Minimization of functionals related to Euler's elastica energy has a wide range applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE) needs be solved, the gradient descent method usually takes computational cost. In this paper, we propose fast efficient numerical algorithm solve minimization problems show variational denoising, inpainting, zooming. We reformulate problem as constrained problem, followed by an operator splitting...

The spatial interactions between malignant and immune cells in the tumor microenvironment (TME) play a crucial role cancer biology treatment response. Understanding these is critical for predicting prognosis assessing immunotherapy effectiveness. Conventional methods, which focus on local features, often struggle to achieve robust analysis due complex heterogeneous cellular distributions. We propose Topological Data Analysis (TDA)-based framework using both global features cells. For...

In this paper, we propose the neural shortest path (NSP), a vector-valued implicit representation (INR) that approximates distance function and its gradient. The key feature of NSP is to learn exact (ESP), which directs an arbitrary point nearest on target surface. decomposed into magnitude direction, variable splitting method used each component gradient, respectively. Unlike existing methods learning itself, ensures simultaneous recovery We mathematically prove guarantees convergence in...

Variable splitting schemes for the function space version of image reconstruction problem with total variation regularization (TV-problem) in its primal and pre-dual formulations are considered.In formulation, while existence a solution cannot be guaranteed, it is shown that quasi-minimizers penalized asymptotically related to original TV-problem.On other hand, formulation family parametrized problems introduced parameter dependent contraction an associated fixed point iteration...

Magnetic resonance electrical impedance tomography (MREIT) is designed to produce high resolution conductivity images of an electrically conducting subject by injecting current and measuring the longitudinal component, Bz, induced magnetic flux density B = (Bx, By, Bz). In MREIT, accurate measurements Bz are essential in producing correct images. However, measured data may contain fundamental defects local regions where MR magnitude image small. These defective result completely wrong values...

Abstract In this paper, we aim to develop a comprehensive ignition model for three-dimensional (3D) computational fluid dynamics (CFD) combustion modeling in spark-ignited (SI) engines. the proposed model, consider following aspects separately spark process comprehensively. An electrical circuit is solved calculation of energy transferred plasma channel. The itself represented by particles monitoring its motion and ignitability. Heat diffusion from toward surrounding mixture calculated with...

In this paper, we present a surface reconstruction via 2D strokes and vector field on the based two-step method. first step, from sparse drawn by artists given strokes, propose nonlinear interpolation combining total variation (TV) H 1 regularization with curl-free con- straint for obtaining dense field. second height map is obtained integrating in step. Jump discontinuities of gradients can be well reconstructed without any distortion. We also provide fast efficient algorithm solving...

Abstract A cell‐centered finite volume method with the Soner boundary condition is proposed to compute signed distance function from a given surface in general three‐dimensional (3D) computational domains discretized by polyhedral cells. The governing equation bidirectional time‐relaxed eikonal and numerical based on semi‐implicit inflow‐implicit outflow‐explicit scheme. Numerical experiments confirm second order accuracy ‐norms for chosen examples smooth solutions. inclusion of has proven...

Abstract The convoluted shape of the cerebral cortex makes it difficult to analyze and visualize neuronal activation area. One way overcoming this problem is use a spherical inflation method draw on surface. task mapping cortical surface sphere has several obstacles, namely, overlap between polygons surface, heavy computation demand, geometric distortions inherent in process. This article proposes three‐dimensional (3D) represented simplex mesh which does not have any minimizes as well time....

We propose a variational segmentation model based on statistical information of intensities in an image. The consists both local region-based energy and global order to handle misclassification which happens typical with assumption that image is mixture two Gaussian distributions. find ambiguous regions where might happen due small difference between Based restricted the regions, we design reduce misclassification. suggest algorithm avoid difficulty Euler-Lagrange equations proposed model.

In this paper, we propose to use the eikonal equation as a boundary condition when advective or normal flow equations in level set formulation are solved numerically on polyhedral meshes three-dimensional domain. Since method can signed distance function an initial condition, is suitable choice at time. Enforcing for later times eliminate need inflow conditions, which typically required transport equations. selected examples where exact solutions available, compare proposed with using...

This paper proposes a theoretical framework for analyzing Modified Incomplete LU (MILU) preconditioners. Considering generalized MILU preconditioner on weighted undirected graph with self-loops, we extend its applicability beyond matrices derived by Poisson equation solvers uniform grids compact stencils. A major contribution is, novel measure, the \textit{Localized Estimator of Condition Number (LECN)}, which quantifies condition number locally at each vertex graph. We prove that maximum...

<p style='text-indent:20px;'>A numerical method for solving diffusion problems on polyhedral meshes is presented. It based a finite volume approximation with the degrees of freedom located in centers computational cells. A gradient defined by least-squares minimization each cell, where we suggest restricted form case discontinuous coefficient. The flux balanced proposed without numerically computing itself at faces cells order to find normal diffusive flux. To apply parallel computations...