Publications
Papers and preprints
A publication index organized by year and topic.
A Computational Method for Image Segmentation Based on a Dirichlet Field and an Analysis of the Asymptotic Accuracy of Spatial Regularizer Discretization
Modeling, Optimization and Information Technology
This paper presents a Dirichlet-field formulation of segmentation with closed-form uncertainty estimation, edge-aware smoothing, and an explicit asymptotic analysis of the spatial regularizers used in the model. Numerical experiments on ACDC, Synapse, and CHAOS show improved calibration and segmentation quality with moderate extra cost.
- Numerical Methods
- Applied Systems
DOI10.26102/2310-6018/2026.54.3.009
Global Existence, Invariant Region, and Enhanced Regularity for an Anisotropic Reaction-Diffusion Model of Myocardial Remodeling in Terms of Dirichlet Concentration Parameters
Zenodo preprint
A multicomponent anisotropic reaction-diffusion model for post-infarction myocardial remodeling is formulated in terms of Dirichlet concentration parameters so that composition and uncertainty are represented together. The paper proves global existence, establishes invariant-region bounds, and derives enhanced regularity and short-time unconditional uniqueness under additional assumptions.
- Nonlinear PDEs
- Applied Systems
On Global Solvability, Entropy Dissipation, and Numerical Analysis of Reaction-Diffusion Systems with Cross-Diffusion and Markov Kinetics
Zenodo preprint
This paper studies multicomponent reaction-diffusion systems with cross-diffusion and Markov kinetics in an entropy-structured setting. It establishes global weak solvability for an admissible class, proves exponential relaxation in the conservative regime, and combines theory with entropy-consistent numerical experiments.
- Nonlinear PDEs
- Numerical Methods
On the Well-Posedness of Discrete Variational Problems with Edge-Aware Regularization
Modern Science: Theory and Practice
This article analyzes why standard edge-aware weights collapse to isotropic behavior under grid refinement. It introduces a scale-consistent formulation based on normalized directional differences and proves convergence to a nontrivial weighted anisotropic Dirichlet energy, supported by numerical validation on synthetic and cardiac MRI data.
- Nonlinear PDEs
- Numerical Methods
DOI10.34660/INF.2026.79.37.103
Semantic Segmentation with Uncertainty Estimation Based on the Dirichlet Model and Anisotropic Regularization
Computational Mathematics and Information Technologies
The paper proposes a semantic segmentation method that couples Dirichlet uncertainty modeling with anisotropic regularization. It proves Gamma-convergence and equicoercivity for the discrete energy family and reports calibrated uncertainty estimation with modest computational overhead.
- Numerical Methods
- Applied Systems
DOI10.23947/2587-8999-2026-10-1-7-20