EM-GPA: Generalized Procrustes analysis with hidden variables for 3D shape modeling

Aligning shapes is essential in many computer vision problems and generalized Procrustes analysis (GPA) is one of the most popular algorithms to align shapes. However, if some of the shape data are missing, GPA cannot be applied. In this paper, we propose EM-GPA, which extends GPA to handle shapes with hidden (missing) variables by using the expectation-maximization (EM) algorithm. For example, 2D shapes can be considered as 3D shapes with missing depth information due to the projection of 3D shapes into the image plane. For a set of 2D shapes, EM-GPA finds scales, rotations and 3D shapes along with their mean and covariance matrix for 3D shape modeling. A distinctive characteristic of EM-GPA is that it does not enforce any rank constraint often appeared in other work and instead uses GPA constraints to resolve the ambiguity in finding scales, rotations, and 3D shapes. The experimental results show that EM-GPA can recover depth information accurately even when the noise level is high and there are a large number of missing variables. By using the images from the FRGC database, we show that EM-GPA can successfully align 2D shapes by taking the missing information into consideration. We also demonstrate that the 3D mean shape and its covariance matrix are accurately estimated. As an application of EM-GPA, we construct a 2D + 3D AAM (active appearance model) using the 3D shapes obtained by EM-GPA, and it gives a similar success rate in model fitting compared to the method using real 3D shapes. EM-GPA is not limited to the case of missing depth information, but it can be easily extended to more general cases.     

Shape averaging and its applications to industrial design

A computer-assisted technique called shape averaging is presented. Shape averaging produces an abstraction of the typical representation from a set of shapes. Since the averaging is assumed to preserve the characteristics of the original shapes, the result is useful in predicting trends in form or extracting stereotypes from a group of related shapes. The technique can be used to create new forms by blending global features of existing unrelated shapes. The syntactic averaging of shapes consisting of 2-D planar polygons or of 3-D objects represented by planar contours is examined. An algorithm is presented to determine the correspondence between polygons defined by arbitrary numbers of vertices. Algorithms to extract the mean, the median, and the mode from the shapes are also introduced. Potential applications of shape averaging in design are illustrated     

ShapeSynth: Parameterizing model collections for coupled shape exploration and synthesis

Recent advances in modeling tools enable non‐expert users to synthesize novel shapes by assembling parts extracted from model databases. A major challenge for these tools is to provide users with relevant parts, which is especially difficult for large repositories with significant geometric variations. In this paper we analyze unorganized collections of 3D models to facilitate explorative shape synthesis by providing high‐level feedback of possible synthesizable shapes. By jointly analyzing arrangements and shapes of parts across models, we hierarchically embed the models into low‐dimensional spaces. The user can then use the parameterization to explore the existing models by clicking in different areas or by selecting groups to zoom on specific shape clusters. More importantly, any point in the embedded space can be lifted to an arrangement of parts to provide an abstracted view of possible shape variations. The abstraction can further be realized by appropriately deforming parts from neighboring models to produce synthesized geometry. Our experiments show that users can rapidly generate plausible and diverse shapes using our system, which also performs favorably with respect to previous modeling tools.     

基于球面调和映射的三维产品形态融合方法研究

三维产品形态的创新设计在产品造型设计中具有重要的地位,是提高产 品竞争力的重要手段。基于球面调和映射,提出一种新算法,在两个产品之间实现形态的变 形,进而产生多种产品形态。首先对两个三维产品形态划分三角网格; 然后将网格化的产品 形态嵌入到一单位球面上,生成嵌入体模型,该嵌入体与其三维产品形态有着相同的拓扑结 构;最后将这两个嵌入体融合,在两个形态之间建立一种对应关系,通过线性插值生成一系 列的中间形态。以两个不同形态的鼠标基体模型为例进行实验研究,结果表明该算法对于产 品形态的融合具有很好的适用性。在计算机辅助产品形态造型设计中将具有良好的应用前 景。     

