A Characteristic Function-based Algorithm for Geodesic Active Contours

Free Form based active contours for image segmentation and free space perception

In this paper we present a novel approach for representing and evolving deformable active contours. The method combines piecewise regular B{é}zier models and curve evolution defined by local Free Form Deformation. The contour deformation is locally constrained which allows contour convergence with almost linear complexity while adapting to various shape settings and handling topology changes of the active contour. We demonstrate the effectiveness of the new active contour scheme for visual free space perception and segmentation using omnidirectional images acquired by a robot exploring unknown…

Active Contour Models for Manifold Valued Image Segmentation

Image segmentation is the process of partitioning a image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Active contours is a popular variational method for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold valued images have come up, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such imag…

Deep ContourFlow：借助深度学习推进主动轮廓模型

Deep ContourFlow: Advancing Active Contours with Deep Learning

本研究提出融合无监督主动轮廓模型与深度学习的Deep ContourFlow框架，支持无监督及单样本图像分割，在标注稀缺的组织学数据集上性能优于现有最优方法。

Template-Based Active Contours

We develop a generalized active contour formalism for image segmentation based on shape templates. The shape template is subjected to a restricted affine transformation (RAT) in order to segment the object of interest. RAT allows for translation, rotation, and scaling, which give a total of five degrees of freedom. The proposed active contour comprises an inner and outer contour pair, which are closed and concentric. The active contour energy is a contrast function defined based on the intensities of pixels that lie inside the inner contour and those that lie in the annulus between the inner a…

Physical Modeling Techniques in Active Contours for Image Segmentation

Physical modeling method, represented by simulation and visualization of the principles in physics, is introduced in the shape extraction of the active contours. The objectives of adopting this concept are to address the several major difficulties in the application of Active Contours. Primarily, a technique is developed to realize the topological changes of Parametric Active Contours (Snakes). The key strategy is to imitate the process of a balloon expanding and filling in a closed space with several objects. After removing the touched balloon surfaces, the objects can be identified by surrou…

State-of-The-Art Fuzzy Active Contour Models for Image Segmentation

Image segmentation is the initial step for every image analysis task. A large variety of segmentation algorithm has been proposed in the literature during several decades with some mixed success. Among them, the fuzzy energy based active contour models get attention to the researchers during last decade which results in development of various methods. A good segmentation algorithm should perform well in a large number of images containing noise, blur, low contrast, region in-homogeneity, etc. However, the performances of the most of the existing fuzzy energy based active contour models have be…

基于局部与全局强度拟合能量的主动轮廓模型及其在SAR图像分割中的应用与快速求解器

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

提出一种基于Aubert-Aujol去噪模型的变分主动轮廓模型，混合测地线主动轮廓与无边缘主动轮廓模型，用于分割乘性伽马噪声图像，并引入两个快速不动点算法求解SAR图像分割问题。

Saliency-Driven Active Contour Model for Image Segmentation

Active contour models have achieved prominent success in the area of image segmentation, allowing complex objects to be segmented from the background for further analysis. Existing models can be divided into region-based active contour models and edge-based active contour models. However, both models use direct image data to achieve segmentation and face many challenging problems in terms of the initial contour position, noise sensitivity, local minima and inefficiency owing to the in-homogeneity of image intensities. The saliency map of an image changes the image representation, making it mor…

Theoretical Analysis of Active Contours on Graphs

Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce geometric approximations of gradient and curvature, which are used in the geodesic active contour model. We prove convergence in probability of our gradient approximation to the true gradient value and derive an asymptotic upper bound for the error of this approximation for the class of random geometric graphs. Two different approaches for the approximation o…

一种可由去噪算法求解的局部统计活动轮廓模型用于SAR图像分割

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

提出基于I散度-TV去噪模型的局部统计活动轮廓模型，融合GAC和ACWE模型，用于分割乘性伽马噪声图像，并通过反应扩散方程和ROF模型转化实现快速求解。

Regional Active Contours based on Variational level sets and Machine Learning for Image Segmentation

