Efficient computations for generalized Zernike moments and image recovery

Deng, An-Wen; Gwo, Chih-Ying

doi:10.1016/j.amc.2018.07.029

Cited by 7 publications

(12 citation statements)

References 17 publications

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“…3 was originally given in terms of Jacobi polynomials as described in ( Szegõ, 1939 ), but different calculation methods of 3D Zernike radial polynomial have been proposed ( Deng and Gwo, 2020 ). In our work, the R nℓ is computed recursively, similar to the Kintner’s P -method in the case of 2D Zernike polynomials ( Kintner, 1976 ; Deng and Gwo, 2018b ), and is presented in Eq. 10.…”

Section: Methods and Resultsmentioning

confidence: 99%

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Brain white matter hyperintensity lesion characterization in 3D T2 fluid-attenuated inversion recovery magnetic resonance images: Shape, texture, and their correlations with potential growth

Gwo

Zhu²,

Zhang³

2022

Front. Neurosci.

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Analyses of age-related white matter hyperintensity (WMH) lesions manifested in T2 fluid-attenuated inversion recovery (FLAIR) magnetic resonance images (MRI) have been mostly on understanding the size and location of the WMH lesions and rarely on the morphological characterization of the lesions. This work extends our prior analyses of the morphological characteristics and texture of WMH from 2D to 3D based on 3D T2 FLAIR images. 3D Zernike transformation was used to characterize WMH shape; a fuzzy logic method was used to characterize the lesion texture. We then clustered 3D WMH lesions into groups based on their 3D shape and texture features. A potential growth index (PGI) to assess dynamic changes in WMH lesions was developed based on the image texture features of the WMH lesion penumbra. WMH lesions with various sizes were segmented from brain images of 32 cognitively normal older adults. The WMH lesions were divided into two groups based on their size. Analyses of Variance (ANOVAs) showed significant differences in PGI among WMH shape clusters (P = 1.57 × 10–3 for small lesions; P = 3.14 × 10–2 for large lesions). Significant differences in PGI were also found among WMH texture group clusters (P = 1.79 × 10–6). In conclusion, we presented a novel approach to characterize the morphology of 3D WMH lesions and explored the potential to assess the dynamic morphological changes of WMH lesions using PGI.

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Section: Methods and Resultsmentioning

confidence: 99%

“…When M is large enough, the function f M can be used to approximate the original image f ( Deng and Gwo, 2018b ). For a binary shape with the background represented by 0, the error rate ℰ r between the original image f and the reconstructed f M can be calculated by…”

Section: Methods and Resultsmentioning

confidence: 99%

Brain white matter hyperintensity lesion characterization in 3D T2 fluid-attenuated inversion recovery magnetic resonance images: Shape, texture, and their correlations with potential growth

Gwo

Zhu²,

Zhang³

2022

Front. Neurosci.

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“…This 3D recursive formula can be regarded as similar to the Kintner's p-method used in the case of 2D Zernike polynomials [22,30]. For the completeness, we provide a proof.…”

Section: D Zernike and 3d Zernike Momentsmentioning

confidence: 95%

“…For a non-negative integer 𝑛 (called order) and an integer 𝑚 (called repetition) for which |𝑚| ≤ 𝑛 and 𝑛 ≡ 𝑚 (mod 2), the 2D Zernike polynomials 𝑉 𝑛𝑚 (𝑧) is the product of 2D Zernike radial polynomial 𝑅 𝑛𝑚 2𝐷 (𝑟) defined over I and the complex exponential function e 𝑖𝑚𝜃 = cos 𝑚𝜃 + 𝑖 sin 𝑚𝜃 defined over the unit circle 𝑆 1 , where 𝑧 = 𝑟𝑒 𝑖𝜃 ∈ 𝐷 stands for a complex number, 𝑟 is its distance to the origin (0, 0) and 𝜃 is the angle from the x-axis. The computations of 2D Zernike polynomials, Zernike moments and their variants were comprehensively studied in [17,[27][28][29][30].…”

Section: D Zernike and 3d Zernike Momentsmentioning

confidence: 99%

Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

Deng¹,

Gwo²

2021

Preprint

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3D Zernike moments based on 3D Zernike polynomials have been successfully applied to the field of voxelized 3D shape retrieval and have attracted more attention in biomedical image processing. As the order of 3D Zernike moments increases, both computational efficiency and numerical accuracy decrease. Due to this phenomenon, a more efficient and stable method for computing high-order 3D Zernike moments was proposed in this study. The proposed recursive formula for computing 3D Zernike radial polynomials combines the recursive calculation of spherical harmonics to develop a voxel-based algorithm for the calculation of 3D Zernike moments. The algorithm was applied to the 3D shape Michelangelo's David with a size of 150×150×150 voxels. As compared to the method without additional acceleration, the proposed method uses a group action of order sixteen orthogonal group and saving unnecessary iterations, the factor of speed-up is 56.783±3.999 when the order of Zernike moments is between 10 and 450. The proposed method also obtained an accurate reconstructed shape with the error rate (normalized mean square error) of 0.00 (4.17×10^-3) when the reconstruction was computed for all moments up to order 450.

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“…In addition, it optimizes the radial polynomial of Zernike moments to reduce computation. Deng and Gwo [27] proposed a generalized Zernike moments method to calculate high-order generalized Zernike moment; the corresponding improvement is made to get the solution that the algorithm was slow in determining the edge point.…”

Section: Introductionmentioning

confidence: 99%

An Improved Canny-Zernike Subpixel Detection Algorithm

Wang

Huang

et al. 2022

Wireless Communications and Mobile Computing

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This paper proposed a new subpixel detection method that detects subpixel edges directly, as opposed to the previous method, which requires crossing the entire image. It shows superior subpixel detection on the edge directly, which enhances subpixel edge detection speed significantly. In order to overcome the problem of noise reduction, this paper employs bilateral filtering. The method first performed coarse localization with the improved operator to determine the coordinates and gradient direction of the edge points. Then, the Zernike moment algorithm was used for subpixel repositioning of edge points. Finally, subpixel level edge positioning of the image is obtained. The detection algorithm is used to identify the edges of large-size workpieces, and the results reveal that the approach has superior positioning accuracy, noise immunity, and fast detection speed.

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Efficient computations for generalized Zernike moments and image recovery

Cited by 7 publications

References 17 publications

Brain white matter hyperintensity lesion characterization in 3D T2 fluid-attenuated inversion recovery magnetic resonance images: Shape, texture, and their correlations with potential growth

Brain white matter hyperintensity lesion characterization in 3D T2 fluid-attenuated inversion recovery magnetic resonance images: Shape, texture, and their correlations with potential growth

Efficient and Stable Voxel-Based Algorithm for Computing 3D Zernike Moments and Shape Reconstruction

An Improved Canny-Zernike Subpixel Detection Algorithm

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