Level Set Curve Research Articles

Box2Mask: Box-Supervised Instance Segmentation via Level-Set Evolution.

In contrast to fully supervised methods using pixel-wise mask labels, box-supervised instance segmentation takes advantage of simple box annotations, which has recently attracted increasing research attention. This paper presents a novel single-shot instance segmentation approach, namely Box2Mask, which integrates the classical level-set evolution model into deep neural network learning to achieve accurate mask prediction with only bounding box supervision. Specifically, both the input image and its deep features are employed to evolve the level-set curves implicitly, and a local consistency module based on a pixel affinity kernel is used to mine the local context and spatial relations. Two types of single-stage frameworks, i.e., CNN-based and transformer-based frameworks, are developed to empower the level-set evolution for box-supervised instance segmentation, and each framework consists of three essential components: instance-aware decoder, box-level matching assignment and level-set evolution. By minimizing the level-set energy function, the mask map of each instance can be iteratively optimized within its bounding box annotation. The experimental results on five challenging testbeds, covering general scenes, remote sensing, medical and scene text images, demonstrate the outstanding performance of our proposed Box2Mask approach for box-supervised instance segmentation. In particular, with the Swin-Transformer large backbone, our Box2Mask obtains 42.4% mask AP on COCO, which is on par with the recently developed fully mask-supervised methods.

Geometric modeling of phase ordering for the isotropic–smectic A phase transition

BackgroundLiquid crystal (LC) mesophases have an orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly the temperature or concentration, is changed, inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out using the Landau–de Gennes (LdG) model, which correlates the free energy of the system with the orientational and positional order.MethodologyThis work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families: (I) level-set curves, steepest descent, and critical points; (II) lines of curvature (LOC) and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, and saddle).ResultsThe experimental data on 12-cyanobiphenyl were used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted the energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone.Conclusion and significanceA direct link between the energy landscape’s topological geometry, phase transitions, and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters (OPs) may lead to novel phase transformation kinetics and droplets with partially ordered surface structures.

A noniterative reconstruction method for the inverse potential problem for a time-fractional diffusion equation

This paper is concerned with the reconstruction of the support of the potential term for a time-fractional diffusion equation from the final measured data. The aim of this paper is to propose an accurate approach based on the topological derivative method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing a given cost function. We derive a topological asymptotic expansion for the fractional model. The unknown support is reconstructed using the level-set curve of the topological gradient. We finally make some numerical examples proving the efficiency and accuracy of the proposed algorithm.

Multilevel thresholding image segmentation algorithm based on Mumford–Shah model

Abstract Image segmentation is one of the important tasks of computer vision and computer image processing, and the purpose of image segmentation is to achieve the extraction and recognition of the target image region. The classical Mumford–Shah (MSh) image segmentation model is used to achieve the segmentation of images. With the goal to get the best segmentation effect on images by minimizing the MSh energy generalization function, a level set strategy is developed, and a model with global information infinite curve evolution is utilized. However, considering the low efficiency of this model for processing level set curves and the general quality of image segmentation. A multi-layer threshold search scheme is proposed to achieve rapid convergence of the target image level set curve. The experimental results showed that the multi-level thresholding image segmentation algorithm based on the MSh model can significantly improve the segmentation effect of images and reduce the segmentation time. The suggested MSK method outperforms the MPO algorithm, SSA algorithm, and EMO algorithm in the picture segmentation convergence time test, respectively, in terms of runtime efficiency by 356, 289, and 71%. Additionally, it performs superbly in both threshold searches and picture quality tests. The research topic has significant reference value for the study of contemporary computer vision imaging technologies.

Total Curvature and the Isoperimetric Inequality in Cartan–Hadamard Manifolds

We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.

Level curves of minimal graphs

We prove an inequality for the curvature of level sets of minimal graphs having vanishing boundary values and show that if the boundary is concave, then all the level sets are concave.

Topological Sensitivity Analysis for the Anisotropic Laplace Problem

This paper is concerned with the reconstruction of objects immersed in anisotropic media from boundary measurements. The aim of this paper is to propose an alternative approach based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The idea is to formulate the reconstruction problem as a topology optimization one minimizing an energy-like function. We derive a topological asymptotic expansion for the anisotropic Laplace operator. The unknown object is reconstructed using level-set curve of the topological gradient. We make finally some numerical examples proving the efficiency and accuracy of the proposed algorithm.

A weighted region-based level set method for image segmentation with intensity inhomogeneity.

