局部区域拟合的快速水平集图像分割方法

目的 由于灰度不均匀图像在不同目标区域的灰度分布存在严重的重叠,对其进行分割仍然是一个难题;同时,图像中的噪声严重降低了图像分割的准确性。因此,传统水平集方法无法鲁棒、精确、快速地对具有灰度不均匀性和噪声的图像进行分割。针对这一问题,提出一种基于局部区域信息的快速水平集图像分割方法。方法 灰度不均匀图像通常被描述为一个分段常数图像乘以一个缓慢变化的偏移场。首先,通过一个经过微调的多尺度均值滤波器来估计图像的偏移场,并对图像进行预处理以减轻图像的不均匀性;然后,利用基于偏移场校正的方法和基于局部区域信息拟合的方法分别构建能量项,并利用演化曲线轮廓内外图像灰度分布的重叠程度,构建权重函数自适应调整两个能量项之间的权重;最后,引入全方差规则项对水平集进行约束,增强了数值计算的稳定性和对噪声的鲁棒性,并通过加性算子分裂策略实现水平集快速演化。结果 在具有不同灰度不均匀性和噪声图像上的分割结果表明,所提方法不但对初始轮廓的位置、灰度不均匀性和各种噪声具有较强的鲁棒性,而且具有高达94.5%的分割精度和较高的分割效率,与传统水平集方法相比分割精度至少提高了20.6%,分割效率是LIC（local intensity clustering）模型的9倍;结论 本文提出一种基于局部区域信息的快速水平集图像分割方法。实验结果表明,与传统水平集方法相比具有较高的分割精度和分割效率,可以很好地应用于具有灰度不均匀和噪声的医学、红外和自然图像等的分割。     

A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples

We address an ill-posed inverse problem of image estimation from sparse samples of its Fourier transform. The problem is formulated as joint estimation of the supports of unknown sparse objects in the image, and pixel values on these supports. The domain and the pixel values are alternately estimated using the level-set method and the conjugate gradient method, respectively. Our level-set evolution shows a unique switching behavior, which stabilizes the level-set evolution. Furthermore, the trade-off between the stability and the speed of evolution can be easily controlled by the number of the conjugate gradient steps, thus avoiding the re-initialization steps in conventional level set approaches.     

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.     

On Symmetry, Perspectivity, and Level-Set-Based Segmentation

We introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion. Information on the symmetry axis of the object and the distorting transformation is obtained as a by--product of the segmentation process. The key idea is the use of a flip or a rotation of the image to segment as if it were another view of the object. We call this generated image the symmetrical counterpart image. We show that the symmetrical counterpart image and the source image are related by planar projective homography. This homography is determined by the unknown planar projective transformation that distorts the object symmetry. The proposed segmentation method uses a level-set-based curve evolution technique. The extraction of the object boundaries is based on the symmetry constraint and the image data. The symmetrical counterpart of the evolving level-set function provides a dynamic shape prior. It supports the segmentation by resolving possible ambiguities due to noise, clutter, occlusions, and assimilation with the background. The homography that aligns the symmetrical counterpart to the source level-set is recovered via a registration process carried out concurrently with the segmentation. Promising segmentation results of various images of approximately symmetrical objects are shown.     

改进的分级多相图像分割模型及其快速实现

提出一种基于分级C-V模型的改进的快速图像分割算法.针对现有的多相水平集图像分割算法存在的问题,本文从曲线演化方程的平均曲率项、水平集函数Φ的狄拉克(Dirac)函数δ(Φ)等方面进行改进,并引入了一个非线性扩散方程对图像进行预处理,从而优化组合了分级C-V模型的全局特性.实验结果表明,改进的图像分割模型不仅保留了原有方法的优势,而且提高了对多目标图像分割算法的速度与精度,同时也可以有效解决具有弱边界物体的分割问题.     

Curvature-Driven PDE Methods for Matrix-Valued Images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edge-like structures in tensor fields, we first generalise Di Zenzo’s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts.     

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.     

风场作用下动态草地场景的建模与绘制

为真实地模拟草在风中摇曳的动态效果,从结构动力学角度将风场视为具有时间和空间相关性的随机过程,利用线性自回归过滤器的方法生成给定条件的风速矢量场,进而运用动力学中有限元分析的方法实时计算风力作用下草的不同部分的受力和形变。在上述基础上,采用基于L系统和基于图像的表示方法对近处的草模型进行参数化建模,并用星形的结构建立远处草体的模型,以便加速场景视点相关的绘制。综合上述算法并结合GPU的可编程功能,可以实时模拟风场作用下草地的动态效果,且真实感比较强。     

Morphological image sequence processing

We present a morphological multi-scale method for image sequence processing, which results in a truly coupled spatio-temporal anisotropic diffusion. The aim of the method is not to smooth the level-sets of single frames but to denoise the whole sequence while retaining geometric features such as spatial edges and highly accelerated motions. This is obtained by an anisotropic spatio-temporal level-set evolution, where the additional artificial time variable serves as the multi-scale parameter. The diffusion tensor of the evolution depends on the morphology of the sequence, given by spatial curvatures of the level-sets and the curvature of trajectories (=acceleration) in sequence-time. We discuss different regularization techniques and describe an operator splitting technique for solving the problem. Finally we compare the new method with existing multi-scale image sequence processing methodologies.     