工艺美术字计算机变形设计研究

本文提出了一种美术字计算机自动设计的新方法.该方法利用“显示字库”所提供的字形笔划结构特征信息,运用多级数学模型,通过计算机软件功能,对字形自动再加工、再造型、美工优化、艺术化,设计出形式多样的新的艺术字型,是一种新的动态软字库技术.设计字型可应用于电视字幕、广告、印刷排版、电脑动画、大屏幕显示、软件包装等领域。     

Drivers for free‐form modular displays

Abstract— When displays of different sizes and shapes are required, a modular display system seems to be a good solution. Many systems offer only a limited freedom of shapes. The display can be scaled, but no irregular shapes can be created. If those shapes can be created, the configuration is often manual. A more intelligent modular system allows all shapes to be created and configures automatically. This paper presents two drivers that can be used in such a modular system. The first driver ensures that the data finds its way to every module and is displayed, even if there are some “holes” in the display due to missing modules. The second driver adds some extra functionality. The precise display configuration can be detected, and in the graphical user interface (used for controlling the display) the user sees an updated view of the display configuration when modules are added or removed. Both drivers have been proven successful and results are presented in this paper.     

Completion and Reconstruction with Primitive Shapes

We consider the problem of reconstruction from incomplete point-clouds. To find a closed mesh the reconstruction is guided by a set of primitive shapes which has been detected on the input point-cloud (e.g. planes, cylinders etc.). With this guidance we not only continue the surrounding structure into the holes but also synthesize plausible edges and corners from the primitives' intersections. To this end we give a surface energy functional that incorporates the primitive shapes in a guiding vector field. The discretized functional can be minimized with an efficient graph-cut algorithm. A novel greedy optimization strategy is proposed to minimize the functional under the constraint that surface parts corresponding to a given primitive must be connected. From the primitive shapes our method can also reconstruct an idealized model that is suitable for use in a CAD system.     

Learning visual models from shape contours using multiscaleconvex/concave structure matching

A novel approach is proposed for learning a visual model from real shape samples of the same class. The approach can directly acquire a visual model by generalizing the multiscale convex/concave structure of a class of shapes, that is, the approach is based on the concept that shape generalization is shape simplification wherein perceptually relevant features are retained. The simplification does not mean the approximation of shapes but rather the extraction of the optimum scale convex/concave structure common to shape samples of the class. The common structure is obtained by applying the multiscale convex/concave structure-matching method to all shape pairs among given shape samples of the class and by integrating the matching results. The matching method, is applicable to heavily deformed shapes and is effectively implemented with dynamic programming techniques. The approach can acquire a visual model from a few samples without any a priori knowledge of the class. The obtained model is very useful for shape recognition. Results of applying the proposed method are presented     

基于两步策略的形状检索

提出一种将全局特征与局部特征相结合的形状检索的两步检索策略，首先由简单的全局特征过滤掉大部分非相关形状，并利用矢量近似方法对所属类别进行快速定位，类别内部，在对轮廓坐标进行平移、比例缩放和旋转等归一化处理的基础上，使用小波变换描述形状的局部特征，其相似性是直接用两个轮廓的小波变换系数的差来计算的，仿真试验表明，该结构能够高效准确地对高分辨遥感图像和航片中的对象进行检索。     

A picture of a butterfly with diffusion-shaped wings

A combination of mathematical methods is used to create the image of a butterfly. The properties of the one-dimensional diffusion equation can be used to produce wing shapes.Mandelbrot set patterns are applied to color the butterfly wings. Finally, another technique using the logarithmic spiral is presented to create natural shapes and patterns.     

