Global Intrinsic Symmetries of Shapes

Although considerable attention in recent years has been given to the problem of symmetry detection in general shapes, few methods have been developed that aim to detect and quantify the intrinsic symmetry of a shape rather than its extrinsic, or pose‐dependent symmetry. In this paper, we present a novel approach for efficiently computing symmetries of a shape which are invariant up to isometry preserving transformations. We show that the intrinsic symmetries of a shape are transformed into the Euclidean symmetries in the signature space defined by the eigenfunctions of the Laplace‐Beltrami operator. Based on this observation, we devise an algorithm which detects and computes the isometric mappings from the shape onto itself. We show that our approach is both computationally efficient and robust with respect to small non‐isometric deformations, even if they include topological changes.     

Generating discriminating cartoon faces using interacting snakes

As a computational bridge between the high-level a priori knowledge of object shape and the low-level image data, active contours (or snakes) are useful models for the extraction of deformable objects. We propose an approach for manipulating multiple snakes iteratively, called interacting snakes, that minimizes the attraction energy functionals on both contours and enclosed regions of individual snakes and the repulsion energy functionals among multiple snakes that interact with each other. We implement the interacting snakes through explicit curve (parametric active contours) representation in the domain of face recognition. We represent human faces semantically via facial components such as eyes, mouth, face outline, and the hair outline. Each facial component is encoded by a closed (or open) snake that is drawn from a 3D generic face model. A collection of semantic facial components form a hypergraph, called semantic face graph, which employs interacting snakes to align the general facial topology onto the sensed face images. Experimental results show that a successful interaction among multiple snakes associated with facial components makes the semantic face graph a useful model for face representation, including cartoon faces and caricatures, and recognition.     

Perception of 3-D surfaces from 2-D contours

Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. The authors survey classes of techniques proposed in the past and provide a critical analysis. They show that two kinds of symmetries in figures, which are known as parallel and skew symmetries, give significant information about surface shape for a variety of objects. They derive the constraints imposed by these symmetries and show how to use them to infer 3-D shape. They also discuss the zero Gaussian curvature (ZGC) surfaces in depth and show results on the recovery of surface orientation for various ZGC surfaces     

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 .     

Topological spines: a structure-preserving visual representation of scalar fields

We present topological spines--a new visual representation that preserves the topological and geometric structure of a scalar field. This representation encodes the spatial relationships of the extrema of a scalar field together with the local volume and nesting structure of the surrounding contours. Unlike other topological representations, such as contour trees, our approach preserves the local geometric structure of the scalar field, including structural cycles that are useful for exposing symmetries in the data. To obtain this representation, we describe a novel mechanism based on the extraction of extremum graphs--sparse subsets of the Morse-Smale complex that retain the important structural information without the clutter and occlusion problems that arise from visualizing the entire complex directly. Extremum graphs form a natural multiresolution structure that allows the user to suppress noise and enhance topological features via the specification of a persistence range. Applications of our approach include the visualization of 3D scalar fields without occlusion artifacts, and the exploratory analysis of high-dimensional functions.     

A Pretopological Approach for Image Segmentation and Edge Detection

We present an approach based on a pretopological formalism that allows the mathematical modeling of image segmentation by region growing. The choice of pretopology is motivated by the fact that it has less axioms than the topology which facilitates its adaptation to discrete spaces and in particularly image processing. In our approach, the pretopological adherency function associated to the pretopological structure is defined by a criterion of homogeneity. We apply our approach to the extraction of handwritten information on check background with images of scene and to edge detection. The aggregation from chosen initial germ ends to a closed part of the image composed by a stroke (a line of handwriting) or a line of contours. The evaluation, undertaken on 60 checks with various background images and different images, gives 92% of good results for the extracted handwriting with a complete elimination of the background and good results for edge detection.     

Shape Matching via Quotient Spaces

We introduce a novel method for non‐rigid shape matching, designed to address the symmetric ambiguity problem present when matching shapes with intrinsic symmetries. Unlike the majority of existing methods which try to overcome this ambiguity by sampling a set of landmark correspondences, we address this problem directly by performing shape matching in an appropriate quotient space, where the symmetry has been identified and factored out. This allows us to both simplify the shape matching problem by matching between subspaces, and to return multiple solutions with equally good dense correspondences. Remarkably, both symmetry detection and shape matching are done without establishing any landmark correspondences between either points or parts of the shapes. This allows us to avoid an expensive combinatorial search present in most intrinsic symmetry detection and shape matching methods. We compare our technique with state‐of‐the‐art methods and show that superior performance can be achieved both when the symmetry on each shape is known and when it needs to be estimated.     

Shape Analysis with Subspace Symmetries

We address the problem of partial symmetry detection, i.e., the identification of building blocks a complex shape is composed of. Previous techniques identify parts that relate to each other by simple rigid mappings, similarity transforms, or, more recently, intrinsic isometries. Our approach generalizes the notion of partial symmetries to more general deformations. We introduce subspace symmetries whereby we characterize similarity by requiring the set of symmetric parts to form a low dimensional shape space. We present an algorithm to discover subspace symmetries based on detecting linearly correlated correspondences among graphs of invariant features. We evaluate our technique on various data sets. We show that for models with pronounced surface features, subspace symmetries can be found fully automatically. For complicated cases, a small amount of user input is used to resolve ambiguities. Our technique computes dense correspondences that can subsequently be used in various applications, such as model repair and denoising.     