Image segmentation is the problem of partitioning an image into different subsets, where each subset may have a different characterization in terms of color, intensity, texture, and/or other features. Segmentation is a fundamental component of image processing, and plays a significant role in computer vision, object recognition, and object tracking. Active Contour Models (ACMs) constitute a powerful energy-based minimization framework for image segmentation, which relies on the concept of contour evolution. Starting from an initial guess, the contour is evolved with the aim of approximating be…

End to End Trainable Active Contours via Differentiable Rendering

We present an image segmentation method that iteratively evolves a polygon. At each iteration, the vertices of the polygon are displaced based on the local value of a 2D shift map that is inferred from the input image via an encoder-decoder architecture. The main training loss that is used is the difference between the polygon shape and the ground truth segmentation mask. The network employs a neural renderer to create the polygon from its vertices, making the process fully differentiable. We demonstrate that our method outperforms the state of the art segmentation networks and deep active con…

A Generalized Asymmetric Dual-front Model for Active Contours and Image Segmentation

The Voronoi diagram-based dual-front active contour models are known as a powerful and efficient way for addressing the image segmentation and domain partitioning problems. In the basic formulation of the dual-front models, the evolving contours can be considered as the interfaces of adjacent Voronoi regions. Among these dual-front models, a crucial ingredient is regarded as the geodesic metrics by which the geodesic distances and the corresponding Voronoi diagram can be estimated. In this paper, we introduce a type of asymmetric quadratic metrics dual-front model. The metrics considered are b…

Meaningful Objects Segmentation from SAR Images via A Multi-Scale Non-Local Active Contour Model

The segmentation of synthetic aperture radar (SAR) images is a longstanding yet challenging task, not only because of the presence of speckle, but also due to the variations of surface backscattering properties in the images. Tremendous investigations have been made to eliminate the speckle effects for the segmentation of SAR images, while few work devotes to dealing with the variations of backscattering coefficients in the images. In order to overcome both the two difficulties, this paper presents a novel SAR image segmentation method by exploiting a multi-scale active contour model based on …

基于Chan-Vese活动轮廓的图像分割

Image Segmentation using Chan-Vese Active Contours

本文全面推导并实现了Chan-Vese活动轮廓模型，利用区域强度差异分割图像，在医学和合成图像上验证了其准确性、抗噪性和优于边缘法的性能。

基于无边缘活动轮廓模型的太阳暗条检测

Solar Filaments Detection using Active Contours Without Edges

本文提出基于无边缘活动轮廓（ACWE）的太阳暗条检测算法，通过预处理、分割和后处理三步实现，在基准数据集上优于经典目标检测方法。

End-to-End Trainable Deep Active Contour Models for Automated Image Segmentation: Delineating Buildings in Aerial Imagery

The automated segmentation of buildings in remote sensing imagery is a challenging task that requires the accurate delineation of multiple building instances over typically large image areas. Manual methods are often laborious and current deep-learning-based approaches fail to delineate all building instances and do so with adequate accuracy. As a solution, we present Trainable Deep Active Contours (TDACs), an automatic image segmentation framework that intimately unites Convolutional Neural Networks (CNNs) and Active Contour Models (ACMs). The Eulerian energy functional of the ACM component i…

A Markov Random Field and Active Contour Image Segmentation Model for Animal Spots Patterns

Non-intrusive biometrics of animals using images allows to analyze phenotypic populations and individuals with patterns like stripes and spots without affecting the studied subjects. However, non-intrusive biometrics demand a well trained subject or the development of computer vision algorithms that ease the identification task. In this work, an analysis of classic segmentation approaches that require a supervised tuning of their parameters such as threshold, adaptive threshold, histogram equalization, and saturation correction is presented. In contrast, a general unsupervised algorithm using …

Unsupervised Microvascular Image Segmentation Using an Active Contours Mimicking Neural Network

