+publisher:"University of South Carolina" +contributor:("Lili Ju")

University of South Carolina

1. Tatano, Rosalia. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.

Degree: MS, Mathematics, 2013, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/1613

► In this thesis we solve two-dimensional linear parabolic partial differential equations with pure Dirichelet boundary conditions, using the bilinear covolume-upwind finite volume method on… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; Crank-Nicolson; finite volume methods; linear parabolic PDE

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APA (6^th Edition):

Tatano, R. (2013). Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/1613

Chicago Manual of Style (16^th Edition):

Tatano, Rosalia. “Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.” 2013. Masters Thesis, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/1613.

MLA Handbook (7^th Edition):

Tatano, Rosalia. “Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations.” 2013. Web. 17 Apr 2021.

Vancouver:

Tatano R. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. [Internet] [Masters thesis]. University of South Carolina; 2013. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/1613.

Council of Science Editors:

Tatano R. Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations. [Masters Thesis]. University of South Carolina; 2013. Available from: https://scholarcommons.sc.edu/etd/1613

University of South Carolina

2. Kiplagat, Meshack K. The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations.

Degree: MS, Mathematics, 2013, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/2515

► In this thesis we apply the compact implicit integration factor (cIIF) scheme towards solving the Allen-Cahn equations with zero-flux or periodic boundary conditions. The… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; Allen-Cahn; central differencing method; compact implicit integration factor; diffusion-reaction; implicit approximation

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APA (6^th Edition):

Kiplagat, M. K. (2013). The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/2515

Chicago Manual of Style (16^th Edition):

Kiplagat, Meshack K. “The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations.” 2013. Masters Thesis, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/2515.

MLA Handbook (7^th Edition):

Kiplagat, Meshack K. “The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations.” 2013. Web. 17 Apr 2021.

Vancouver:

Kiplagat MK. The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations. [Internet] [Masters thesis]. University of South Carolina; 2013. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/2515.

Council of Science Editors:

Kiplagat MK. The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations. [Masters Thesis]. University of South Carolina; 2013. Available from: https://scholarcommons.sc.edu/etd/2515

University of South Carolina

3. Yuan, Shuai. An Ensemble-Based Projection Method and Its Numerical Investigation.

Degree: PhD, Mathematics, 2020, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/5777

► In many cases, partial differential equation (PDE) models involve a set of parameters whose values may vary over a wide range in application problems,… (more)

Subjects/Keywords: Mathematics; partial differential equation; numerical simulations; Navier-Stokes equations; Navier-Stokes

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APA (6^th Edition):

Yuan, S. (2020). An Ensemble-Based Projection Method and Its Numerical Investigation. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/5777

Chicago Manual of Style (16^th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Doctoral Dissertation, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/5777.

MLA Handbook (7^th Edition):

Yuan, Shuai. “An Ensemble-Based Projection Method and Its Numerical Investigation.” 2020. Web. 17 Apr 2021.

Vancouver:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Internet] [Doctoral dissertation]. University of South Carolina; 2020. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/5777.

Council of Science Editors:

Yuan S. An Ensemble-Based Projection Method and Its Numerical Investigation. [Doctoral Dissertation]. University of South Carolina; 2020. Available from: https://scholarcommons.sc.edu/etd/5777

University of South Carolina

4. Zhang, Chenfei. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.

Degree: PhD, Mathematics, 2019, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/5445

► Many problems in the fields of science and engineering, particularly in materials science and fluid dynamic, involve flows with multiple phases and components. From… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; numerical solutions; two-phase diffuse interface model; Peng-Robinson equation of state; unconditional energy stabilities; invariant energy quadratization approach; temporal semi-discretizations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhang, C. (2019). Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/5445

Chicago Manual of Style (16^th Edition):

Zhang, Chenfei. “Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.” 2019. Doctoral Dissertation, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/5445.

MLA Handbook (7^th Edition):

Zhang, Chenfei. “Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State.” 2019. Web. 17 Apr 2021.

Vancouver:

Zhang C. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. [Internet] [Doctoral dissertation]. University of South Carolina; 2019. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/5445.

