基于Grassmann流形的仿射不变形状识别

传统的Kendall形状空间理论仅适用于相似变换, 然而成像过程中目标发生的几何变形在更多情形时应该用仿射变换来刻画. 基于Grassmann流形理论, 本文分析了仿射不变形状空间的非线性几何结构, 提出了基于Grassmann流形的仿射不变形状识别算法. 算法首先对训练集中的每类形状分别计算形状均值和方差, 进而在形状均值附近的切空间构建多变量正态分布; 最后,根据测试形状的观测和先验形状模型求解测试形状的最大似然类, 对形状进行贝叶斯分类. MPEG 7形状数据库的实验结果表明, 与传统Kendall形状分析中的基于Procrustean度量识别算法相比, 本文识别算法具有明显优势; 真实场景中的目标识别结果进一步表明, 本文算法对仿射变形有更好的适应能力, 在复杂场景下能以较高的后验概率辨识出目标类别.     

Elastic shapes models for improving segmentation of object boundaries in synthetic aperture sonar images

We present a variational framework for naturally incorporating prior shape knowledge in guidance of active contours for boundary extraction in images. This framework is especially suitable for images collected outside the visible spectrum, where boundary estimation is difficult due to low contrast, low resolution, and presence of noise and clutter. Accordingly, we illustrate this approach using the segmentation of various objects in synthetic aperture sonar (SAS) images of underwater terrains. We use elastic shape analysis of planar curves in which the shapes are considered as elements of a quotient space of an infinite dimensional, non-linear Riemannian manifold. Using geodesic paths under the elastic Riemannian metric, one computes sample mean and covariances of training shapes in each classes and derives statistical models for capturing class-specific shape variability. These models are then used as shape priors in a variational setting to solve for Bayesian estimation of desired contours as follows. In traditional active contour models curves are driven towards minimum of an energy composed of image and smoothing terms. We introduce an additional shape term based on shape models of relevant shape classes. The minimization of this total energy, using iterated gradient-based updates of curves, leads to an improved segmentation of object boundaries. This is demonstrated using a number of shape classes in two large SAS image datasets.     

Continuous Generalized Procrustes analysis

Two-dimensional shape models have been successfully applied to solve many problems in computer vision, such as object tracking, recognition, and segmentation. Typically, 2D shape models are learned from a discrete set of image landmarks (corresponding to projection of 3D points of an object), after applying Generalized Procustes Analysis (GPA) to remove 2D rigid transformations. However, the standard GPA process suffers from three main limitations. Firstly, the 2D training samples do not necessarily cover a uniform sampling of all the 3D transformations of an object. This can bias the estimate of the shape model. Secondly, it can be computationally expensive to learn the shape model by sampling 3D transformations. Thirdly, standard GPA methods use only one reference shape, which can might be insufficient to capture large structural variability of some objects.To address these drawbacks, this paper proposes continuous generalized Procrustes analysis (CGPA). CGPA uses a continuous formulation that avoids the need to generate 2D projections from all the rigid 3D transformations. It builds an efficient (in space and time) non-biased 2D shape model from a set of 3D model of objects. A major challenge in CGPA is the need to integrate over the space of 3D rotations, especially when the rotations are parameterized with Euler angles. To address this problem, we introduce the use of the Haar measure. Finally, we extended CGPA to incorporate several reference shapes. Experimental results on synthetic and real experiments show the benefits of CGPA over GPA.     

On Shape of Plane Elastic Curves

We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques. The shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics. Elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models. Applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated.     

