融合凹点检测与仿射变换的活动轮廓模型

目的 针对基于矢量场的活动轮廓模型,如经典的梯度矢量流（GVF）模型、矢量场卷积（VFC）模型等,在提取凹形物体时矢量场常出现平衡点,不能较好地收敛到凹陷区域、尤其是深而窄的凹形及复杂凹陷区域的问题。提出一种融合凹点检测与仿射变换的活动轮廓模型。方法 首先利用活动轮廓模型进行曲线演化,得到演化后轮廓曲线上各点的坐标并求出各点的法线方向;然后基于凹点检测的方法,判断各点的凹凸性,利用梯度判断法,检测出未收敛到目标边界的凹点;其次对各凹点进行法向方向的仿射变换。在接近且不越过目标边界的情况下求出可变换的最大距离,变换后的点穿越了平衡点区域,让变换后的点代替原来的点形成新的轮廓曲线;最后为保证提取边界的精确性,将变换后的轮廓曲线再次演化并最终收敛到目标边界。结果 通过对具有凹陷区域的合成图像进行分割,计算提出模型分割结果的平均Jaccard相似系数（JS）值为95.51%,相比目前先进的GVF模型,VFC模型和自适应扩散流（ADF）模型分别提高了15.08%,12.09%和10.70%,整体效果上优于几种先进的模型。然后又对单/多目标真实图像及含噪的图像进行分割,证实提出模型分割性能的鲁棒性。结论 提出的模型有效地避免了凹形区域内的平衡点问题,可以对深凹形及复杂凹形图像进行有效分割,并且提高了分割精度。此外,该模型能融合到任何基于矢量场的活动轮廓模型中,具有广泛的普适性。     

Moment-based alignment for shape prior with variational B-spline level set

This paper presents a new shape prior-based implicit active contour model for image segmentation. The paper proposes an energy functional including a data term and a shape prior term. The data term, inspired from the region-based active contour approach, evolves the contour based on the region information of the image to segment. The shape prior term, defined as the distance between the evolving shape and a reference shape, constraints the evolution of the contour with respect to the reference shape. Especially, in this paper, we present shapes via geometric moments, and utilize the shape normalization procedure, which takes into account the affine transformation, to align the evolving shape with the reference one. By this way, we could directly calculate the shape transformation, instead of solving a set of coupled partial differential equations as in the gradient descent approach. In addition, we represent the level-set function in the proposed energy functional as a linear combination of continuous basic functions expressed on a B-spline basic. This allows a fast convergence to the segmentation solution. Experiment results on synthetic, real, and medical images show that the proposed model is able to extract object boundaries even in the presence of clutter and occlusion.     

Part I: Modeling image curves using invariant 3-D object curvemodels-a path to 3-D recognition and shape estimation from imagecontours

This paper and its companion are concerned with the problems of 3-D object recognition and shape estimation from image curves using a 3-D object curve model that is invariant to affine transformation onto the image space, and a binocular stereo imaging system. The objects of interest here are the ones that have markings (e.g., characters, letters, special drawings and symbols, etc.) on their surfaces. The 3-D curves on the object are modeled as B-splines, which are characterized by a set of parameters (the control points) from which the 3-D curve can be totally generated. The B-splines are invariant under affine transformations. That means that the affine projected object curve onto the image space is a B-spline whose control points are related to the object control points through the affine transformation. Part I deals with issues relating to the curve modeling process. In particular, the authors address the problems of estimating the control points from the data curve, and of deciding on the “best” order B-spline and the “best” number of control points to be used to model the image or object curve(s). A minimum mean-square error (mmse) estimation technique which is invariant to affine transformations is presented as a noniterative, simple, and fast approach for control point estimation. The “best” B-spline is decided upon using a Bayesian selection rule. Finally, we present a matching algorithm that allocates a sample curve to one of p prototype curves when the sample curve is an a priori unknown affine transformation of one of the prototype curves stored in the data base. The approach is tried on a variety of images of real objects     

分水岭优化的Snake模型肝脏图像分割

Snake算法是主动轮廓模型的经典算法,是近年来图像分割和视频领域研究的热点。针对Snake模型中存在的初始轮廓敏感和能量函数中曲率约束不足等问题,提出将分水岭变换和主动轮廓模型相结合的主动轮廓分割算法。首先通过引入标记函数和强制最小值技术解决传统分水岭变换可能导致的过分割问题,然后利用改进的强制标记分水岭算法优化Snake模型的初始轮廓曲线,最后通过在Snake模型中增加一项与曲线形状相关的外部力弥补能量约束函数中曲率约束的不足,从而实现更精确的图像分割。改进后的Snake模型应用于腹部MR图像中,对肝脏图像的识别和分割取得了良好效果。     

Extracting Group Transformations from Image Moments

Image distortion induced by the relative motion between an observer and the scene is an important cue for recovering the motion and the structure of the scene. It is known that the distortion in images can be described by transformation groups, such as Euclidean, affine, and projective groups. In this paper, we investigate how the moments of image curves are changed by group transformations, and we derive a relationship between the change in image moments and the invariant vector fields of the transformation groups. The results are used to formalize a method for extracting invariant vector fields of affine transformations from changes in the moments of orientation of curve segments in images. The method is applied to a realtime robot visual navigation task.     