Council of Science Editors:

Zhang C. Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State. [Doctoral Dissertation]. University of South Carolina; 2019. Available from: https://scholarcommons.sc.edu/etd/5445

University of South Carolina

5. Zhou, Youjie. Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods.

Degree: PhD, Computer Science and Engineering, 2015, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/3633

► Propagated image segmentation is the problem of utilizing the existing segmentation of an image for obtaining a new segmentation of, either a neighboring image… (more)

▼ Propagated image segmentation is the problem of utilizing the existing segmentation of an image for obtaining a new segmentation of, either a neighboring image in a sequence, or the same image but in different scales. We name these two cases as the inter-image propagation and the intra-image propagation respectively. The inter-image propagation is particularly important to material science, where efficient and accurate segmentation of a sequence of 2D serial-sectioned images of 3D material samples is an essential step to understand the underlying micro-structure and related physical properties. For natural images with objects in different scales, the intra-image propagation, where segmentations are propagated from the finest scale to coarser scales, is able to better capture object boundaries than single-shot segmentations on a fixed image scale. In this work, we first propose an inter-image propagation method named Edge- Weighted Centroid Voronoi Tessellation with Propagation of Consistency Constraint (CCEWCVT) to effectively segment material images. CCEWCVT segments an image sequence by repeatedly propagating a 2D segmentation from one slice to another, and in each step of this propagation, we apply the proposed consistency constraint in the pixel clustering process such that stable structures identified from the previous slice can be well-preserved. We further propose a non-rigid transformation based association method to find the correspondence of propagated stable structures in the next slice when the inter-image distance becomes large. We justify the effectiveness of the proposed CCEWCVT method on 3D material image sequences, and we compare its performance against several state-of-the-art 2D, 3D, propagated segmentation methods. Then for the intra-image propagation, we propose a superpixel construction method named Hierarchical Edge-Weighted Centroidal Voronoi Tessellation (HEWCVT) to accurately capture object boundaries in natural images. We model the problem as a multilevel clustering process: superpixels in one level are clustered to obtain larger size superpixels in the next level. The clustering energy involves both color similarities and the proposed boundary smoothness of superpixels. We further extend HEWCVT to obtain supervoxels on 3D images or videos. Both quantitative and qualitative evaluation results on several standard datasets show that the proposed HEWCVT method achieves superior or comparable performances to other state-of-the-art methods. vi Advisors/Committee Members: Song Wang, Lili Ju.

Subjects/Keywords: Computer Sciences; Engineering; Image Segmentation; Edge-Weighted; Centroidal Voronoi Tessellation; based Methods

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhou, Y. (2015). Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/3633

Chicago Manual of Style (16^th Edition):

Zhou, Youjie. “Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods.” 2015. Doctoral Dissertation, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/3633.

MLA Handbook (7^th Edition):

Zhou, Youjie. “Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods.” 2015. Web. 17 Apr 2021.

Vancouver:

Zhou Y. Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods. [Internet] [Doctoral dissertation]. University of South Carolina; 2015. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/3633.

Council of Science Editors:

Zhou Y. Propagated image Segmentation Using Edge-Weighted Centroidal Voronoi Tessellation based Methods. [Doctoral Dissertation]. University of South Carolina; 2015. Available from: https://scholarcommons.sc.edu/etd/3633

6. Cao, Yu. 3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods.

Degree: PhD, Computer Science and Engineering, 2013, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/2349

► Accurate grain segmentation on 3D superalloy images is very important in materials science and engineering. From grain segmentation, we can derive the underlying superalloy… (more)

