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.     

Shape Metrics Based on Elastic Deformations

Deformations of shapes and distances between shapes are an active research topic in computer vision. We propose an energy of infinitesimal deformations of continuous 1- and 2-dimensional shapes that is based on the elastic energy of deformed objects. This energy defines a shape metric which is inherently invariant with respect to Euclidean transformations and yields very natural deformations which preserve details. We compute shortest paths between planar shapes based on elastic deformations and apply our approach to the modeling of 2-dimensional shapes.

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 Shape Models for Face Analysis Using Curvilinear Coordinates

This paper studies the problem of analyzing variability in shapes of facial surfaces using a Riemannian framework, a fundamental approach that allows for joint matchings, comparisons, and deformations of faces under a chosen metric. The starting point is to impose a curvilinear coordinate system, named the Darcyan coordinate system, on facial surfaces; it is based on the level curves of the surface distance function measured from the tip of the nose. Each facial surface is now represented as an indexed collection of these level curves. The task of finding optimal deformations, or geodesic paths, between facial surfaces reduces to that of finding geodesics between level curves, which is accomplished using the theory of elastic shape analysis of 3D curves. The elastic framework allows for nonlinear matching between curves and between points across curves. The resulting geodesics between facial surfaces provide optimal elastic deformations between faces and an elastic metric for comparing facial shapes. We demonstrate this idea using examples from FSU face database.

A Theory of Shape by Space Carving

In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarily-shaped scene from multiple photographs taken at known but arbitrarily-distributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a special member of this class, the photo hull, that (1) can be computed directly from photographs of the scene, and (2) subsumes all other members of this class. We then give a provably-correct algorithm, called Space Carving, for computing this shape and present experimental results on complex real-world scenes. The approach is designed to (1) capture photorealistic shapes that accurately model scene appearance from a wide range of viewpoints, and (2) account for the complex interactions between occlusion, parallax, shading, and their view-dependent effects on scene-appearance.     

Sketching in Gestalt Space: Interactive Shape Abstraction through Perceptual Reasoning

We present an interactive method that allows users to easily abstract complex 3D models with only a few strokes. The key idea is to employ well‐known Gestalt principles to help generalizing user inputs into a full model abstraction while accounting for form, perceptual patterns and semantics of the model. Using these principles, we alleviate the user's need to explicitly define shape abstractions. We utilize structural characteristics such as repetitions, regularity and similarity to transform user strokes into full 3D abstractions. As the user sketches over shape elements, we identify Gestalt groups and later abstract them to maintain their structural meaning. Unlike previous approaches, we operate directly on the geometric elements, in a sense applying Gestalt principles in 3D. We demonstrate the effectiveness of our approach with a series of experiments, including a variety of complex models and two extensive user studies to evaluate our framework.     

Shape retrieval using triangle-area representation and dynamic space warping

In this paper, we present a shape retrieval method using triangle-area representation for nonrigid shapes with closed contours. The representation utilizes the areas of the triangles formed by the boundary points to measure the convexity/concavity of each point at different scales (or triangle side lengths). This representation is effective in capturing both local and global characteristics of a shape, invariant to translation, rotation, and scaling, and robust against noise and moderate amounts of occlusion. In the matching stage, a dynamic space warping (DSW) algorithm is employed to search efficiently for the optimal (least cost) correspondence between the points of two shapes. Then, a distance is derived based on the optimal correspondence. The performance of our method is demonstrated using four standard tests on two well-known shape databases. The results show the superiority of our method over other recent methods in the literature.     

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.     

基于曲率尺度空间的VOP形状编码算法

首先对曲率尺度空间（CSS）算法进行改进，并用改进的CSS算法对任意形状物体的形状信息进行特征点的分层提取；其次，用自适应算术编码算法对固定长度的八分圆编码算法进行改进，并对所提取的特征点进行算术编码，实验结果表明，这种新的基于特征点提取的形状编码方法比MPEG-4校验模型中基于上下文的算术形状编码算法，在Dn相同的条件下，主观质量更好，且压缩比更高。     

基于正切空间的多尺度面实体形状匹配

针对多尺度面状要素的一对多匹配问题,提出基于正切空间的多尺度面实体形状相似性匹配方法。通过源多边形外扩缓冲区搜索候选匹配集,对候选匹配集中的面要素进行组合,组合生成的多边形与源多边形进行形状匹配,从而获得最佳匹配集。实验结果表明,该方法计算过程简单,容易实现且匹配效率较高。     

一种新的局部空间排列算法

局部切空间排列算法(local tangent space alignment, LTSA)是一种经典的非线性流形学习方法,能够有效地对非线性分布数据进行降维,但它无法学习局部高曲率数据集.针对此问题,给出了描述数据集局部曲率的参数,并提出一种局部最小偏差空间排列(locally minimal deviation space alignment, LMDSA)算法.该算法考虑到局部切空间低鲁棒性的缺陷,在计算局部最小偏差空间的同时,能够发现数据的局部高曲率现象,通过参数控制及邻域间的连接信息,减少计算局部高曲率空间的可能,进而利用空间排列技术进行降维,手工流形及真实数据集的实验证实了该算法学习局部高曲率数据集的有效性.     