The task of blood vessel segmentation in microscopy images is crucial for many diagnostic and research applications. However, vessels can look vastly different, depending on the transient imaging conditions, and collecting data for supervised training is laborious. We present a novel deep learning method for unsupervised segmentation of blood vessels. The method is inspired by the field of active contours and we introduce a new loss term, which is based on the morphological Active Contours Without Edges (ACWE) optimization method. The role of the morphological operators is played by novel pool…

Learning deep structured active contours end-to-end

The world is covered with millions of buildings, and precisely knowing each instance's position and extents is vital to a multitude of applications. Recently, automated building footprint segmentation models have shown superior detection accuracy thanks to the usage of Convolutional Neural Networks (CNN). However, even the latest evolutions struggle to precisely delineating borders, which often leads to geometric distortions and inadvertent fusion of adjacent building instances. We propose to overcome this issue by exploiting the distinct geometric properties of buildings. To this end, we pres…

A Local Active Contour Model for Image Segmentation with Intensity Inhomogeneity

A novel locally statistical active contour model (ACM) for image segmentation in the presence of intensity inhomogeneity is presented in this paper. The inhomogeneous objects are modeled as Gaussian distributions of different means and variances, and a moving window is used to map the original image into another domain, where the intensity distributions of inhomogeneous objects are still Gaussian but are better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying a bias field with the original signal within the window. A statis…

End-to-End Deep Convolutional Active Contours for Image Segmentation

The Active Contour Model (ACM) is a standard image analysis technique whose numerous variants have attracted an enormous amount of research attention across multiple fields. Incorrectly, however, the ACM's differential-equation-based formulation and prototypical dependence on user initialization have been regarded as being largely incompatible with the recently popular deep learning approaches to image segmentation. This paper introduces the first tight unification of these two paradigms. In particular, we devise Deep Convolutional Active Contours (DCAC), a truly end-to-end trainable image seg…

Deep Active Contours Using Locally Controlled Distance Vector Flow

Active contours Model (ACM) has been extensively used in computer vision and image processing. In recent studies, Convolutional Neural Networks (CNNs) have been combined with active contours replacing the user in the process of contour evolution and image segmentation to eliminate limitations associated with ACM's dependence on parameters of the energy functional and initialization. However, prior works did not aim for automatic initialization which is addressed here. In addition to manual initialization, current methods are highly sensitive to initial location and fail to delineate borders ac…

Multi-feature driven active contour segmentation model for infrared image with intensity inhomogeneity

Infrared (IR) image segmentation is essential in many urban defence applications, such as pedestrian surveillance, vehicle counting, security monitoring, etc. Active contour model (ACM) is one of the most widely used image segmentation tools at present, but the existing methods only utilize the local or global single feature information of image to minimize the energy function, which is easy to cause false segmentations in IR images. In this paper, we propose a multi-feature driven active contour segmentation model to handle IR images with intensity inhomogeneity. Firstly, an especially-design…

利用活动轮廓重新构想图像分割：从Chan-Vese算法到一种新颖的函数损失框架

Reimagining Image Segmentation using Active Contour: From Chan Vese Algorithm into a Proposal Novel Functional Loss Framework

本文系统研究Chan-Vese算法，提出基于活动轮廓和水平集的函数分割损失，并通过与经典损失函数在常见分割数据集上的对比验证其有效性。

基于自由端点参数轮廓的图像分割与修复

Image Segmentation and Restoration Using Parametric Contours With Free Endpoints

本文提出一种新型自由端点主动轮廓方法，通过离散化穆恩-沙赫功能实现图像分割与修复，结合曲线法向流动和端点切向流动演化规律，采用参数化轮廓与边缘保持去噪实现快速分割与修复。

MARL-MambaContour：释放多智能体深度强化学习用于医学图像分割中的主动轮廓优化

MARL-MambaContour: Unleashing Multi-Agent Deep Reinforcement Learning for Active Contour Optimization in Medical Image Segmentation