▼ Accurate grain segmentation on 3D superalloy images is very important in materials science and engineering. From grain segmentation, we can derive the underlying superalloy grains' micro-structures, based on which many important physical, mechanical and chemical properties of the superalloy samples can be evaluated. However, grain segmentation is usually a very challenging problem since: 1) even a small 3D superalloy sample may contain hundreds of grains; 2) carbides and noises may degrade the imaging quality; and 3) the intensity within a grain may not be homogeneous. In addition, the same grain may present different appearances, i.e. intensities, under different microscope settings. In practice, a 3D superalloy image may contain multichannel information where each channel corresponds to a specific microscope setting. In this work, we develop a Multichannel Edge-Weighted Centroidal Voronoi Tessellation (MCEWCVT) algorithm to effectively and robustly segment the superalloy grains in 3D multichannel superalloy images. MCEWCVT performs segmentation by minimizing an energy function which encodes both the mul tichannel voxel-intensity similarity within each cluster in the intensity domain and the smoothness of segmentation in the 3D image domain. Based on MCEWCVT, we further develop a Constrained Multichannel Edge-Weighted Centroidal Voronoi Tessellation (CMEWCVT) algorithm which can take manual segmentation on a small number of selected 2D slices as constraints from the problem domain, and incorporate them into the energy minimization process to further improve the segmentation accuracy. We quantitatively evaluate the MCEWCVT and the CMEWCVT algorithms on an authentic Ni-based dataset and two synthesized datasets against ground-truth segmentation. The qualitative and quantitative comparisons among the MCEWCVT, the CMEWCVT and 18 existing image segmentation algorithms on the authentic dataset demonstrate the effectiveness and robustness of the MCEWCVT and the CMEWCVT algorithms. In addition, the experiments on two synthesized datasets indicate that the optimal algorithm parameters found in the testing on the authentic dataset can be used on other superalloy datasets which have similar size and number of grains. Advisors/Committee Members: Song Wang, Lili Ju.

Subjects/Keywords: Computer Sciences; Electrical and Computer Engineering; Engineering; Physical Sciences and Mathematics; 3D; CVT; Segmentation; Superalloy

…Segmentation 24 Yu Cao, Lili Ju, Qin Zou, Chengzhang Qu and Song Wang IEEE Conference on Computer… …Lili Ju, Youjie Zhou and Song Wang IEEE Transactions on Image Processing (TIP)…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Cao, Y. (2013). 3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/2349

Chicago Manual of Style (16^th Edition):

Cao, Yu. “3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods.” 2013. Doctoral Dissertation, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/2349.

MLA Handbook (7^th Edition):

Cao, Yu. “3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods.” 2013. Web. 17 Apr 2021.

Vancouver:

Cao Y. 3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods. [Internet] [Doctoral dissertation]. University of South Carolina; 2013. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/2349.

Council of Science Editors:

Cao Y. 3D Grain Segmentation in Superalloy Images Using Multichannel Edge-Weighted Centroidal Voronoi Tessellation Based Methods. [Doctoral Dissertation]. University of South Carolina; 2013. Available from: https://scholarcommons.sc.edu/etd/2349

University of South Carolina

7. Xiao, Xiao. Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations.

Degree: MS, Mathematics, 2010, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/295

► Centrodial Voronoi tessellation (CVT) is a Voronoi tessellation of a region whose generating points are also the mass centroids of the corresponding Voronoi regions.… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Xiao, X. (2010). Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/295

Chicago Manual of Style (16^th Edition):

Xiao, Xiao. “Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations.” 2010. Masters Thesis, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/295.

MLA Handbook (7^th Edition):

Xiao, Xiao. “Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations.” 2010. Web. 17 Apr 2021.

Vancouver:

Xiao X. Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations. [Internet] [Masters thesis]. University of South Carolina; 2010. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/295.

Council of Science Editors:

Xiao X. Over-Relaxation Lloyd Method For Computing Centroidal Voronoi Tessellations. [Masters Thesis]. University of South Carolina; 2010. Available from: https://scholarcommons.sc.edu/etd/295

University of South Carolina

8. Liu, Jing. Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions.

Degree: MA, Mathematics, 2010, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/364

► A Voronoi tessellation whose generating points coincide with the centroids (mass centers) of the corresponding Voronoi regions is called a centroidal Voronoi tessellation (CVT).… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, J. (2010). Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions. (Masters Thesis). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/364

Chicago Manual of Style (16^th Edition):

Liu, Jing. “Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions.” 2010. Masters Thesis, University of South Carolina. Accessed April 17, 2021. https://scholarcommons.sc.edu/etd/364.

MLA Handbook (7^th Edition):

Liu, Jing. “Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions.” 2010. Web. 17 Apr 2021.

Vancouver:

Liu J. Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions. [Internet] [Masters thesis]. University of South Carolina; 2010. [cited 2021 Apr 17]. Available from: https://scholarcommons.sc.edu/etd/364.

Council of Science Editors:

Liu J. Construction of Centroidal Voronoi Tessellations Using A Conjugate Gradient Method Based On Trust Regions. [Masters Thesis]. University of South Carolina; 2010. Available from: https://scholarcommons.sc.edu/etd/364

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