3D Curves Reconstruction Based on Deformable Models

We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography.     

基于LBF方法的测地线活动轮廓模型

经典的测地线活动轮廓模型分割含有弱边界的目标时,难以得到真实边界。为解决这一问题,文中将结合局部二元拟合(LBF)方法和测地线活动轮廓模型的优点,提出一种基于LBF方法的测地线活动轮廓模型。首先,将LBF方法的能量泛函进行归一化处理,取代测地线活动轮廓模型的边缘停止函数。其次,构建梯度下降流,促使轮廓曲线运动到目标边界上。最后,对5组含有弱边界的图像进行仿真实验。实验结果表明,文中模型能准确分割含有弱边界的目标,具有抗噪性,同时对初始曲线的位置不敏感,优于其它常见改进的测地线活动轮廓模型。     

Regularized Laplacian Zero Crossings as Optimal Edge Integrators

We view the fundamental edge integration problem for object segmentation in a geometric variational framework. First we show that the classical zero-crossings of the image Laplacian edge detector as suggested by Marr and Hildreth, inherently provides optimal edge-integration with regard to a very natural geometric functional. This functional accumulates the inner product between the normal to the edge and the gray level image-gradient along the edge. We use this observation to derive new and highly accurate active contours based on this functional and regularized by previously proposed geodesic active contour geometric variational models. We also incorporate a 2D geometric variational explanation to the Haralick edge detector into the geometric active contour framework.     

Multiple piecewise constant with geodesic active contours (MPC-GAC) framework for interactive image segmentation using graph cut optimization

This paper proposes an improved variational model, multiple piecewise constant with geodesic active contour (MPC-GAC) model, which generalizes the region-based active contour model by Chan and Vese, 2001 [11] and merges the edge-based active contour by Caselles et al., 1997 [7] to inherit the advantages of region-based and edge-based image segmentation models. We show that the new MPC-GAC energy functional can be iteratively minimized by graph cut algorithms with high computational efficiency compared with the level set framework. This iterative algorithm alternates between the piecewise constant functional learning and the foreground and background updating so that the energy value gradually decreases to the minimum of the energy functional. The k-means method is used to compute the piecewise constant values of the foreground and background of image. We use a graph cut method to detect and update the foreground and background. Numerical experiments show that the proposed interactive segmentation method based on the MPC-GAC model by graph cut optimization can effectively segment images with inhomogeneous objects and background.     

MAC: magnetostatic active contour model

We propose an active contour model using an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries. The major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations, weak edges and broken boundaries. The proposed method is shown to achieve significant improvements when compared against six well-known and state-of-the-art shape recovery methods, including the geodesic snake, the generalized version of GVF snake, the combined geodesic and GVF snake, and the charged particle model.     

Sobolev Active Contours

All previous geometric active contour models that have been formulated as gradient flows of various energies use the same L ²-type inner product to define the notion of gradient. Recent work has shown that this inner product induces a pathological Riemannian metric on the space of smooth curves. However, there are also undesirable features associated with the gradient flows that this inner product induces. In this paper, we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with Sobolev-type inner products. We call the resulting flows Sobolev active contours. Sobolev metrics induce favorable regularity properties in their gradient flows. In addition, Sobolev active contours favor global translations, but are not restricted to such motions; they are also less susceptible to certain types of local minima in contrast to traditional active contours. These properties are particularly useful in tracking applications. We demonstrate the general methodology by reformulating some standard edge-based and region-based active contour models as Sobolev active contours and show the substantial improvements gained in segmentation.     

基于GVF和压力Snake模型的哑铃型目标提取

针对传统活动模型初始化曲线严格的位置选择问题和梯度矢量流场模型存在的哑铃型目标"临界点"问题,提出了梯度矢量流场构造出气球压力的活动轮廓改进模型.利用了梯度矢量流场决定形变点的压力方向,在该构造压力与图像外力及轮廓曲线内力的共同作用下模型完成目标提取.结合实例对改进模型和算法进行了试验分析,结果表明了模型的可行性和算法的有效性.     

Mesh Snapping: Robust Interactive Mesh Cutting Using Fast Geodesic Curvature Flow

This paper considers the problem of interactively finding the cutting contour to extract components from a given mesh. Some existing methods support cuts of arbitrary shape but require careful and tedious input from the user. Others need little user input however they are sensitive to user input and need a postprocessing step to smooth the generated jaggy cutting contours. The popular geometric snake can be used to optimize the cutting contour, but it cannot deal with the topology change. In this paper, we propose a geodesic curvature flow based framework to overcome all these problems. Since in many cases the meaningful cutting contour on a 3D mesh is locally shortest in the sense of some weighted curve length, the geodesic curvature flow is an ideal tool for our problem. It evolves the cutting contour to the nearby local minimum. We should mention that the previous numerical scheme, discretized geodesic curvature flow (dGCF) is too slow and has not been applied to mesh segmentation. With a careful observation to dGCF, we devise here a fast computation scheme called fast geodesic curvature flow (FGCF), which only needs to solve a smaller and easier problem. The initial cutting contour is generated by a variant of random walks algorithm, which is very fast and gives reasonable cutting result with little user input. Experiment results on the benchmark mesh segmentation data set show that our proposed framework is robust to user input and capable of producing good results reflecting geometric features and human shape perception.     