Nonrigid Matching of Undersampled Shapes via Medial Diffusion

We introduce medial diffusion for the matching of undersampled shapes undergoing a nonrigid deformation. We construct a diffusion process with respect to the medial axis of a shape, and use the quantity of heat diffusion as a measure which is both tolerant of missing data and approximately invariant to nonrigid deformations. A notable aspect of our approach is that we do not define the diffusion on the shape's medial axis, or similar medial representation. Instead, we construct the diffusion process directly on the shape. This permits the diffusion process to better capture surface features, such as varying spherical and cylindrical parts, as well as combine with other surface‐based diffusion processes. We show how to use medial diffusion to detect intrinsic symmetries, and for computing correspondences between pairs of shapes, wherein shapes contain substantial missing data.     

Hierarchical aggregation for efficient shape extraction

This paper presents an efficient framework which supports both automatic and interactive shape extraction from surfaces. Unlike most of the existing hierarchical shape extraction methods, which are based on computationally expensive top-down algorithms, our framework employs a fast bottom-up hierarchical method with multiscale aggregation. We introduce a geometric similarity measure, which operates at multiple scales and guarantees that a hierarchy of high-level features are automatically found through local adaptive aggregation. We also show that the aggregation process allows easy incorporation of user-specified constraints, enabling users to interactively extract features of interest. Both our automatic and the interactive shape extraction methods do not require explicit connectivity information, and thus are applicable to unorganized point sets. Additionally, with the hierarchical feature representation, we design a simple and effective method to perform partial shape matching, allowing efficient search of self-similar features across the entire surface. Experiments show that our methods robustly extract visually meaningful features and are significantly faster than related methods.     

基于形状分割的手写汉字笔划提取方法

笔迹鉴别的目的是区分不同的书写者,而笔划提取是笔迹鉴别的基础。本文提出了一种用于笔迹鉴别的手写汉字笔划提取算法,该算法定义了凹凸点与四种基本笔划相交类型的对应关系,通过字符图像轮廓上的凹凸点检测来确定笔划相交区域和相交类型;接着,在各个相交区域上,根据其笔划相交类型进行形状分割;最后,用对笔划轮廓两侧对应点进行跟踪的方法来进行细化。我们将该算法与基于细化和基于段化的笔划提取算法进行比较,实验结果表明,该提取算法具有比较高的准确率和有效性,因此本文提出的基于形状分割的手写汉字笔划提取方法具有较高的可操作性和实用价值。     

Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional

We present a modification of the Mumford-Shah functional and its cartoon limit which facilitates the incorporation of a statistical prior on the shape of the segmenting contour. By minimizing a single energy functional, we obtain a segmentation process which maximizes both the grey value homogeneity in the separated regions and the similarity of the contour with respect to a set of training shapes. We propose a closed-form, parameter-free solution for incorporating invariance with respect to similarity transformations in the variational framework. We show segmentation results on artificial and real-world images with and without prior shape information. In the cases of noise, occlusion or strongly cluttered background the shape prior significantly improves segmentation. Finally we compare our results to those obtained by a level set implementation of geodesic active contours.     

Classification of silhouettes using contour fragments

In this paper, we propose a fragment-based approach for classification and recognition of shape contours. According to this method, first the perceptual landmarks along the contours are localized in a scale invariant manner, which makes it possible to extracts the contour fragments. Using a predefined dictionary for the fragments, these landmarks and the parts between them are transformed into a symbolic representation that is a compact representation. Using a string kernel-like approach, an invariant high-dimensional feature space is created from the symbolic representation and later the most relevant lower dimensions are extracted by principal component analysis. Finally, support vector machine is used for classification of the feature space. The experimental results show that the proposed method has similar performance to the best approaches for shape recognitions while it has lower complexity.     

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.     

Harmonic Embeddings for Linear Shape Analysis

We present a novel representation of shape for closed contours in ℝ² or for compact surfaces in ℝ³ explicitly designed to possess a linear structure. This greatly simplifies linear operations such as averaging, principal component analysis or differentiation in the space of shapes when compared to more common embedding choices such as the signed distance representation linked to the nonlinear Eikonal equation. The specific choice of implicit linear representation explored in this article is the class of harmonic functions over an annulus containing the contour. The idea is to represent the contour as closely as possible by the zero level set of a harmonic function, thereby linking our representation to the linear Laplace equation. We note that this is a local represenation within the space of closed curves as such harmonic functions can generally be defined only over a neighborhood of the embedded curve. We also make no claim that this is the only choice or even the optimal choice within the class of possible linear implicit representations. Instead, our intent is to show how linear analysis of shape is greatly simplified (and sensible) when such a linear representation is employed in hopes to inspire new ideas and additional research into this type of linear implicit representations for curves. We conclude by showing an application for which our particular choice of harmonic representation is ideally suited.     

多目标轮廓Mumford-Shah水平集提取

目标轮廓的快速检测进而提取其几何形状,在图形图像处理中有着重要的作用.提出了一种多目标轮廓的水平集提取方法,对基于Mumford-Shah模型的C-V方法从两方面进行了改进:增加梯度矢量场和曲线法方向的融合作为边界吸引场,生成可以驱动主动轮廓向边缘进化的双向几何变形流,保留原图像分布信息作为区域进化能,解决未考虑局部几何信息造成的区域能量捕捉信息不全,或边缘梯度场和演化曲线法线方向正交时无法实现拓扑结构变化的缺陷;对水平集函数进行修正,使得它在收敛过程中能自动进行调整,确保其满足符号距离函数的要求,扩大初始化前迭代搜索区域,减少初始化次数,提高收敛效率;最后给出所提方法的数字化求解方案.实验表明该方法可行且具有较好的鲁棒性.