Image segmentation is a fundamental task in image processing and is still a challenging problem when processing images with high noise, low resolution and intensity inhomogeneity. In this paper, a weighted region-based level set method, which is based on the techniques of local statistical theory, level set theory and curve evolution, is proposed. Specifically, a new weighted pressure force function (WPF) is first presented to flexibly drive the closed contour to shrink or expand outside and inside of the object. Second, a faster and smoother regularization term is added to ensure the stability of the curve evolution and that there is no need for initialization in curve evolution. Third, the WPF is integrated into the region-based level set framework to accelerate the speed of the curve evolution and improve the accuracy of image segmentation. Experimental results on medical and natural images demonstrate that the proposed segmentation model is more efficient and robust to noise than other state-of-the-art models.

A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications

This paper is devoted to a game-theoretic approach to the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under the comparison principle for the dynamic boundary problem, we construct a family of deterministic discrete games, whose value functions approximate the unique viscosity solution. We also apply the game approximation to study the convexity preserving properties and the fattening phenomenon for this geometric dynamic boundary problem.

Topological sensitivity method for reconstruction of the spatial component in the source term of a time-fractional diffusion equation

In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. Several numerical simulations are presented to show the efficiency and the accuracy of the algorithm.

Cartoon and Texture Image Decomposition Driven by Weighted Curvature

In this paper, we propose a curvature-guided model with divergence-free constraints to facilitate image decomposition. Since basic TV regularization has difficulty in processing edge geometry information of cartoon image, in order to preserve the edge features, we introduce a level set curvature term to smooth the uniform area, and use the edge indicator function as the weighted regularization to preserve the edge. In addition, to control the smoothness, a gradient function is proposed to balance the edge indicator function and the curvature term. On the other hand, we find that the existing partial decomposition models measure the oscillation function with the $H^{-1}$ functional, but this functional ignores the divergence-free vector field during the Hodge decomposition process, then the texture will lose some vector direction information, and then affects the decomposition results. By analyzing the theory of divergence-free vector field, a new decomposition model with the constraint of divergence-free vector field is proposed in this paper. Numerical experiments show that the proposed model can well preserves the edges of cartoon and protects the texture of repetitive patterns.

Labeling and clustering-based level set method for automated segmentation of lung tumor stages in CT images

An unconstrained growth of abnormal cells in the lung causes tumors. The aim of the work is the accurate diagnoses of tumor at its early stage through hybrid segmentation algorithm. The objective of this paper is to propose a novel labeled cluster active contour method to improve the performance of automated lung tumor segmentation from 2D CT slices. To the input 2D slice, an 8-connected component analysis is implemented to differentiate the image spatial information and obtain the RGB labeled data. The tumor location is foreseen using an unsupervised k-means clustering algorithm. Then, an automated level set algorithm is carried out to appropriately localize and extract the tumor region. The amount of initial level set curve evolution is controlled by the clustering efficiency of k-Means and labeling efficacy of connected component analysis. The quantitative evaluation of segmentation is carried out based on Shape features like area, perimeter, eccentricity, convex area, solidity, and roundness. The statistical object-based and distance-based metrics were used to find the similarity between manual and proposed methods. Also, performance metrics like accuracy, specificity, sensitivity, precision, and recall are used to validate the segmentation results of the proposed method. The proposed system is evaluated over 42 datasets from the commonly available large dataset LIDC (Lung Image Database Consortium). The accuracy, specificity, sensitivity and precision of the proposed hybrid method are 97.5%, 97.43%, 91.67%, and 98.79%, which exhibited the best competence as compared to traditional methods on the same dataset. The statistical and quantitative analysis shows the efficiency of the present work.

A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes

SummaryIn this article, a new framework to design high‐order approximations in the context of node‐centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High‐performance computing context. This method is based on deconvolution between nodal and volume‐average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh‐to‐mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high‐rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third‐order expansion. This method, although tightly connected to the k‐exact schemes theory, does not rely on successive corrections: the high‐order property is obtained in a single operation, which makes them more attractive in terms of performances.

An novel image de-noising model based on gradient and adaptive curvature features and its application

In this paper, an image de-noising model with gradient and adaptive curvature features is proposed for the visual inspection of the appearance defects of high-density flexible integrated circuit package substrates with strict line-width and line distance. Firstly, the model proposed in this paper adaptively adjusts the weight of the level set curvature feature and the gradient feature of the image, and uses more abundant first-order differential and second-order differential information of the image as the detection factor for image de-noising. Secondly, theoretical analysis shows that the diffusion intensity of the model in the flat region is larger than that of the classical model, and the de-noising effect is better. Furthermore, at the corners and peaks of the image, the proposed model can suppress the reduction of the gray value and preserve more detailed information of the image and edges. Finally, the experimental analysis shows that the proposed model has the best de-noising effect compared with other models. The method proposed in this paper can effectively remove the noise of the image of the high-density flexible integrated circuit package substrate, and at the same time retain more original details and edge information of the image which has practical significance.