Canonical Decomposition of Steerable Functions

This paper describes a general mathematical formulation for the problem of constructing steerable functions. The formulation is based on Lie group theory and is thus applicable to transformations which are Lie groups, such as, rotation, translation, scaling, and affine transformation. For one-parameter and Abelian multi-parameter Lie transformation groups, a canonical decomposition of all possible steerable functions, derived using the Jordan decomposition of matrices, is developed. It is shown that any steerable function under Lie transformation groups can be described using this decomposition. Finally, a catalog of steerable functions for several common multi-parameter image transformation groups is also provided.     

Learning the Lie groups of visual invariance

A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.     

结合谱聚类与改进RSF模型的医学图像分割

现有的可变区域拟合能量（RSF）模型基于初始轮廓内外灰度值的近似,较好地处理了图像分割中存在的图像灰度不均匀的问题。但当选择不恰当的初始轮廓时,由于RSF模型能量函数的非凸性质,极易陷入局部最小值。为了保证初始化的鲁棒性,提出了一种拟合函数优化的RSF模型。在曲线演化过程中,在演化方向相反的区域增加一个函数来交换曲线内外拟合值,使整条曲线沿物体的同侧边界演化。又将谱图理论引入该模型,使其能对大数据样本聚类且快速收敛至全局最优解。将改进模型应用于医学图像分割,实验结果表明该模型较RSF模型获得了更鲁棒的分割结果和较高的分割效率。     

Prior-based Segmentation and Shape Registration in the Presence of Perspective Distortion

Challenging object detection and segmentation tasks can be facilitated by the availability of a reference object. However, accounting for possible transformations between the different object views, as part of the segmentation process, remains difficult. Recent statistical methods address this problem by using comprehensive training data. Other techniques can only accommodate similarity transformations. We suggest a novel variational approach to prior-based segmentation, using a single reference object, that accounts for planar projective transformation. Generalizing the Chan-Vese level set framework, we introduce a novel shape-similarity measure and embed the projective homography between the prior shape and the image to segment within a region-based segmentation functional. The proposed algorithm detects the object of interest, extracts its boundaries, and concurrently carries out the registration to the prior shape. We demonstrate prior-based segmentation on a variety of images and verify the accuracy of the recovered transformation parameters.     

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.     

Application of Lie Algebras to Visual Servoing

A novel approach to visual servoing is presented, which takes advantage of the structure of the Lie algebra of affine transformations. The aim of this project is to use feedback from a visual sensor to guide a robot arm to a target position. The target position is learned using the principle of teaching by showing in which the supervisor places the robot in the correct target position and the system captures the necessary information to be able to return to that position. The sensor is placed in the end effector of the robot, the camera-in-hand approach, and thus provides direct feedback of the robot motion relative to the target scene via observed transformations of the scene. These scene transformations are obtained by measuring the affine deformations of a target planar contour (under the weak perspective assumption), captured by use of an active contour, or snake. Deformations of the snake are constrained using the Lie groups of affine and projective transformations. Properties of the Lie algebra of affine transformations are exploited to provide a novel method for integrating observed deformations of the target contour. These can be compensated with appropriate robot motion using a non-linear control structure. The local differential representation of contour deformations is extended to allow accurate integration of an extended series of small perturbations. This differs from existing approaches by virtue of the properties of the Lie algebra representation which implicitly embeds knowledge of the three-dimensional world within a two-dimensional image-based system. These techniques have been implemented using a video camera to control a 5 DoF robot arm. Experiments with this implementation are presented, together with a discussion of the results.     

一种改进的活动区域轮廓模型——无需水平集重新初始化

基于区域的活动区域模型已经成功应用在图像分割、目标跟踪等领域,较之基于梯度的活动轮廓模型具有很多优点。但是,这些水平集模型在演化过程中,为了保持为符号距离函数,必须对其重新初始化,降低了曲线演化速度,增加了实现复杂度。为了解决重新初始化问题,在测地活动区域模型的能量函数中,加入惩罚项来约束水平集保持为符号距离函数,无需再重新初始化,极大地提高了演化速度。将其运用在纹理图像、脑MR图像分割以及视频跟踪中,实验证明该模型是有效的。     

显著性驱动的局部相似拟合模型分割算法研究

灰度不均匀和噪声图像的分割是计算机视觉中的难点。现有的活动轮廓模型尽管能够取得较好的分割效果,但仍然对噪声图像分割效果不理想,初始轮廓曲线的选取敏感,优化易陷入局部极小导致演化速度慢等问题。针对该问题,首先使用局部区域灰度的均值和方差拟合高斯分布,构建新的能量泛函,均值和方差随着能量的最小化过程而变化,从而增强了灰度不均匀和噪声图像的分割能力。此外,结合视觉显著性检测算法获取待分割目标的先验形状信息,并自适应地创建水平集函数,从而降低了初始轮廓位置敏感性及计算时间复杂度,实现全自动的图像分割。实验结果证明,提出的算法可以用于灰度不均匀和噪声图像分割,并取得了较好的分割性能,消除了算法对初始轮廓位置敏感性,减少了迭代次数。     

