Circle packings and total geodesic curvatures in hyperbolic background geometry

In this paper, we study a new type of circle packings in hyperbolic background geometry. Horocycles and hypercycles are also considered in this packing. We give the existence and rigidity of this type of circle packing with conical singularities in terms of the total geodesic curvature. Moreover, we introduce the combinatorial curvature flow on surfaces to find the desired circle packing with the prescribed total geodesic curvature

SAR image segmentation algorithms based on I-divergence-TV model

In this paper, we propose a novel variational active contour model based on I-divergence-TV model to segment Synthetic aperture radar (SAR) images with multiplicative gamma noise, which hybrides edge-based model with region-based model. The proposed model can efficiently stop the contours at weak or blurred edges, and can automatically detect the exterior and interior boundaries of images. We incorporate the global convex segmentation method and split Bregman technique into the proposed model, and propose a fast fixed point algorithm to solve the global convex segmentation question[25]. Experimental results for synthetic images and real SAR images show that the proposed fast fixed point algorithm is robust and efficient compared with the state-of-the-art approach.Comment: 22 pages,28 figures. arXiv admin note: substantial text overlap with arXiv:2312.0837

Active contours driven by local and global intensity fitting energy with application to SAR image segmentation and its fast solvers

In this paper, we propose a novel variational active contour model based on Aubert-Aujol (AA) denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model and can be used to segment images corrupted by multiplicative gamma noise. We transform the proposed model into classic ROF model by adding a proximity term. Inspired by a fast denosing algorithm proposed by Jia-Zhao recently, we propose two fast fixed point algorithms to solve SAR image segmentation question. Experimental results for real SAR images show that the proposed image segmentation model can efficiently stop the contours at weak or blurred edges, and can automatically detect the exterior and interior boundaries of images with multiplicative gamma noise. The proposed fast fixed point algorithms are robustness to initialization contour, and can further reduce about 15% of the time needed for algorithm proposed by Goldstein-Osher.Comment: 20 pages,28 figures. arXiv admin note: substantial text overlap with arXiv:2312.08376, arXiv:2312.0936

Effect of bone morphogenetic protein-2 on diabetic retinopathy and its mechanism of action

Purpose: To investigate the effect of bone morphogenetic protein-2 (BMP-2) on human retinal vascular endothelial cells (RECs) and human retinal pigment epithelial cells (RPE) cultured in high glucose (HG) in vitro, and the underlying mechanism. Methods: Cell counting kit-8 (CCK-8) was used to determine cell proliferation while Western blot was used to assay the expressions of extracellular matrix and angiogenesis-related factors, Expressions of cytokines and chemokines were assessed by quantitative real time polymerase chain reaction (qRTPCR) and enzyme-linked immunosorbent assay (ELISA). Changes in Smad, ERK, JNK and p38MAPK signal pathway were measured by transfection and interference. Results: The level of expression of BMP-2 in HG group was higher than that in normal glucose (NG) culture group. The expressions of angiogenesis-related factors i.e. vascular endothelial growth factor (VEGF) and intercellular cell adhesion molecule-1 (ICAM1), pro-inflammatory factors i.e. IL-6 and chemokine monocyte chemokine protein-1 (MCP1), increased significantly in HG group compared to NG and HG + BMP-2 groups. Phosphorylation of Smad1/5/8 and activation of ERK, JNK and p38MAPK signaling pathways were enhanced by BMP-2. Conclusion: These results suggest that BMP-2 promotes angiogenesis and enhances the expressions of inflammatory cytokines via Smad signaling pathway

A locally statistical active contour model for SAR image segmentation can be solved by denoising algorithms

In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be used to segment images corrupted by multiplicative gamma noise. By adding a diffusion term into the level set evolution (LSE) equation of the proposed model, we construct a reaction-diffusion (RD) equation, which can gradually regularize the level set function (LSF) to be piecewise constant in each segment domain and gain the stable solution. We further transform the proposed model into classic ROF model by adding a proximity term. Inspired by a fast denoising algorithm proposed by Jia-Zhao recently, we propose two fast fixed point algorithms to solve SAR image segmentation question. Experimental results for real SAR images show that the proposed image segmentation model can efficiently stop the contours at weak or blurred edges, and can automatically detect the exterior and interior boundaries of images with multiplicative gamma noise. The proposed FPRD1/FPRD2 models are about 1/2 (or less than) of the time required for the SBRD model based on the Split Bregman technique.Comment: 18 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:2312.11849, arXiv:2312.08376, arXiv:2312.0936

Hyperbolic Circle Packings and Total Geodesic Curvatures on Surfaces with Boundary

This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with boundary. We mainly focus on the existence and rigidity of circle packing whose contact graph is the $1$-skeleton of a finite polygonal cellular decomposition, which is analogous to the construction of Bobenko and Springborn [4]. Motivated by Colin de Verdi\`ere's method [6], we introduce the variational principle for generalized hyperbolic circle packings on polygons. By analyzing limit behaviours of generalized circle packings on polygons, we give an existence and rigidity for the generalized hyperbolic circle packing with conical singularities regarding the total geodesic curvature on each vertex of the contact graph. As a consequence, we introduce the combinatoral Ricci flow to find a desired circle packing with a prescribed total geodesic curvature on each vertex of the contact graph.Comment: 26 pages, 7 figure