Incorporating shape prior into geodesic active contours for detecting partially occluded object

A new method to incorporate shape prior knowledge into geodesic active contours for detecting partially occluded object is proposed in this paper. The level set functions of the collected shapes are used as training data. They are projected onto a low dimensional subspace using PCA and their distribution is approximated by a Gaussian function. A shape prior model is constructed and is incorporated into the geodesic active contour formulation to constrain the contour evolution process. To balance the strength between the image gradient force and the shape prior force, a weighting factor is introduced to adaptively guide the evolving curve to move under both forces. The curve converges with due consideration of both local shape variations and global shape consistency. Experimental results demonstrate that the proposed method makes object detection robust against partial occlusions.     

Geometric active contours without re-initialization for image segmentation

A geometric active contour model without re-initialization that can be used for grey and color image segmentation is presented in this paper. It combines directional information about edge location based on Cumani operator as a part of driving force, with the improved geodesic active contours containing Bays error based statistical region information. Moreover, an extra term that penalizes the deviation of the level set function from a signed distance function is also included in the model, thus the costly re-initialization procedure can be completely eliminated and all these measures are integrated in a unified frame. Experimental results on real grey and color images have shown that our model can precisely extract contours of images and its performance is much better and faster than the geodesic-aided C-V (GACV) model.     

Dynamic active contours for visual tracking

Visual tracking using active contours is usually set in a static framework. The active contour tracks the object of interest in a given frame of an image sequence. A subsequent prediction step ensures good initial placement for the next frame. This approach is unnatural; the curve evolution gets decoupled from the actual dynamics of the objects to be tracked. True dynamical approaches exist, all being marker particle based and thus prone to the shortcomings of such particle-based implementations. In particular, topological changes are not handled naturally in this framework. The now classical level set approach is tailored for evolutions of manifolds of codimension one. However, dynamic curve evolution is at least a codimension two problem. We propose an efficient, level set based approach for dynamic curve evolution, which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation. It is based on a new energy minimization functional which, for the first time, puts dynamics into the geodesic active contour framework.     

基于多分辨率方法的主动轮廓线跟踪算法

由Ｋａｓｓ等１９８７年首次提出的主动次轮廓线模型，在数字图像分析和计算机视觉领域得到了越来越广泛的应用，基于单分辨率的主动轮廓线跟踪算法在一个共同的缺点，即：要求初始轮廓线离目标的真实轮廓线很近，这样的算法用于跟踪将只能跟踪缓慢运动的目标，从而限制了主动轮廓线跟踪算法的应用范围，本文提出了一种基于多分辨率的主动轮廓线跟踪算法，它不但继承了基于单分辨率的主动轮廓线算法的优点，而且降低了对初始轮廓线的     

用于图像分割的活动轮廓模型综述

图像分割和边界提取对于图像理解、图像分析、模式识别、计算机视觉等具有非常重要的意义,而活动轮廓模型(Active Contour Model)则是图像分割和边界提取的重要工具之一,它主要包括参数活动轮廓模型和几何活动轮廓模型两类。相对于参数活动轮廓模型,几何活动轮廓模型具有很多的优点,如计算的简单性和在变形的过程中能够处理曲线的拓扑变化,等等。近年来,几何活动轮廓模型在理论和应用方面的研究都有很大的发展,令人关注。为了使人们对这一技术有一概略了解,首先提出了一种新的分类方式用来描述参数活动轮廓模型、几何活动轮廓模型以及它们之间的联系,然后通过重点分析几个经典的活动轮廓模型及其算法实现来综述活动轮廓模型的研究、发展及其应用情况,最后指出了进一步进行活动轮廓模型理论与应用研究的方向。     

Global and Local Active Contours for Head Boundary Extraction

Active contours are an attractive choice to extract the head boundary, for deployment within a face recognition or model-based coding scenario. However, conventional snake approaches can suffer difficulty in initialisation and parameterisation. A dual active contour configuration using dynamic programming has been developed to resolve these difficulties by using a global energy minimisation technique and a simplified parameterisation, to enable a global solution to be obtained. The merits of conventional gradient descent based snake (local) approaches, and search-based (global) approaches are discussed. In application to find head and face boundaries in front-view face images, the new technique employing dynamic programming is deployed to extract the inner face boundary, along with a conventional normal-driven contour to extract the outer (head) boundary. The extracted contours appear to offer sufficient discriminatory capability for inclusion within an automatic face recognition system.     