双重轮廓演化曲线的图像分割水平集模型

目的几何活动轮廓模型的标志性模型C-V模型及其改进LBF模型受到关注,然而这两个模型对初始轮廓曲线较强的依赖性使得模型在实际图像目标分割中表现出不稳定性或具有较高的时间复杂性。本文在对C-V模型及LBF模型的原理及对初始轮廓曲线的依赖特性进行分析的基础上,提出一种基于双重轮廓演化曲线的图像分割水平集模型。方法所提出模型的主要过程如下:1)通过设置内、外两条轮廓线,使模型在演化过程中分别从目标的内部和外部向目标边界逼近,两条轮廓线的设计原则简单,其分别位于目标的外部和与目标有重叠;2)两条轮廓线的演化走向是通过在模型中设置相关项自动控制的,即演化过程中通过最小化内、外轮廓之间的差异来自动控制两条轮廓曲线的演化趋向,使之同时从目标的内部和外部向目标边界逼近,并逐渐稳定于目标的边界。结果所提出的模型通过设置内部能量泛函项,避免了对符号距离函数的重新初始化;通过采用全局化的正则函数,增加了模型对复杂异质区域边界的捕捉能力;通过采用内、外轮廓线同时演化机制,避免了模型对初始轮廓线的过依赖性。结论所提出的模型很好地解决了传统基于区域的分割模型对轮廓曲线初始化的过依赖问题,对初始轮廓线的设置较为简单且具有较强的鲁棒性,对图像目标的分割较为准确和稳定。     

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.     

A Variational Model for Object Segmentation Using Boundary Information and Shape Prior Driven by the Mumford-Shah Functional

In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by three complementary terms. The first one is based on a shape model which constrains the active contour to get a shape of interest. The second term detects object boundaries from image gradients. And the third term drives globally the shape prior and the active contour towards a homogeneous intensity region. The segmentation of the object of interest is given by the minimum of our energy functional. This minimum is computed with the calculus of variations and the gradient descent method that provide a system of evolution equations solved with the well-known level set method. We also prove the existence of this minimum in the space of functions with bounded variation. Applications of the proposed model are presented on synthetic and medical images.     

Discrete contours in multiple views: approximation and recognition

Recognition of discrete planar contours under similarity transformations has received a lot of attention but little work has been reported on recognizing them under more general transformations. Planar object boundaries undergo projective or affine transformations across multiple views. We present two methods to recognize discrete curves in this paper. The first method computes a piecewise parametric approximation of the discrete curve that is projectively invariant. A polygon approximation scheme and a piecewise conic approximation scheme are presented here. The second method computes an invariant sequence directly from the sequence of discrete points on the curve in a Fourier transform space. The sequence is shown to be identical up to a scale factor in all affine related views of the curve. We present the theory and demonstrate its applications to several problems including numeral recognition, aircraft recognition, and homography computation.     

Multiphase B-spline level set and incremental shape priors with applications to segmentation and tracking of left ventricle in cardiac MR images

This paper presents a new multiphase active contour model for object segmentation and tracking. The paper introduces an energy functional which incorporates image feature information to drive contours toward desired boundaries, and shape priors to constrain the evolution of the contours with respect to reference shapes. The shape priors, in the model, are constructed by performing the incremental principal component analysis (iPCA) on a set of training shapes and newly available shapes which are the resulted shapes derived from preceding segmented images. By performing iPCA, the shape priors are updated without repeatedly performing PCA on the entire training set including the existing shapes and the newly available shapes. In addition, by incrementally updating the resulted shape information of consecutive frames, the approach allows to encode shape priors even when the database of training shapes is not available. Moreover, in shape alignment steps, we exploit the shape normalization procedure, which takes into account the affine transformation, to directly calculate pose transformations instead of solving a set of coupled partial differential equations as in gradient descent-based approaches. Besides, we represent the level set functions as linear combinations of continuous basic functions expressed on B-spline basics for a fast convergence to the segmentation solution. The model is applied to simultaneously segment/track both the endocardium and epicardium of left ventricle from cardiac magnetic resonance (MR) images. Experimental results show the desired performances of the proposed model.     

一种新的基于snake模型的水平集图像分割方法

介绍了一种新的变分函数来替代传统水平集方法中的符号距离函数,因而可以完全忽略重复初始化符号距离函数的步骤,提高了计算效率。用一个能量函数来表示基于snake模型水平集函数的变化情况。其中能量函数主要由内部能量和外部能量表示。利用内部能量描述曲线的张力和平滑性;外部能量则基于图像数据,并在图像的目标边界形成极小值。同时最小化内部和外部能量,产生内力和外力：内力控制曲线演化的方向,并保持曲线不被过度弯曲;外力则吸引曲线到达目标边缘。