Retrieving Similar Shapes Effectively and Efficiently

In this paper, we address the following problem: given a large collection of shapes and a query shape, retrieve all shapes (from the shape database) that are similar to the query shape. A generalized centroid-radii model is used to model all forms of shapes — convex shapes, concave shapes and shapes with holes. Under the model, a shape is represented by a set of vectors, each obtained from the radii emanating from the centroid of a virtual concentric ring.The model can also facilitate multi-resolution and similarity retrievals. Furthermore, using the model, the shape of an object can be transformed into a point in a high dimensional data space. To speed up the retrieval of similar shapes, we also propose a multi-level R-tree index, called the Nested R-trees (NR-trees). Unlike traditional high-dimensional index structures that index a high-dimensional point as it is (with its full dimension), the NR-trees splits the dimensionality of the point into a set of lower dimensions that are indexed by levels of the NR-trees. We also proposed a quick filtering mechanism to further prune the search space.We implemented a shape retrieval system that employs the generalized centroid-radii model and the NR-trees with the filtering mechanism. Our experimental study shows the effectiveness of the proposed shape model, and the efficiency of the NR-trees. The results also show that the filtering mechanism can significantly reduce the retrieval time.     

Interactive Image‐Guided Modeling of Extruded Shapes

A recent trend in interactive modeling of 3D shapes from a single image is designing minimal interfaces, and accompanying algorithms, for modeling a specific class of objects. Expanding upon the range of shapes that existing minimal interfaces can model, we present an interactive image‐guided tool for modeling shapes made up of extruded parts. An extruded part is represented by extruding a closed planar curve, called base, in the direction orthogonal to the base. To model each extruded part, the user only needs to sketch the projected base shape in the image. The main technical contribution is a novel optimization‐based approach for recovering the 3D normal of the base of an extruded object by exploring both geometric regularity of the sketched curve and image contents. We developed a convenient interface for modeling multi‐part shapes and a method for optimizing the relative placement of the parts. Our tool is validated using synthetic data and tested on real‐world images.     

Shape optimization of curves and surfaces considering fairness metrics and elastic stiffness

A method is presented for generating round curves and surfaces allowing discontinuities in tangent vectors and curvatures. The distance of the centre of curvature from the specified point is used for formulating the objective function which is a continuous function of the design variables through convex and concave shapes. It is shown that a shell with and without ribs can be generated within the same problem formulation if the minimization problem is converted into a maximization problem and the parameter region where integration is to be carried out is restricted in view of the curvature. Optimal shapes are also found under constraints on the compliance against static loads. A multiobjective optimization problem is solved by the constraint method to generate a trade-off design between roundness and mechanical performance.An erratum to this article can be found at     

A Stochastic Order of Shape Variability with an Application to Cell Nuclei Involved in Mastitis

Variability of shapes of bidimensional closed curves is a key matter in many fields of research. A statistical order of bidimensional shape variability is introduced in this paper. For such a purpose a special class of random elements is considered. The order is defined on such a class and the main properties of the order are analyzed. Such an order involves the curvature of a special parameterization of bidimensional closed curves. The new order can be used as a basis for implementing statistical procedures, such as hypothesis testing on variability of shapes. An example is developed by means of the image analysis of cell nuclei, namely the shapes of cell nuclei in mastitis-affected cow milk and non-affected cow milk are compared.     

Printed slot antennas for various wideband applications using shape blending

This article presents a novel design of wide slot antenna for various wideband applications created using a shape‐blending algorithm. The proposed printed antenna consists of a wide rectangular slot and a tuning stub, which is formed by blending the shapes of from a cross and a square. Various bandwidths can be obtained based on the structure with different blended shapes. The impact of the antenna geometry on the antenna performance has been investigated and analyzed in detail. To verify the proposed designs, six prototypes of slot antennas with various tuning stub shapes are designed, fabricated, and measured. The simulated results are compared with the measured performance and show good agreement. A bandwidth range from 38.5 to 126.4% for voltage standing wave ratio (VSWR) less than 2 is exhibited by selecting different blended shapes, which can be served as an antenna design guideline. Moreover, the proposed type of antenna has a compact size and a simple structure, which make it an excellent candidate for wideband applications. © 2015 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:3–12, 2016.     

基于概念的形状分类和识别

基于中文自然语言中的形状名词，提出了一种基于概念的形状分类方法。利用简单的形状描述参数进行二分类与利用复杂的形状参数进行模糊分类相结合的原则，实现形状分层分类。给出了17类基本形状的分类实验结果，表明该方法的可行性。