本文提出首个基于多智能体强化学习的轮廓级医学图像分割框架MARL-MambaContour，通过将轮廓点建模为自主智能体并结合SAC算法、ERAM机制与Mamba策略网络，实现了拓扑一致的精确分割。

一种用于描绘冰川崩解前沿的深度活动轮廓模型

A Deep Active Contour Model for Delineating Glacier Calving Fronts

本文将冰川崩解前沿描绘重构为轮廓追踪任务，提出结合CNN与活动轮廓模型的COBRA，在格陵兰冰川数据集上优于分割和边缘检测方法，并改善不确定性量化。

基于区域的Randers测地线图像分割方法

A Region-based Randers Geodesic Approach for Image Segmentation

提出一种基于区域Randers测地线的新变分图像分割模型，通过构建区域活动轮廓能量泛函的Randers度量，将分割转化为求解Randers程函PDE，并采用Finsler快速行进法实现高效计算，实验验证了其有效性。

A Novel Image Segmentation Enhancement Technique based on Active Contour and Topological Alignments

Topological alignments and snakes are used in image processing, particularly in locating object boundaries. Both of them have their own advantages and limitations. To improve the overall image boundary detection system, we focused on developing a novel algorithm for image processing. The algorithm we propose to develop will based on the active contour method in conjunction with topological alignments method to enhance the image detection approach. The algorithm presents novel technique to incorporate the advantages of both Topological Alignments and snakes. Where the initial segmentation by To…

基于双曲平均曲率流驱动的主动轮廓模型用于图像分割

Active Contour Models Driven by Hyperbolic Mean Curvature Flow for Image Segmentation

针对抛物线平均曲率流驱动的主动轮廓模型（PMCF-ACMs）在高噪声下因锯齿现象退化的问题，提出双曲平均曲率流驱动的ACM（HMCF-ACMs），通过可调加速场调节演化平滑度，经理论证明和实验验证，其在高噪声下参数敏感性更低、鲁棒性更强、精度更高。

DARNet: Deep Active Ray Network for Building Segmentation

In this paper, we propose a Deep Active Ray Network (DARNet) for automatic building segmentation. Taking an image as input, it first exploits a deep convolutional neural network (CNN) as the backbone to predict energy maps, which are further utilized to construct an energy function. A polygon-based contour is then evolved via minimizing the energy function, of which the minimum defines the final segmentation. Instead of parameterizing the contour using Euclidean coordinates, we adopt polar coordinates, i.e., rays, which not only prevents self-intersection but also simplifies the design of the …

基于主动轮廓驱动的形状变换用于类别不平衡的半监督医学图像分割

Shape Transformation Driven by Active Contour for Class-Imbalanced Semi-Supervised Medical Image Segmentation

针对半监督医学图像分割中器官尺寸差异导致的类别不平衡问题，本文提出STAC方法，利用主动轮廓和符号距离函数对较小器官进行形状变换以缓解不平衡，并在两个基准数据集上验证了其优于现有方法。

Instance segmentation of fallen trees in aerial color infrared imagery using active multi-contour evolution with fully convolutional network-based intensity priors

In this paper, we introduce a framework for segmenting instances of a common object class by multiple active contour evolution over semantic segmentation maps of images obtained through fully convolutional networks. The contour evolution is cast as an energy minimization problem, where the aggregate energy functional incorporates a data fit term, an explicit shape model, and accounts for object overlap. Efficient solution neighborhood operators are proposed, enabling optimization through metaheuristics such as simulated annealing. We instantiate the proposed framework in the context of segment…

IEOPF: An Active Contour Model for Image Segmentation with Inhomogeneities Estimated by Orthogonal Primary Functions

Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clu…

用于快速交互式图像分割的边界提议分组

Grouping Boundary Proposals for Fast Interactive Image Segmentation

本文提出一种基于最小测地线框架的图像分割模型，结合自适应割的圆形最优路径计算和基于图的边界提议分组方案，通过利用图像边缘连通性信息解决复杂场景下的捷径问题，优于现有最先进方法。

