Semantic segmentation plays a foundational role in biomedical image analysis, providing precise information about cellular, tissue, and organ structures in both biological and medical imaging modalities. Traditional a...Semantic segmentation plays a foundational role in biomedical image analysis, providing precise information about cellular, tissue, and organ structures in both biological and medical imaging modalities. Traditional approaches often fail in the face of challenges such as low contrast, morphological variability, and densely packed structures. Recent advancements in deep learning have transformed segmentation capabilities through the integration of fine-scale detail preservation, coarse-scale contextual modeling, and multi-scale feature fusion. This work provides a comprehensive analysis of state-of-the-art deep learning models, including U-Net variants, attention-based frameworks, and Transformer-integrated networks, highlighting innovations that improve accuracy, generalizability, and computational efficiency. Key architectural components such as convolution operations, shallow and deep blocks, skip connections, and hybrid encoders are examined for their roles in enhancing spatial representation and semantic consistency. We further discuss the importance of hierarchical and instance-aware segmentation and annotation in interpreting complex biological scenes and multiplexed medical images. By bridging methodological developments with diverse application domains, this paper outlines current trends and future directions for semantic segmentation, emphasizing its critical role in facilitating annotation, diagnosis, and discovery in biomedical research.展开更多
We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal d...We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.展开更多
基金Open Access funding provided by the National Institutes of Health(NIH)The funding for this project was provided by NCATS Intramural Fund.
文摘Semantic segmentation plays a foundational role in biomedical image analysis, providing precise information about cellular, tissue, and organ structures in both biological and medical imaging modalities. Traditional approaches often fail in the face of challenges such as low contrast, morphological variability, and densely packed structures. Recent advancements in deep learning have transformed segmentation capabilities through the integration of fine-scale detail preservation, coarse-scale contextual modeling, and multi-scale feature fusion. This work provides a comprehensive analysis of state-of-the-art deep learning models, including U-Net variants, attention-based frameworks, and Transformer-integrated networks, highlighting innovations that improve accuracy, generalizability, and computational efficiency. Key architectural components such as convolution operations, shallow and deep blocks, skip connections, and hybrid encoders are examined for their roles in enhancing spatial representation and semantic consistency. We further discuss the importance of hierarchical and instance-aware segmentation and annotation in interpreting complex biological scenes and multiplexed medical images. By bridging methodological developments with diverse application domains, this paper outlines current trends and future directions for semantic segmentation, emphasizing its critical role in facilitating annotation, diagnosis, and discovery in biomedical research.
基金The author gratefully acknowledges valuable support provided by the Department of Mathematics,NIT Calicut and the DST,Government of India,for providing support to carry out this work under the scheme TIST(No.SR/FST/MS-I/2019/40).
文摘We study spatially semidiscrete and fully discrete two-scale composite nite element method for approximations of the nonlinear parabolic equations with homogeneous Dirichlet boundary conditions in a convex polygonal domain in the plane.This new class of nite elements,which is called composite nite elements,was rst introduced by Hackbusch and Sauter[Numer.Math.,75(1997),pp.447-472]for the approximation of partial di erential equations on domains with complicated geometry.The aim of this paper is to introduce an effcient numerical method which gives a lower dimensional approach for solving partial di erential equations by domain discretization method.The composite nite element method introduces two-scale grid for discretization of the domain,the coarse-scale and the ne-scale grid with the degrees of freedom lies on the coarse-scale grid only.While the ne-scale grid is used to resolve the Dirichlet boundary condition,the dimension of the nite element space depends only on the coarse-scale grid.As a consequence,the resulting linear system will have a fewer number of unknowns.A continuous,piecewise linear composite nite element space is employed for the space discretization whereas the time discretization is based on both the backward Euler and the Crank-Nicolson methods.We have derived the error estimates in the L^(∞)(L^(2))-norm for both semidiscrete and fully discrete schemes.Moreover,numerical simulations show that the proposed method is an efficient method to provide a good approximate solution.