Reconstruction of contact regions in semiconductor transistors using Dirichlet-Neumann cost functional approach

In this paper, we study the inverse problem of reconstructing an interior interface appearing in an elliptic equation in a bounded domain Ω from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn–Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown contact interface is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

M‐WRSF model for medical image segmentation

In this Letter, multichannel weighted region-scalable fitting segmentation model (M-WRSF) is proposed for medical image segmentation. The authors have utilised a new edge detection function to improve the performance of image segmentation approaches that already exists on weak edges and the grey-scale inhomogeneity of some medical images. The M-WRSF model introduces a novel punishment item to improve numerical stability and augments time interval to boost iterative efficiency. The Gaussian kernel function is added on the basis of original model to enhance robustness. On the other side, the original medical images need to make de-noising operation before the multichannel active contour model segment them, and also level-set initial curve has no effect on the segmentation results. The benefits of the new M-WRSF model, specifically, the increased efficiency and usability, are verified in the simulation experiment.

Research on Image Smoothing Diffusion Model With Gradient and Curvature Features

In this paper, two image smoothing models are proposed for the visual inspection of high-density flexible IC package substrates with strict requirements on line width and line distance which are applied to the de-noising of high-density flexible IC package substrate images. First of all, the two models proposed in this paper combines the level set curvature feature of the image with gradient threshold, using more abundant second-order differential information as the detection factor to remove the noise in the image. Second, the theoretical analysis shows that the de-noised image obtained by the two models proposed can retain more detailed texture information and edge information of the original image. What is more, the experimental analysis shows that the proposed models have the highest structural similarity and peak signal-to-noise ratio, and have a relatively high edge-preserving index and the lowest mean squared error compared with other models. In particular, the de-noised image through Model 1 has the highest structural similarity and peak signal-to-noise ratio, as well as the lowest mean squared error. The de-noised image through Model 2 has a relatively high edge retention index. The methods proposed in this paper can effectively remove the noise of the image of the high-density flexible IC package substrate and can retain the original details and edges information of the image.

Automatic image segmentation method for cotton leaves with disease under natural environment

In order to improve the image segmentation performance of cotton leaves in natural environment, an automatic segmentation model of diseased leaf with active gradient and local information is proposed. Firstly, a segmented monotone decreasing edge composite function is proposed to accelerate the evolution of the level set curve in the gradient smooth region. Secondly, canny edge detection operator gradient is introduced into the model as the global information. In the process of the evolution of the level set function, the guidance information of the energy function is used to guide the curve evolution according to the local information of the image, and the smooth contour curve is obtained. And the main direction of the evolution of the level set curve is controlled according to the global gradient information, which effectively overcomes the local minima in the process of the evolution of the level set function. Finally, the Heaviside function is introduced into the energy function to smooth the contours of the motion and to increase the penalty function φ(x) to calibrate the deviation of the level set function so that the level set is smooth and closed. The results showed that the model of cotton leaf edge profile curve could be obtained in the model of cotton leaf covered by bare soil, straw mulching and plastic film mulching, and the ideal edge of the ROI could be realized when the light was not uniform. In the complex background, the model can segment the leaves of the cotton with uneven illumination, shadow and weed background, and it is better to realize the ideal extraction of the edge of the blade. Compared with the Geodesic Active Contour (GAC) algorithm, Chan-Vese (C-V) algorithm and Local Binary Fitting (LBF) algorithm, it is found that the model has the advantages of segmentation accuracy and running time when processing seven kinds of cotton disease leaves images, including uneven lighting, leaf disease spot blur, adhesive diseased leaf, shadow, complex background, unclear diseased leaf edges, and staggered condition. This model can not only conduct image segmentation of cotton leaves under natural conditions, but also provide technical support for the accurate identification and diagnosis of cotton diseases.

Adaptive curvature-guided image filtering for structure + texture image decomposition.

A preliminary structure + texture image decomposition is very useful for a number of digital image processing tasks, as different strategies are supposed to be employed for processing the structure and texture image components. In this paper, a new variational structure + texture image decomposition method is developed. The main ingredients of the proposed approach are: (1) using a low-pass filtered level-set curvature of the input image as a guidance image; (2) texture suppressing by minimizing a variable exponent energy, where the variable exponent is learned from the result of the curvature-guided image filtering. Numerical experiments demonstrate that the method is competitive with the current state of the art in structure + texture image decomposition. Several applications are considered.

A new reconstruction method for a parabolic inverse source problem

ABSTRACTIn this paper, we focus on the detection of the shape and location of a discontinuous source term from the knowledge of boundary measurements. We propose a non-iterative reconstruction algorithm based on the Kohn-Vogelius formulation and the topological sensitivity analysis method. The inverse source problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from an energy-like cost function. The unknown shape of the term source support is reconstructed using a level-set curve of the topological gradient. The efficiency of our algorithm is illustrated by some numerical simulations.