Variational Segmentation of Image Sequences Using Region-Based Active Contours and Deformable Shape Priors

In this paper we address the problem of segmentation in image sequences using region-based active contours and level set methods. We propose a novel method for variational segmentation of image sequences containing nonrigid, moving objects. The method is based on the classical Chan-Vese model augmented with a novel frame-to-frame interaction term, which allow us to update the segmentation result from one image frame to the next using the previous segmentation result as a shape prior. The interaction term is constructed to be pose-invariant and to allow moderate deformations in shape. It is expected to handle the appearance of occlusions which otherwise can make segmentation fail. The performance of the model is illustrated with experiments on synthetic and real image sequences.     

Using the Shape Gradient for Active Contour Segmentation: from the Continuous to the Discrete Formulation

A variational approach to image or video segmentation consists in defining an energy depending on local or global image characteristics, the minimum of which being reached for objects of interest. This study focuses on energies written as an integral on a domain of a function which can depend on this domain. The derivative of the energy with respect to the domain, the so-called shape derivative, is a function of a velocity field applied to the domain boundary. For a given, non-optimal domain, the velocity should be chosen such that the shape derivative is negative, thus indicating a way to deform the domain in order to decrease its energy. Minimizing the energy through an iterative deformation process is known as the active contour method. In the continuous framework, setting the velocity to the opposite of the gradient associated with the L ² inner product is a common practice. In this paper, it is noted that the negativity of the shape derivative is not preserved, in general, by the discretization of this velocity required by implementation. In order to guarantee that the negativity condition holds in the discrete framework, it is proposed to choose the velocity as a linear combination of pre-defined velocities. This approach also gives more flexibility to the active contour process by allowing to introduce some a priori knowledge about the optimal domain. Some experimental results illustrate the differences between the classical and the proposed approach.

From Inpainting to Active Contours

Background subtraction is an elementary method for detection of foreground objects and their segmentations. Obviously it requires an observation image as well as a background one. In this work we attempt to remove the last requirement by reconstructing the background from the observation image and a guess on the location of the object to be segmented via variational inpainting method. A numerical evaluation of this reconstruction provides a “disocclusion measure” and the correct foreground segmentation region is expected to maximize this measure. This formulation is in fact an optimal control problem, where controls are shapes/regions and states are the corresponding inpaintings. Optimization of the disocclusion measure leads formally to a coupled contour evolution equation, an inpainting equation (the state equation) as well as a linear PDE depending on the inpainting (the adjoint state equation). The contour evolution is implemented in the framework of level sets. Finally, the proposed method is validated on various examples. We focus among others in the segmentation of calcified plaques observed in radiographs from human lumbar aortic regions.     

一种鲁棒的区域活动轮廓图像分割方法

针对分割灰度不均或者边缘模糊图像时出现的问题,提出一种改进的活动轮廓模型。首先,利用图像的统计信息构建新的全局力和局部力。其次,将这两种力加权组合得到一个混合的能量函数。采用水平集方法最小化该能量泛函,得到水平集演化方程并不断更新。最后,采用高斯滤波方法规则化水平集方程。合成图像和真实图像的实验结果表明:优化模型能有效地分割非同质或弱边缘图像,对噪声以及初始轮廓曲线具有较好的鲁棒性以及高的计算效率等优点。     

Stochastic Motion and the Level Set Method in Computer Vision: Stochastic Active Contours

Based on recent work on Stochastic Partial Differential Equations (SPDEs), this paper presents a simple and well-founded method to implement the stochastic evolution of a curve. First, we explain why great care should be taken when considering such an evolution in a Level Set framework. To guarantee the well-posedness of the evolution and to make it independent of the implicit representation of the initial curve, a Stratonovich differential has to be introduced. To implement this differential, a standard Ito plus drift approximation is proposed to turn an implicit scheme into an explicit one. Subsequently, we consider shape optimization techniques, which are a common framework to address various applications in Computer Vision, like segmentation, tracking, stereo vision etc. The objective of our approach is to improve these methods through the introduction of stochastic motion principles. The extension we propose can deal with local minima and with complex cases where the gradient of the objective function with respect to the shape is impossible to derive exactly. Finally, as an application, we focus on image segmentation methods, leading to what we call Stochastic Active Contours.     

New Possibilities with Sobolev Active Contours

Recently, the Sobolev metric was introduced to define gradient flows of various geometric active contour energies. It was shown that the Sobolev metric outperforms the traditional metric for the same energy in many cases such as for tracking where the coarse scale changes of the contour are important. Some interesting properties of Sobolev gradient flows include that they stabilize certain unstable traditional flows, and the order of the evolution PDEs are reduced when compared with traditional gradient flows of the same energies. In this paper, we explore new possibilities for active contours made possible by Sobolev metrics. The Sobolev method allows one to implement new energy-based active contour models that were not otherwise considered because the traditional minimizing method render them ill-posed or numerically infeasible. In particular, we exploit the stabilizing and the order reducing properties of Sobolev gradients to implement the gradient descent of these new energies. We give examples of this class of energies, which include some simple geometric priors and new edge-based energies. We also show that these energies can be quite useful for segmentation and tracking. We also show that the gradient flows using the traditional metric are either ill-posed or numerically difficult to implement, and then show that the flows can be implemented in a stable and numerically feasible manner using the Sobolev gradient. Sundaramoorthi and Yezzi were supported by NSF CCR-0133736, NIH/NINDS R01-NS-037747, and Airforce MURI; Sapiro was partially supported by NSF, ONR, NGA, ARO, DARPA, and the McKnight Foundation.     