Geodesic Models with Convexity Shape Prior

The minimal geodesic models based on the Eikonal equations are capable of finding suitable solutions in various image segmentation scenarios. Existing geodesic-based segmentation approaches usually exploit image features in conjunction with geometric regularization terms, such as Euclidean curve length or curvature-penalized length, for computing geodesic curves. In this paper, we take into account a more complicated problem: finding curvature-penalized geodesic paths with a convexity shape prior. We establish new geodesic models relying on the strategy of orientation-lifting, by which a plana…

Using the Split Bregman Algorithm to Solve the Self-repelling Snake Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snake model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model (GAC). The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algori…

Automated Segmentation of Retinal Layers from Optical Coherent Tomography Images Using Geodesic Distance

Optical coherence tomography (OCT) is a non-invasive imaging technique that can produce images of the eye at the microscopic level. OCT image segmentation to localise retinal layer boundaries is a fundamental procedure for diagnosing and monitoring the progression of retinal and optical nerve disorders. In this paper, we introduce a novel and accurate geodesic distance method (GDM) for OCT segmentation of both healthy and pathological images in either two- or three-dimensional spaces. The method uses a weighted geodesic distance by an exponential function, taking into account both horizontal a…

骨折交互测地主动轮廓用于骨分割

Fracture interactive geodesic active contours for bone segmentation

本文提出一种针对骨骨折分割的改进测地主动轮廓算法，通过结合强度和梯度范数的边缘检测函数，提升骨分割的鲁棒性和准确性。

An Object Aware Hybrid U-Net for Breast Tumour Annotation

In the clinical settings, during digital examination of histopathological slides, the pathologist annotate the slides by marking the rough boundary around the suspected tumour region. The marking or annotation is generally represented as a polygonal boundary that covers the extent of the tumour in the slide. These polygonal markings are difficult to imitate through CAD techniques since the tumour regions are heterogeneous and hence segmenting them would require exhaustive pixel wise ground truth annotation. Therefore, for CAD analysis, the ground truths are generally annotated by pathologist e…

SCR: Smooth Contour Regression with Geometric Priors

While object detection methods traditionally make use of pixel-level masks or bounding boxes, alternative representations such as polygons or active contours have recently emerged. Among them, methods based on the regression of Fourier or Chebyshev coefficients have shown high potential on freeform objects. By defining object shapes as polar functions, they are however limited to star-shaped domains. We address this issue with SCR: a method that captures resolution-free object contours as complex periodic functions. The method offers a good compromise between accuracy and compactness thanks to…

基于渐进式学习的循环通用轮廓实例分割

Recurrent Generic Contour-based Instance Segmentation with Progressive Learning

本文提出 PolySnake 循环轮廓细化网络，通过迭代更新与语义表示实现通用实例分割，并在场景文本和车道检测任务上验证其泛化优势。

Analysis of Amoeba Active Contours

Subject of this paper is the theoretical analysis of structure-adaptive median filter algorithms that approximate curvature-based PDEs for image filtering and segmentation. These so-called morphological amoeba filters are based on a concept introduced by Lerallut et al. They achieve similar results as the well-known geodesic active contour and self-snakes PDEs. In the present work, the PDE approximated by amoeba active contours is derived for a general geometric situation and general amoeba metric. This PDE is structurally similar but not identical to the geodesic active contour equation. It r…

Geodesic Paths for Image Segmentation with Implicit Region-based Homogeneity Enhancement

Minimal paths are regarded as a powerful and efficient tool for boundary detection and image segmentation due to its global optimality and the well-established numerical solutions such as fast marching method. In this paper, we introduce a flexible interactive image segmentation model based on the Eikonal partial differential equation (PDE) framework in conjunction with region-based homogeneity enhancement. A key ingredient in the introduced model is the construction of local geodesic metrics, which are capable of integrating anisotropic and asymmetric edge features, implicit region-based homo…

