmetrical, from even and complete order sets with 7 × 7 numerical scheme. ...
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... have also reconstructed Figure 4 (b) from the even and complete order sets and shown some results in Figure 11 and the corresponding PSNR values in Table 5. Figure 12 illustrates some reconstructed Figure 4 (c), which is centrally symmetrical, from even and complete order sets with 7 × 7 numerical scheme. ...
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... to the first column of Table 6, it shows that image reconstructions from even order sets are identical to those from corresponding order sets when the original image is centrally symmetrical. By observing the reconstructed images shown in Figure 10, Figure 11 and Figure 12, and Table 6, we have the same conclusion as we did for Zernike moments. If the original image Figure 10. ...
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... to the first column of Table 6, it shows that image reconstructions from even order sets are identical to those from corresponding order sets when the original image is centrally symmetrical. By observing the reconstructed images shown in Figure 10, Figure 11 and Figure 12, and Table 6, we have the same conclusion as we did for Zernike moments. If the original image Figure 10. ...
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... to the first column of Table 6, it shows that image reconstructions from even order sets are identical to those from corresponding order sets when the original image is centrally symmetrical. By observing the reconstructed images shown in Figure 10, Figure 11 and Figure 12, and Table 6, we have the same conclusion as we did for Zernike moments. If the original image Figure 10. ...
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... observing the reconstructed images shown in Figure 10, Figure 11 and Figure 12, and Table 6, we have the same conclusion as we did for Zernike moments. If the original image Figure 10. Image reconstructions from odd order sets of pseudo-Zernike moments in the first and second rows, those from even order sets in the third and fourth rows, and those from complete order sets in the last two rows. ...
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... centrally symmetrical, the reconstructed images from even order sets of pseudo-Zernike moments are identical to those from the corresponding complete order sets of pseudo-Zernike moments. Figure 11. Image reconstructions from even order sets of pseudo-Zernike moments in the first and second rows, and those from complete order sets in the last two rows. ...
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... reconstructions from even order sets of pseudo-Zernike moments in the first and second rows, and those from complete order sets in the last two rows. Figure 12. Image reconstructions from even order sets in the first and second rows, and those from complete order sets in the last two rows. ...
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Citations
... All in all, ZMs because of its numerous advantages: good retrieval accuracy, compact features, low computation complexity, robust retrieval performance and hierarchical coarse to fine representation, has been successful applied in various image processing applications like optical character recognition [22,23], object recognition and pattern classification [24][25][26][27][28], content-based image retrieval [29][30][31][32], image watermarking [33][34][35], image reconstruction [36][37][38], palmprint and iris verification [39,40], image denoising [41], image super-resolution [42], and biomedical image segmentation [43]. Moreover, ZMs is capable enough to extract both texture and shape features from an image with very less number of features as compared to LDEP, ULBP and LBP. ...
Success of any image retrieval system depends heavily on the feature extraction capability of its feature descriptor. In this paper, we present a biomedical image retrieval system which uses Zernike moments (ZMs) for extracting features from CT and MRI medical images. ZMs belong to the class of orthogonal rotation invariant moments (ORIMs) and possess very useful characteristics such as superior information representation capability with minimum redundancy, insensitivity to image noise etc. Existence of these properties as well as the ability of lower order ZMs to discriminate between different image shapes and textures motivated us to explore ZMs for biomedical retrieval application. To prove the effectiveness of our system, experiments have been carried out on both noise-free and noisy versions of two different medical databases i.e. Emphysema-CT database for CT image retrieval and OASIS-MRI database for MRI image retrieval. The proposed ZMs-based approach has been compared with the existing and recently published approaches based on local binary pattern (LBP), local ternary patterns (LTP), local diagonal extrema pattern (LDEP), etc., in terms of various evaluation measures like ARR, ARP, F _ score, and mAP. The results after being investigated have shown a significant improvement (10–14% and 15–17% in case of noise-free and noisy images, respectively) in comparison to the state-of-the-art techniques on the respective databases.
... The low order ZMs are mainly used in applications including optical character recognition [2,3], object recognition and pattern classification [4][5][6][7][8], content based image retrieval [9][10][11][12], 2D/3D object recognition through sketches [13,14], estimation of rotation angle between images and determination of image symmetry [15][16][17], image denoising [18], image super-resolution [19], etc. While, the high order moments are mainly used in biometric studies where identification and classification of human characteristics involves subtle and complex patterns. Therefore, high order ZMs are used in palmprint verification [20], recognition of facial information [21], hand shape verification [22], etc. Apart from biometric identification, high order ZMs are used in applications like image watermarking [23][24][25] and image reconstruction [26][27][28][29]. ...