A refined particle filter based on determined level set model for robust contour tracking

Traditional particle filter which uses simple geometric shapes for representation cannot track objects with complex shape accurately. In this paper, we propose a refined particle filter method for contour tracking based on a determined binary level set model (DBLSM). In contrast with other previous work, the computational efficiency is greatly improved due to the simple form of the level set function. The DBLSM adds prior knowledge of the target model to the implementation of curve evolution which improves the curve acting principle and ensures a more accurate convergence to the target. Finally, we perform curve evolution in the update step of particle filter to make good use of the observation at current time. Some appearance information are considered together with the energy function to measure weights for particles, which can identify the target more accurately. Experiment results on several challenging video sequences have verified the proposed algorithm is efficient and effective in many complicated scenes.     

采用测地线活动轮廓模型检测与跟踪运动目标

水平集几何活动轮廓模型能较好地适应曲线的拓扑变化.为了跟踪和获取刚体和非刚体运动目标的轮廓信息,提出了一种基于改进测地线活动轮廓(GAC)模型和Kalman滤波相结合的算法以检测和跟踪运动目标.该算法首先采用高斯混合模型和背景差分获取目标的运动区域,在运动区域内采用引入距离规则化项的GAC模型进行曲线演化,使改进GAC模型在运动目标的真实轮廓处收敛;然后通过结合Kalman滤波预测目标下一帧的位置,实现对目标轮廓跟踪.实验结果表明,该方法适用于刚体和非刚体目标,在部分遮挡的情况下也能保持良好的检测和跟踪效果.     

Improving performance of distribution tracking through background mismatch

This paper proposes a new density matching method based on background mismatching for tracking of nonrigid moving objects. The new tracking method extends the idea behind the original density-matching tracker, which tracks an object by finding a contour in which the photometric density sampled from the enclosed region most closely matches a model density. This method can be quite sensitive to the initial curve placements and model density. The new method eliminates these sensitivities by adding a second term to the optimization: the mismatch between the model density and the density sampled from the background. By maximizing this term, the tracking algorithm becomes significantly more robust in practice. Furthermore, we show the enhanced ability of the algorithm to deal with target objects, which possess smooth or diffuse boundaries. The tracker is in the form of a partial differential equation, and is implemented using the level-set framework. Experiments on synthesized images and real video sequences show our proposed methods are effective and robust; the results are compared with several existing methods.     

基于策略演化水平集的医学图像快速分割

医学图像分割在疾病诊断、手术规划和手术引导等实际应用中有着重要的作用。提出了一种基于策略演化水平集算法的快速医学图像分割方法,其策略是通过转换外部轮廓曲线/曲面上的点为内部轮廓曲线/曲面上的点（或做相反操作时）,检验能量函数是否减小来决策水平集演化;如此扫描内外轮廓曲线/曲面,使得分割曲线/曲面向目标边界移动。相对于传统水平集算法,该方法不需要解偏微分方程,可极大地减小计算量、提高图像分割的速度。同时,该算法克服了直接计算能量函数水平集方法中存在的问题(陷入局部能量最小和需要扫描整个图像)。最后通过2维和3维医学图像的分割实验,展示了该算法的快速性与精确性。     

Edge and corner detection by photometric quasi-invariants

Feature detection is used in many computer vision applications such as image segmentation, object recognition, and image retrieval. For these applications, robustness with respect to shadows, shading, and specularities is desired. Features based on derivatives of photometric invariants, which we is called full invariants, provide the desired robustness. However, because computation of photometric invariants involves nonlinear transformations, these features are unstable and, therefore, impractical for many applications. We propose a new class of derivatives which we refer to as quasi-invariants. These quasi-invariants are derivatives which share with full photometric invariants the property that they are insensitive for certain photometric edges, such as shadows or specular edges, but without the inherent instabilities of full photometric invariants. Experiments show that the quasi-invariant derivatives are less sensitive to noise and introduce less edge displacement than full invariant derivatives. Moreover, quasi-invariants significantly outperform the full invariant derivatives in terms of discriminative power.     