Interactive Segmentation via Deep Learning and B-Spline Explicit Active Surfaces

Automatic medical image segmentation via convolutional neural networks (CNNs) has shown promising results. However, they may not always be robust enough for clinical use. Sub-optimal segmentation would require clinician's to manually delineate the target object, causing frustration. To address this problem, a novel interactive CNN-based segmentation framework is proposed in this work. The aim is to represent the CNN segmentation contour as B-splines by utilising B-spline explicit active surfaces (BEAS). The interactive element of the framework allows the user to precisely edit the contour in r…

Deep Learning of Unified Region, Edge, and Contour Models for Automated Image Segmentation

Image segmentation is a fundamental and challenging problem in computer vision with applications spanning multiple areas, such as medical imaging, remote sensing, and autonomous vehicles. Recently, convolutional neural networks (CNNs) have gained traction in the design of automated segmentation pipelines. Although CNN-based models are adept at learning abstract features from raw image data, their performance is dependent on the availability and size of suitable training datasets. Additionally, these models are often unable to capture the details of object boundaries and generalize poorly to un…

快速概率蛇算法

Fast probabilistic snake algorithm

本文提出了一种基于概率方法的快速且高精度的主动轮廓算法，用于图像分割，该算法受 A. Blake 和法国 P. Réfrégier 团队研究的启发，且易于适应各种特定应用。

Matching-Constrained Active Contours

In object segmentation by active contours, the initial contour is often required. Conventionally, the initial contour is provided by the user. This paper extends the conventional active contour model by incorporating feature matching in the formulation, which gives rise to a novel matching-constrained active contour. The numerical solution to the new optimization model provides an automated framework of object segmentation without user intervention. The main idea is to incorporate feature point matching as a constraint in active contour models. To this effect, we obtain a mathematical model of…

FFPN：用于超声图像分割的傅里叶特征金字塔网络

FFPN: Fourier Feature Pyramid Network for Ultrasound Image Segmentation

针对超声图像分割中现有DTS框架轮廓编码不足、编码信息利用不充分的问题，提出基于傅里叶锚点的FFPN框架与CSR细化模块，在三个数据集上实现了精度与效率的双重提升，且具备良好泛化性。

Active Contour with A Tangential Component

Conventional edge-based active contours often require the normal component of an edge indicator function on the optimal contours to approximate zero, while the tangential component can still be significant. In real images, the full gradients of the edge indicator function along the object boundaries are often small. Hence, the curve evolution of edge-based active contours can terminate early before converging to the object boundaries with a careless contour initialization. We propose a novel Geodesic Snakes (GeoSnakes) active contour that requires the full gradients of the edge indicator to va…

用于建筑轮廓自动提取的混合特征嵌入

Hybrid Feature Embedding For Automatic Building Outline Extraction

针对传统CNN模型难以精准提取高分辨率航空影像建筑轮廓的问题，提出结合CNN、Transformer与主动轮廓模型的方法，搭配三分支解码器，在两个数据集上取得优于基线的mIoU表现。

PICS in Pics：用于快速图像分割的物理信息轮廓选择

PICS in Pics: Physics Informed Contour Selection for Rapid Image Segmentation

本文提出物理信息轮廓选择算法 PICS，用三次样条替代深度网络并直接最小化基于区域的损失，结合非稳态 PDE 建模与迁移学习，实现无需标注的快速三维医学图像分割。

Learning Euler's Elastica Model for Medical Image Segmentation

Image segmentation is a fundamental topic in image processing and has been studied for many decades. Deep learning-based supervised segmentation models have achieved state-of-the-art performance but most of them are limited by using pixel-wise loss functions for training without geometrical constraints. Inspired by Euler's Elastica model and recent active contour models introduced into the field of deep learning, we propose a novel active contour with elastica (ACE) loss function incorporating Elastica (curvature and length) and region information as geometrically-natural constraints for the i…