Linear Transformation Groups and Shape Space

The problem of modelling variabilities of ensembles of objects leads to the study of the shape of point sets and of transformations between point sets. Linear models are only able to amply describe variabilities between shapes that are sufficiently close and require the computation of a mean configuration. Olsen and Nielsen (2000) introduced a Lie group model based on linear vector fields and showed that this model could describe a wider range of variabilities than linear models. The purpose of this paper is to investigate the mathematics of this Lie group model further and determine its expressibility. This is a necessary foundation for any future work on inference techniques in this model.Let ^k _m denote Kendall's shape space of sets of k points in m-dimensional Euclidean space (k > m): this consists of point sets up to equivalence under rotation, scaling and translation. Not all linear transformations on point sets give well-defined transformations of shapes. However, we show that a subgroup of transformations determined by invertible real matrices of size k – 1 does act on ^k _m. For m > 2, this group is maximal, whereas for m = 2, the maximal group consists of the invertible complex matrices. It is proved that these groups are able to transform any generic shape to any other. Moreover, we establish that for k > m + 1 this may be done via one-parameter subgroups. Each one-parameter subgroup is given by exponentiation of an arbitrary (k – 1) × (k – 1) matrix. Shape variabilities may thus be modelled by elements of a (k – 1)²-dimensional vector space.     

一种基于改进地貌形状上下文的形状匹配方法

在基于地貌形状上下文的形状匹配方法中,计算地貌空间测地距离消耗时间较高,对应形状特征提取过程的效率较低.针对这一问题,本文提出了一种基于地貌模糊形状上下文的快速形状匹配方法.在形状特征提取过程中,通过引入最短路径算法对轮廓采样点间的测地距离进行快速计算.在此基础上结合对数极坐标模糊直方图构造地貌模糊形状上下文,其能够更好地描述轮廓点分布情况进而有效提升形状描述符的表达能力.考虑到轮廓点集顺序已知,进一步引入动态规划分析不同地貌空间下形状片段间的对应关系,以获取准确的形状匹配结果.通过对不同的数据集进行实验仿真分析,验证了本文方法能够有效地提升运算效率并取得较好形状检索精度.     

Shape based local thresholding for binarization of document images

This paper presents a novel local threshold algorithm for the binarization of document images. Stroke width of handwritten and printed characters in documents is utilized as the shape feature. As a result, in addition to the intensity analysis, the proposed algorithm introduces the stroke width as shape information into local thresholding. Experimental results for both synthetic and practical document images show that the proposed local threshold algorithm is superior in terms of segmentation quality to the threshold approaches that solely use intensity information.     

Shape optimization in oppositely directed coupled diffusion within composite structures

Some textile dressings contain the microcapsulated therapeutic substance. The diffusion of the activating agent (the exudate) from the wound through the material initiates the chemical reaction within microcapsules and releases the therapeutic agent. The semi-permeable membrane within the dressing reduces the diffusion of therapeutic agent to surrounding, whereas the exudate diffuses normally. The oppositely directed coupled diffusion is analyzed within 2D cross-section of dressing. State variables are both activating agent concentration and therapeutic substance concentration. State equations, boundary and initial conditions are determined. The sensitivity of an arbitrary functional is analyzed by means of direct and adjoint approaches and implemented into the problem of shape optimization. The objective functionals and the optimality conditions are formulated. Numerical example of 2D shape optimization is presented.     

Shape transformation in space-time

We present a method for transforming shapes in a plane. The primary strength of the proposed method is that it can handle scenes containing moving obstacles. We attain a smooth transformation between two given polygonal shapes and ensure that the shape does not collide with any obstacle during the transformation. We minimize a cost function associated with each transformation path that controls its length, smoothness, and collision freedom. Then a population of tentative transformation paths is generated by path planning for an anchor point in the shape. Next, collision detection and shape deformation techniques, applied to keyframes along the paths, minimize the occurrence of collision. Lastly, a genetic algorithm refines the population of transformation paths.     

一种改进的局部切空间排列算法

局部切空间排列算法(local tangent space alignment,简称LTSA)是一种新的流形学习算法,能有效地学习出高维采样数据的低维嵌入坐标,但也存在一些不足,如不能处理样本数较大的样本集和新来的样本点.针对这些缺点,提出了一种基于划分的局部切空间排列算法(partitional local tangent space alignment,简称PLTSA).它建立在VQPCA(vector quantization principal component analysis)算法和LTSA