Modeling individual’s aging within a bacterial population using a pi-calculus paradigm

We propose an aging mechanism which develops in artificial bacterial populations fighting against antibiotic molecules. The mechanism is based on very elementary information gathered by each individual and elementary reactions as well. Though we do not interpret the aging process in strictly biological terms, it appears compliant with recent studies on the field, and physically feasible. The root of the aging mechanism is an adaptation strategy based on a thresholding operation that derives from theoretical results on stochastic monotone games. The methods for implementing it denote their rationale in that they represent a sophisticated dialect of pi-calculus, a widespread computational paradigm for implementing dynamics of massive populations with bipolar reactions. As a result we may implement processes that explain some typical patterns of the evolution of the immunosystems.     

Generalised Nonlocal Image Smoothing

We propose a discrete variational approach for image smoothing consisting of nonlocal data and smoothness constraints that penalise general dissimilarity measures defined on image patches. One of such dissimilarity measures is the weighted L ₂ distance between patches. In such a case we derive an iterative neighbourhood filter that induces a new similarity measure in the photometric domain. It can be regarded as an extended patch similarity measure that evaluates not only the patch similarity of two chosen pixels, but also the similarity of their corresponding neighbours. This leads to a more robust smoothing process since the pixels selected for averaging are more coherent with the local image structure. By slightly modifying the way the similarities are computed we obtain two related filters: The NL-means filter of Buades et al. (SIAM Multiscale Model. Simul. 4(2):490–530, 2005b) and the NDS filter of Mrázek et al. (Geometric Properties for Incomplete Data, Computational Imaging and Vision, vol. 31, pp. 335–352, Springer, Dordrecht, 2006). In fact, the proposed approach can be considered as a generalisation of the latter filter to the space of patches. We also provide novel insights into relations of the NDS filter with diffusion/regularisation methods as well as with some recently proposed graph regularisation techniques. We evaluate our method for the task of denoising greyscale and colour images degraded with Gaussian and salt-and-pepper noise, demonstrating that it compares very well to other more sophisticated approaches.     

Noise Reduction in Surface Reconstruction from a Given Gradient Field

We present a gradient space technique for noise reduction in surfaces reconstructed from a noisy gradient field. We first analyze the error sources in the recovered gradient field of a surface using a three-image photometric stereo method. Based on this analysis, we propose an additive noise model to describe the errors in the surface gradient estimates. We then use a vector space formulation and construct a multiscale orthonormal expansion for gradient fields. Using the sparse representation properties of this expansion, we develop techniques for reducing the gradient field noise by coefficient selection with thresholding. The simulation results indicate that the proposed technique provides significant improvement on the noise levels of both the estimated gradient fields and the reconstructed surfaces under heavy noise levels. Furthermore, the experiments using noisy photometric stereo image triplets of real range data suggest that the additive model remains viable after the nonlinear photometric stereo operation to provide accurate noise removal.     

A New Poisson Noise Filter Based on Weights Optimization

We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the observed image. But in contrast to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some “oracle” weights are defined by minimizing a very tight upper bound of the Mean Square Error. For a practical application the weights are estimated from the observed image. We prove that the proposed filter converges at the usual optimal rate to the true image. Simulation results are presented to compare the performance of the presented filter with conventional filtering methods.     

A variational binary level-set method for elliptic shape optimization problems

We present a variational binary level-set method to solve a class of elliptic problems in shape optimization. By the ‘ersatz material’ approach, which amounts to fill the holes by a weak phase, the original shape optimization model is approximated by a two-phase optimization problem. Under the binary level-set framework, we need to optimize a smooth functional under a binary constraint. We propose an augmented Lagrangian method to solve the constrained optimization problem. Numerical results are presented and compared with those obtained by level-set methods, which demonstrate the robustness and efficiency of our method.     

Filtering image records using wavelets and the Zakai equation

Consider the problem of detecting and localizing a faint object moving in an “essentially stationary” background, using a sequence of 2D low S/N ratio images of the scene. A natural approach consists of “digitizing” each snapshot into a discrete set of observations, sufficiently (perhaps not exactly) matched to the object in question, then tracking the object using an appropriate stochastic filter. The tracking would be expected to make up for the low S/N ratio, thus allowing one to “coherently” process successive images in order to beat down the noise and localize the object. The problem then becomes one of choosing the appropriate image representation as well as the optimal (and necessarily nonlinear) filter. We propose exact and approximate solutions using wavelets and the Zakai equation. The smoothness of the wavelets used is required in the derivation of the evolution equation for the conditional density giving the filter, and their orthogonality makes it possible to carry out actual computations of the Ito- and change-of-gauge-terms in the algorithm effectively