A sketching interface for feature curve recovery of free-form surfaces

In this paper, we present a semi-automatic approach to efficiently and robustly recover the characteristic feature curves of a given free-form surface where we do not have to assume that the input is a proper manifold. The technique supports a sketch-based interface where the user just has to roughly sketch the location of a feature by drawing a stroke directly on the input mesh. The system then snaps this initial curve to the correct position based on a graph-cut optimization scheme that takes various surface properties into account. Additional position constraints can be placed and modified manually which allows for an interactive feature curve editing functionality. We demonstrate the usefulness of our technique by applying it to two practical scenarios. At first, feature curves can be used as handles for surface deformation, since they describe the main characteristics of an object. Our system allows the user to manipulate a curve while the underlying non-manifold surface adopts itself to the deformed feature. Secondly, we apply our technique to a practical problem scenario in reverse engineering. Here, we consider the problem of generating a statistical (PCA) shape model for car bodies. The crucial step is to establish proper feature correspondences between a large number of input models. Due to the significant shape variation, fully automatic techniques are doomed to failure. With our simple and effective feature curve recovery tool, we can quickly sketch a set of characteristic features on each input model which establishes the correspondence to a pre-defined template mesh and thus allows us to generate the shape model. Finally, we can use the feature curves and the shape model to implement an intuitive modeling metaphor to explore the shape space spanned by the input models.     

Curve/surface representation and evolution using vector level sets with application to the shape-based segmentation problem

In this paper, we revisit the implicit front representation and evolution using the vector level set function (VLSF) proposed in (H. E. Abd El Munim, et al., Oct. 2005). Unlike conventional scalar level sets, this function is designed to have a vector form. The distance from any point to the nearest point on the front has components (projections) in the coordinate directions included in the vector function. This kind of representation is used to evolve closed planar curves and 3D surfaces as well. Maintaining the VLSF property as the distance projections through evolution will be considered together with a detailed derivation of the vector partial differential equation (PDE) for such evolution. A shape-based segmentation framework will be demonstrated as an application of the given implicit representation. The proposed level set function system will be used to represent shapes to give a dissimilarity measure in a variational object registration process. This kind of formulation permits us to better control the process of shape registration, which is an important part in the shape-based segmentation framework. The method depends on a set of training shapes used to build a parametric shape model. The color is taken into consideration besides the shape prior information. The shape model is fitted to the image volume by registration through an energy minimization problem. The approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the evolution (PDEs). It is also suitable for multidimensional data and computationally efficient. Results in 2D and 3D of real and synthetic data will demonstrate the efficiency of the framework     

Search strategies for shape regularized active contour

Nonlinear shape models have been shown to improve the robustness and flexibility of contour-based object segmentation when there are appearance ambiguities between the object and the background. In this paper, we focus on a new search strategy for the shape regularized active contour (ShRAC) model, which adopts existing nonlinear shape models to segment objects that are similar to a set of training shapes. The search for optimal contour is performed by a coarse-to-fine algorithm that iterates between combinatorial search and gradient-based local optimization. First, multi-solution dynamic programming (MSDP) is used to generate initial candidates by minimizing only the image energy. In the second step, a combination of image energy and shape energy is minimized starting from these initial candidates using a local optimization method and the best one is selected. To generate diverse initial candidates while reducing invalid shapes, we apply two pruning methods to the search space of MSDP. Our search strategy combines the advantages of global combinatorial search and local optimization, and has shown excellent robustness to local minima caused by distracting suboptimal solutions. Experimental results on segmentation of different anatomical structures using ShRAC, as well as preliminary results on human silhouette segmentation are provided.     

Embedding Gestalt laws in Markov random fields

The goal of this paper is to study a mathematical framework of 2D object shape modeling and learning for middle level vision problems, such as image segmentation and perceptual organization. For this purpose, we pursue generic shape models which characterize the most common features of 2D object shapes. In this paper, shape models are learned from observed natural shapes based on a minimax entropy learning theory. The learned shape models are Gibbs distributions defined on Markov random fields (MRFs). The neighborhood structures of these MRFs correspond to Gestalt laws-colinearity, cocircularity, proximity, parallelism, and symmetry. Thus, both contour-based and region-based features are accounted for. Stochastic Markov chain Monte Carlo (MCMC) algorithms are proposed for learning and model verification. Furthermore, this paper provides a quantitative measure for the so-called nonaccidental statistics and, thus, justifies some empirical observations of Gestalt psychology by information theory. Our experiments also demonstrate that global shape properties can arise from interactions of local features     