基于几何活动轮廓模型的人脸轮廓提取方法

针对在结构性噪声较严重的情况下 ,常规几何活动轮廓模型无法获得理想分割效果的问题 ,提出一种基于几何活动轮廓模型的人脸轮廓提取方法 ,该方法首先将人脸形状的椭圆性约束作为算子嵌入到几何活动轮廓模型中 ,并利用几何活动轮廓模型提取任意轮廓的优势来快速抽取出图象中类似椭圆的目标边缘 ;然后根据图象中人脸的先验知识 ,通过对检测到的椭圆目标进行进一步验证来找出最终人脸轮廓 .由于采用变分水平集方法做数值计算 ,因此该方法不仅能够自然地处理曲线的拓扑变化和能较精确地提取出图象中的人脸轮廓 ,而且同时可以给出人脸水平旋转的大致角度等信息 .实验结果表明 ,该方法是有效的 .     

针对凹陷轮廓改进的主动轮廓模型

针对传统主动轮廓模型不能有效拟合凹陷轮廓的问题进行研究,从内部、外部能量两方面进行分析。通过模拟流体压力的思路对内部能量项中的弹性能量进行改进,提出一种针对凹陷轮廓改进的主动轮廓模型——Area Snake,并对其理论模型、实现细节和不足进行讨论。实验表明,Area Snake对凹陷轮廓有着较好的拟合性能。     

Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images

We present a framework for incorporating prior information about high-probability shapes in the process of contour extraction and object recognition in images. Here one studies shapes as elements of an infinite-dimensional, non-linear quotient space, and statistics of shapes are defined and computed intrinsically using differential geometry of this shape space. Prior models on shapes are constructed using probability distributions on tangent bundles of shape spaces. Similar to the past work on active contours, where curves are driven by vector fields based on image gradients and roughness penalties, we incorporate the prior shape knowledge in the form of vector fields on curves. Through experimental results, we demonstrate the use of prior shape models in the estimation of object boundaries, and their success in handling partial obscuration and missing data. Furthermore, we describe the use of this framework in shape-based object recognition or classification.     

一种基于主动轮廓模型的心脏核磁共振图像分割方法

提出一种基于主动轮廓模型的左室壁内、外膜分割方法.首先构造了主动轮廓模型的广义法向有偏梯度矢量流外力模型GNBGVF,作为对梯度矢量流(GVF)的改进,该外力场同时保持了切线方向和法线方向有偏的扩散,具有捕捉范围大、抗噪能力强,且在弱边界泄漏等问题上性能突出.就左室壁内膜的分割而言,考虑到左室壁的近似为圆形的特点,引入了圆形约束的能量项,有利于克服由于图像灰度不均、乳突肌等而导致的局部极小.对于左室壁外膜的分割,采用内膜的分割结果初始化,即通过重新组合梯度分量来构造外力场.该外力场能够克服原始梯度矢量流的不足,使得左室壁外膜边缘很弱时也能得到保持,可以自动、准确地分割外膜.实验结果表明,该方法能高效准确地分割左室壁内、外膜.     

Using classifiers as heuristics to describe local structure in Active Shape Models with small training sets

Active Shape Models (ASM) are a successful image segmentation technique that is widely used by the image processing community. This technique is very appealing when the results of the segmentation are going to be used to perform some kind of classification, as it provides a mathematical model of the segmented contours. Nevertheless, little attention has been paid to the development of general local appearance models for small image training sets and most researchers have resorted to ad hoc solutions. In this paper we propose a heuristic approach to this problem. A general procedure for the use of heuristics to guide the ASM search algorithm and an implementation using machine learning classifiers is presented. This procedure is also extended to cope with multichannel images. Tests are carried out over small synthetic and real image datasets. The performance of this approach is compared to the most commonly used Mahalanobis appearance model and the simpler edge search strategy. The results show that the heuristic approach performs better than the other two procedures.     

基于变分域的主动形状模型标记点自动标定

针对主动形状模型(Active Shape Model,ASM)的标定问题,提出了变分域的概念,并且利用变分域实现主动形状模型的自动标定.算法首先通过对样本集变分映射以得到形状变化的幅度、频度和位置,然后在D-P曲线采样算法的基础上,根据变分域信息动态设定平均形状标记点的位置和密度分布,从而把样本集的变化信息作为先验知识引入到标定中,提高了标记点对样本集变化的描述能力.实验表明,该方法能够得到更合理的标记点分布和更准确的样本形状及变化描述,而且ASM形状模型更加紧致.     

Active Contours Under Topology Control—Genus Preserving Level Sets

We present a novel framework to exert topology control over a level set evolution. Level set methods offer several advantages over parametric active contours, in particular automated topological changes. In some applications, where some a priori knowledge of the target topology is available, topological changes may not be desirable. This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge. However, topologically constrained evolutions often generate topological barriers that lead to large geometric inconsistencies. We introduce a topologically controlled level set framework that greatly alleviates this problem. Unlike existing work, our method allows connected components to merge, split or vanish under some specific conditions that ensure that the genus of the initial active contour (i.e. its number of handles) is preserved. We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.