2015-2017, Post Doctoral Associate | UPMC, Pittsburgh, PA, USA
2008-2009, Subject Matter Expert | Cramster. Learning Inc., Visakhapatnam, India
Research Interest
Mathematical modelling using partial differential equations to solve image inpainting problems.
Finding a global solution to the problem of fiber tracking in human brain white matter using variational calculus and nonlinear optimization techniques.
Awards
2010 – Junior Research Fellowship – CSIR-UGC
Memberships
Publications
A PDE Based Image Segmentation Using Fourier Spectral Method
Article, Differential Equations and Dynamical Systems, 2022, DOI Link
View abstract ⏷
A PDE based binary image segmentation model using a modified Cahn–Hilliard equation with weaker fidelity parameter (λ) and double well potential has been introduced. The threshold of separation γ is flexibly chosen between 0 and 1. Convexity splitting is used for time discretization and then Fourier-spectral method is used to solve the proposed modified Cahn–Hilliard equation. The proposed model is tested on bio-medical images.
Higher order PDE based model for segmenting noisy image
In this study, a fourth-order non-linear partial differential equation (PDE) model together with multi-well potential has been proposed for greyscale image segmentation. The multi-well potential is constructed from the histogram of the given image to make the segmentation process fully automatic and unsupervised. Further, the model is refined for effective segmentation of noisy greyscale image. The fourth-order anisotropic term with the multi-well potential is shown to properly segment noisy images. Fourier spectral method in space with semi-implicit convexity splitting in time is used to derive an unconditionally stable scheme. Numerical studies on some standard test images and comparison of results with those in literature clearly depict the superiority of the anisotropic variant of the non-linear PDE model.
Patents
A system and method for optimized structural design of a plot of land
2015-2017, Post Doctoral Associate | UPMC, Pittsburgh, PA, USA
2008-2009, Subject Matter Expert | Cramster. Learning Inc., Visakhapatnam, India
Research Interests
Mathematical modelling using partial differential equations to solve image inpainting problems.
Finding a global solution to the problem of fiber tracking in human brain white matter using variational calculus and nonlinear optimization techniques.
Awards & Fellowships
2010 – Junior Research Fellowship – CSIR-UGC
Memberships
Publications
A PDE Based Image Segmentation Using Fourier Spectral Method
Article, Differential Equations and Dynamical Systems, 2022, DOI Link
View abstract ⏷
A PDE based binary image segmentation model using a modified Cahn–Hilliard equation with weaker fidelity parameter (λ) and double well potential has been introduced. The threshold of separation γ is flexibly chosen between 0 and 1. Convexity splitting is used for time discretization and then Fourier-spectral method is used to solve the proposed modified Cahn–Hilliard equation. The proposed model is tested on bio-medical images.
Higher order PDE based model for segmenting noisy image
In this study, a fourth-order non-linear partial differential equation (PDE) model together with multi-well potential has been proposed for greyscale image segmentation. The multi-well potential is constructed from the histogram of the given image to make the segmentation process fully automatic and unsupervised. Further, the model is refined for effective segmentation of noisy greyscale image. The fourth-order anisotropic term with the multi-well potential is shown to properly segment noisy images. Fourier spectral method in space with semi-implicit convexity splitting in time is used to derive an unconditionally stable scheme. Numerical studies on some standard test images and comparison of results with those in literature clearly depict the superiority of the anisotropic variant of the non-linear PDE model.
Contact Details
vijayakrishna.r@srmap.edu.in
Scholars
Doctoral Scholars
Jyotiranjan Nayak
Interests
Human brain white matter fiber tractography using diffusion MRI data
Partial differential equations applied to image procesing problems
2015-2017, Post Doctoral Associate | UPMC, Pittsburgh, PA, USA
2008-2009, Subject Matter Expert | Cramster. Learning Inc., Visakhapatnam, India
Research Interests
Mathematical modelling using partial differential equations to solve image inpainting problems.
Finding a global solution to the problem of fiber tracking in human brain white matter using variational calculus and nonlinear optimization techniques.
Awards & Fellowships
2010 – Junior Research Fellowship – CSIR-UGC
Memberships
Publications
A PDE Based Image Segmentation Using Fourier Spectral Method
Article, Differential Equations and Dynamical Systems, 2022, DOI Link
View abstract ⏷
A PDE based binary image segmentation model using a modified Cahn–Hilliard equation with weaker fidelity parameter (λ) and double well potential has been introduced. The threshold of separation γ is flexibly chosen between 0 and 1. Convexity splitting is used for time discretization and then Fourier-spectral method is used to solve the proposed modified Cahn–Hilliard equation. The proposed model is tested on bio-medical images.
Higher order PDE based model for segmenting noisy image
In this study, a fourth-order non-linear partial differential equation (PDE) model together with multi-well potential has been proposed for greyscale image segmentation. The multi-well potential is constructed from the histogram of the given image to make the segmentation process fully automatic and unsupervised. Further, the model is refined for effective segmentation of noisy greyscale image. The fourth-order anisotropic term with the multi-well potential is shown to properly segment noisy images. Fourier spectral method in space with semi-implicit convexity splitting in time is used to derive an unconditionally stable scheme. Numerical studies on some standard test images and comparison of results with those in literature clearly depict the superiority of the anisotropic variant of the non-linear PDE model.