目标边界点集的层次化描述及其形状检索应用

提出用于轮廓线形状和区域形状图像检索的形状描述方法,该方法将目标形状的边界（包括内边界）表示为一个无序的点集,沿各方向对点集的迭代分割,建立层次化的边界点集描述模型.通过对各层形状边界的分割比和分散度的几何特征度量,产生各层的形状特征描述,对它们进行组合,建立对目标形状的层次化描述.两个目标形状的差异性度量定义为它们的层次化描述子的L-1距离.该方法具有：（1）通用性.能够描述轮廓线形状和区域形状这两种不同类型的形状;（2）可扩展性.基于所提出的分层描述框架,可以将分割比和分散度这两种几何度量进行扩展,纳入更多其他几何特征度量,以进一步提高形状描述的精度;（3）多尺度描述特性.提出的分层的描述机制,使得描述子具有内在的由粗到细的形状表征能力;（4）较低的计算复杂性.由于仅仅计算目标图像的边界像素点,使得算法具有较高的计算效率.用MPEG-7 CE-2区域形状图像库和MPEG-7 CE-1轮廓线形状图像库这两个标准测试集对该方法进行评估,并与同类的其他形状描述方法进行比较,实验结果表明：提出的方法在综合考虑检索精确率、检索效率和一般应用能力等指标的情况下,其性能上要优于各种参与比较的方法.     

Object representation and recognition in shape spaces

In this paper, we describe a shape space based approach for invariant object representation and recognition. In this approach, an object and all its similarity transformed versions are identified with a single point in a high-dimensional manifold called the shape space. Object recognition is achieved by measuring the geodesic distance between an observed object and a model in the shape space. This approach produced promising results in 2D object recognition experiments: it is invariant to similarity transformations and is relatively insensitive to noise and occlusion. Potentially, it can also be used for 3D object recognition.     

Shape Morphing-Based Control of Robotic Visual Servoing

We present an approach for controlling robotic interactions with objects, using synthetic images generated by morphing shapes. In particular, we attempt the problem of positioning an eye-in-hand robotic system with respect to objects in the workspace for grasping and manipulation. In our formulation, the grasp position (and consequently the approach trajectory of the manipulator), varies with each object. The proposed solution to the problem consists of two parts. First, based on a model-based object recognition framework, images of the objects taken at the desired grasp pose are stored in a database. The recognition and identification of the grasp position for an unknown input object (selected from the family of recognizable objects) occurs by morphing its contour to the templates in the database and using the virtual energy spent during the morph as a dissimilarity measure. In the second step, the images synthesized during the morph are used to guide the eye-in-hand system and execute the grasp. The proposed method requires minimal calibration of the system. Furthermore, it conjoins techniques from shape recognition, computer graphics, and vision-based robot control in a unified engineering amework. Potential applications range from recognition and positioning with respect to partially-occluded or deformable objects to planning robotic grasping based on human demonstration.     

Circulant dissimilarity-based shape registration for object segmentation

ABSTRACT

A shape prior-based object segmentation is developed in this paper by using a shape transformation distance to constrain object contour evolution. In the proposed algorithm, the transformation distance measures the dissimilarity between two unaligned shapes by cyclic shift, which is called ‘circulant dissimilarity’. This dissimilarity with respect to transformation of the object shape is represented by circular convolution, which could be efficiently computed by using fast Fourier transform. Given a set of training shapes, the kernel density estimation is adopted to model shape prior. By integrating low-level image feature, high-level shape prior and transformation distance, a variational segmentation model is proposed to solve the transformation invariance of shape prior. Numerical experiments demonstrate that circulant dissimilarity-based shape registration outperforms the iterative optimization on explicit pose parameters, and show promising results and highlight the potential of the method for object registration and segmentation.     

基于椭圆傅里叶描述子的形状表示的研究

形状表示是模式识别和计算机视觉中最重要的研究内容之一。针对传统形状表示算法对形状的整体特征和细节信息不能同时描述、通用性不高的问题,提出了一种基于高斯多尺度分析下的椭圆傅里叶描述算子。提出的算法利用高斯函数与目标形状的复坐标函数进行卷积,通过选择高斯曲线的参数,将形状的边界信息呈现到不同的尺度空间之中;利用椭圆傅里叶变换将其展开得到表示该形状的特征向量。实验结果表明,该方法的优点在于描述同类形状时,特征向量之间的相关系数高,具有很好的平移、旋转以及尺度不变性;在描述不同类形状时,相关系数低,有很强的形状区分能力。该方法在形状分类实验中也有较高的检索准确率。     