融合区域和测地线的活动轮廓模型与图割相结合的自然图像分割

针对活动轮廓模型利用水平集函数演化来分割图像时,只能分割灰度均匀的图像 问题以及容易陷入能量泛函局部极小值的缺点,提出一种新的图像分割模型。模型将区域中的 局部和全局信息融合的活动轮廓模型与边界模型相结合,然后利用图切割进行优化。实验表明, 该方法对初始曲线不敏感,能分割灰度不均的自然图像,避免陷入局部极小,并能有效提高图 像分割的速度和精度。     

基于力场分析的主动轮廓模型

传统Snake模型存在的缺点是，其初始轮廓必须靠近图像中感兴趣目标的真实边缘，否则会得到错误结果，且由于Snake模型的非凸性，结果不能进入感兴趣目标的深凹部分，很容易陷入局部极小点，由此该文提出一种基于力场分析的主动轮廓模型，详细分析了基于欧氏距离变换的距离势能力场分布，归纳出感兴趣目标上真轮廓点与假轮廓点的判别标准，建立了由曲线能量到最终结果的有效方法，避免了Snake陷入局部极小点，实验结果表明，该模型具有较大的捕获区域，能够进入感兴趣目标的深凹部分，准确提取感兴趣目标的轮廓，与GVF Snake模型相比，该模型具有很小的计算量。     

利用区域信息融合混合活动轮廓模型的 河流遥感图像分割

目的 河流遥感图像是背景复杂的非匀质图像,利用传统的活动轮廓模型进行分割往往不够准确。针对这一问题,提出了基于区域信息融合的混合活动轮廓模型来分割河流遥感图像。方法 该混合模型将Chan-Vese(CV)模型和基于交叉熵的活动轮廓模型的外部能量约束项相结合,并赋予归一化调节比例系数。通过计算轮廓曲线内外区域像素灰度的方差和交叉熵,指导曲线逼近目标边缘。为了加速混合模型的演化,引入曲线内外区域像素灰度的类内绝对差,取代原有的内外区域能量权值,以提高混合模型的分割效率。结果 大量实验结果表明,相较于CV模型、测地线模型、基于交叉熵的活动轮廓模型、CV模型和测地线模型的混合模型以及局部全局灰度拟合能量模型(LGIF),本文混合模型分割河流遥感图像的灵敏度和上述方法都接近于100%,准确率大幅提升,在90%以上,虚警率则下降了约50%,且所需迭代次数和运行时间更少。结论 本文提出的混合模型主要适用于具有一定对比度的河流遥感图像,在分割性能和分割效率两个方面,都有明显的优势。     

Template-driven segmentation of confocal microscopy images

High quality 3D visualization of anatomic structures is necessary for many applications. The anatomic structures first need to be segmented. A variety of segmentation algorithms have been developed for this purpose. For confocal microscopy images, the noise introduced during the specimen preparation process, such as the procedure of penetration or staining, may cause images to be of low contrast in some regions. This property will make segmentation difficult. Also, the segmented structures may have rugged surfaces in 3D visualization. In this paper, we present a hybrid method that is suitable for segmentation of confocal microscopy images. A rough segmentation result is obtained from the atlas-based segmentation via affine registration. The boundaries of the segmentation result are close to the object boundaries, and are regarded as the initial contours of the active contour models. After convergence of the snake algorithm, the resulting contours in regions of low contrast are locally refined by parametric bicubic surfaces to alleviate the problem of incorrect convergence. The proposed method increases the accuracy of the snake algorithm because of better initial contours. Besides, it can provide smoother segmented results in 3D visualization.     

实时三维超声心动图中二尖瓣的提取

二尖瓣的复杂结构和不规则运动特性使得自动提取非常困难，因而依据二尖瓣解剖形状的先验知识，采用人机交互方式构造符合二尖瓣生理形状的柱状区域，把该区域作为测地活动轮廓模型的区域约束项，在levelset框架下对二尖瓣进行分割提取。该方法通过对大量三维超声瓣膜进行实验，取得了良好的分割效果，能够直接准确提取三维心脏二尖瓣。     

Active Rays: Polar-transformed Active Contours for Real-Time Contour Tracking

In this paper we describe a new approach to contour extraction and tracking, which is based on the principles of active contour models and overcomes its shortcomings. We formally introduce active rays, describe the contour extraction as an energy minimization problem and discuss what active contours and active rays have in common.The main difference is that for active rays a unique ordering of the contour elements in the 2D image plane is given, which cannot be found for active contours. This is advantageous for predicting the contour elements' position and prevents crossings in the contour. Further, another advantage is that instead of an energy minimization in the 2D image plane the minimization is reduced to a 1D search problem. The approach also shows any-time behavior, which is important with respect to real-time applications. Finally, the method allows for the management of multiple hypotheses of the object's boundary. This is an important aspect if concave contours are to be tracked.Results on real image sequences (tracking a toy train in a laboratory scene, tracking pedestrians in an outdoor scene) show the suitability of this approach for real-time object tracking in a closed loop between image acquisition and camera movement. The contour tracking can be done within the image frame rate (25 fps) on standard Unix workstations (HP 735) without any specialized hardware.