OBJCUT: Efficient Segmentation Using Top-Down and Bottom-Up Cues

We present a probabilistic method for segmenting instances of a particular object category within an image. Our approach overcomes the deficiencies of previous segmentation techniques based on traditional grid conditional random fields (CRF), namely that 1) they require the user to provide seed pixels for the foreground and the background and 2) they provide a poor prior for specific shapes due to the small neighborhood size of grid CRF. Specifically, we automatically obtain the pose of the object in a given image instead of relying on manual interaction. Furthermore, we employ a probabilistic model which includes shape potentials for the object to incorporate top-down information that is global across the image, in addition to the grid clique potentials which provide the bottom-up information used in previous approaches. The shape potentials are provided by the pose of the object obtained using an object category model. We represent articulated object categories using a novel layered pictorial structures model. Nonarticulated object categories are modeled using a set of exemplars. These object category models have the advantage that they can handle large intraclass shape, appearance, and spatial variation. We develop an efficient method, OBJCUT, to obtain segmentations using our probabilistic framework. Novel aspects of this method include: 1) efficient algorithms for sampling the object category models of our choice and 2) the observation that a sampling-based approximation of the expected log-likelihood of the model can be increased by a single graph cut. Results are presented on several articulated (e.g., animals) and nonarticulated (e.g., fruits) object categories. We provide a favorable comparison of our method with the state of the art in object category specific image segmentation, specifically the methods of Leibe and Schiele and Schoenemann and Cremers.     

Fourier domain representation of planar curves for recognition in multiple views

Recognition of planar shapes is an important problem in computer vision and pattern recognition. The same planar object contour imaged from different cameras or from different viewpoints looks different and their recognition is non-trivial. Traditional shape recognition deals with views of the shapes that differ only by simple rotations, translations, and scaling. However, shapes suffer more serious deformation between two general views and hence recognition approaches designed to handle translations, rotations, and/or scaling would prove to be insufficient. Many algebraic relations between matching primitives in multiple views have been identified recently. In this paper, we explore how shape properties and multiview relations can be combined to recognize planar shapes across multiple views. We propose novel recognition constraints that a planar shape boundary must satisfy in multiple views. The constraints are on the rank of a Fourier-domain measurement matrix computed from the points on the shape boundary. Our method can additionally compute the correspondence between the curve points after a match is established. We demonstrate the applications of these constraints experimentally on a number of synthetic and real images.     

Silhouette-based isolated object recognition through curvaturescale space

A complete, fast and practical isolated object recognition system has been developed which is very robust with respect to scale, position and orientation changes of the objects as well as noise and local deformations of shape (due to perspective projection, segmentation errors and non-rigid material used in some objects). The system has been tested on a wide variety of three-dimensional objects with different shapes and material and surface properties. A light-box setup is used to obtain silhouette images which are segmented to obtain the physical boundaries of the objects which are classified as either convex or concave. Convex curves are recognized using their four high-scale curvature extrema points. Curvature scale space (CSS) representations are computed for concave curves. The CSS representation is a multi-scale organization of the natural, invariant features of a curve (curvature zero-crossings or extrema) and useful for very reliable recognition of the correct model since it places no constraints on the shape of objects. A three-stage, coarse-to-fine matching algorithm prunes the search space in stage one by applying the CSS aspect ratio test. The maxima of contours in CSS representations of the surviving models are used for fast CSS matching in stage two. Finally, stage three verifies the best match and resolves any ambiguities by determining the distance between the image and model curves. Transformation parameter optimization is then used to find the best fit of the input object to the correct model     

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.     

Compactly-supported smooth interpolators for shape modeling with varying resolution

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape itself. Additionally, models for shape representation often need to provide local shape control and they need to be able to reproduce common shape primitives such as ellipsoids, spheres, cylinders, or tori. We present a general framework to construct families of compactly-supported interpolators that are piecewise-exponential polynomial. They can be designed to satisfy regularity constraints of any order and they enable one to build parametric deformable shape models by suitable linear combinations of interpolators. They allow to change the resolution of shapes based on the refinability of B-splines. We illustrate their use on examples to construct shape models that involve curves and surfaces with applications to interactive modeling and character design.