基于面积分布的3D模型检索技术

基于内容的3D模型检索技术难以提取形状特征,该文通过提取表面面积分布来表示3D模型的形状特征,采用主分量分析方法确保特征满足平移不变性、旋转不变性、对称不变性。以切分块内三角面片面积和与总面积的比值作为特征,确保缩放不变性。二次型形式的距离公式计算的相似度能够有效地区分特征分量的空间位置。实验表明,基于面积分布的检索技术具有较好的检索效果。     

Wavejets: A Local Frequency Framework for Shape Details Amplification

Detail enhancement is a well‐studied area of 3D rendering and image processing, which has few equivalents for 3D shape processing. To enhance details, one needs an efficient analysis tool to express the local surface dynamics. We introduce Wavejets, a new function basis for locally decomposing a shape expressed over the local tangent plane, by considering both angular oscillations of the surface around each point and a radial polynomial. We link the Wavejets coefficients to surface derivatives and give theoretical guarantees for their precision and stability with respect to an approximate tangent plane. The coefficients can be used for shape details amplification, to enhance, invert or distort them, by operating either on the surface point positions or on the normals. From a practical point of view, we derive an efficient way of estimating Wavejets on point sets and demonstrate experimentally the amplification results with respect to noise or basis truncation.     

Conceptual design and modification of freeform surfaces using dual shape representations in augmented reality environments

This paper enables the rapid creation and modification of freeform surfaces inside an augmented reality environment, and focuses on methods for enabling increased flexibility during exploratory, conceptual industrial product design through three-dimensional (3D) sketch-based user input. Specifically, we address the role of multiple shape representations with varying uncertainty levels during 3D conceptual sketching, along with methods to transform between those representations. The main contributions of this work are: (1) the formulation of virtual shape data in multiple, concurrent representations (points and surfaces), and a regression method to transition fluidly back and forth between these representations during design, (2) methods for deforming and exploring the product shape using these multiple representations, and (3) representations of these forms such that designers can explore conceptual designs without the need for detailed surface operations such as trimming or continuity enforcement. Through incorporating these contributions, we introduce techniques that can be incorporated in future computer-aided conceptual design systems. These contributions are demonstrated for freeform surface design, with examples of computer mouse and car seat exterior surfaces.     

Spherical harmonic molecular surfaces

Starlike surfaces can be defined in spherical coordinates by a function r(&thetas;, φ) on the unit sphere, which can be expanded in spherical harmonics to give a consequence of smooth approximations to the surface. This method has been used to approximate the solvent-accessible surface of a molecule. The coefficients in the expansion provide a small collection of numbers that characterize the molecular shape. The resulting smooth surfaces can be rendered with random dots or smooth shading. These spherical harmonic surfaces have advantages for modeling overall molecular shape, particularly time-averaged shapes relevant to electrostatic and other intermolecular interactions     

Constrained 3D shape reconstruction using a combination of surface fitting and registration

We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.     

斜对称面检测在二次曲面体中的应用

对称是三维重建中的一个十分重要的约束条件,真实的对称在全局观察视角下变成了斜对称。斜对称检测可以大大降低三维重建的复杂度。本文提出了二次曲面体的斜对称面检测方法,该方法首先将SUGIMOTO等提出的斜对称检测方法扩展到任意二次曲线,然后将二次曲面体进行面域提取,对提取的各个面域运用前面的斜对称检测方法进行斜对称轴检测,从所有检测到的对称轴中提取出对称面多边形的边界,采用极左邻边搜索法构造对称面多边形即斜对称面同实体的相交面。由于算法对于物体的摆放位置没有要求,因而扩展了实体的覆盖域。     

A central profile-based 3D face pose estimation

In this study, we develop a central profile-based 3D face pose estimation algorithm. The central profile is a unique curve on a 3D face surface that starts from forehead center, goes down through nose ridge, nose tip, mouth center, and ends at a chin tip. The points on the central profile are co-planar and belong to a symmetry plane that separates human face into two identical parts. The central profile is protrusive and has a certain length. Most importantly, the normal vectors of the central profile points are parallel to the symmetry plane. Based on the properties of the central profile, Hough transform is employed to determine the symmetry plane by invoking a voting procedure. An objective function is introduced in the parameter space to quantify the vote importance for face profile points and map the central profile to an accumulator cell with the maximal value. Subsequently, a nose model matching algorithm is used to detect nose tip on the central profile. A pitch angle estimation algorithm is also proposed. The pose estimation experiments completed for a synthetic 3D face model and the FRGC v2.0 3D database demonstrate the effectiveness of the proposed pose estimation algorithm. The obtained central profile detection rate is 99.9%, and the nose tip detection rate has reached 98.16% with error not larger than 10 mm.     

Modeling deformable surfaces with level sets

This article describes how to use level sets to represent and compute deformable surfaces. A deformable surface is a sequence of surface models obtained by taking an initial model and incrementally modifying its shape. Typically, we can parameterize the deformation over time, and thus we can imagine that a surface moves or flows under the influence of a vector field. The surface flow, v, can be determined as a function of spatial position (and time), or it can depend on the shape of the surface itself. The latter is called a geometric flow. Deformable surfaces have been used to solve a variety of problems in image processing, computer vision, visualization, and graphics. In graphics, for instance, deformable surface models have been used to form sequences of shapes that animate the morphing of one object into another. They have also been used to denoise or smooth surface models derived from a set of noisy 3D measurements.     

基于柱坐标B样条活动曲面模型的3D分割方法

基于长轴和短轴系列核磁共振图像重建3D左心室内外表面是提取左心室基本形态参数以及左心室运动分析的基础.提出了柱坐标B样条主动表面(CBAS)模型,将其用于3D分割左心室内外膜表面. CBAS模型的等参曲线网格由B-snake模型组成,根据短轴、长轴成像平面在3D空间中的位置关系,网格中的节点在两幅短轴及长轴图像上寻找对应的边缘点,节点间的采样点则在单一的短轴或长轴图像上获得图像能量.首先利用改进的模糊Hough变换确定短轴图像中左心室心肌内外轮廓的大致位置,其次用其构建柱坐标B样条主动曲面模型的初始表面.对左心室表面的分割过程在柱坐标下进行,使得模型在SA图像及LA图像上形状的改变能够统一为一个参数的变化,减小了模型的复杂度.最后通过与手工分割结果的线性回归分析证明了方法的准确性.     

A deformation model to reduce the effect of expressions in 3D face recognition

In 3D face recognition, most work utilizes the rigid parts of face surfaces for matching to exclude the distortion caused by expressions. However, across a broad range of expressions, the rigid parts may not always be uniform and cover large parts of faces. On the other hand, the non-rigid regions of face surfaces also contain useful information for recognition. In this paper, we include the non-rigid regions besides the rigid parts for 3D face recognition. A deformation model is proposed to deform the non-rigid regions to the shapes that are more similar between intra-personal samples but less similar between inter-personal samples. Together with the rigid regions, the deformed parts make samples more discriminable so that the effect of expressions is reduced. The first part of our model uses the target gradient fields from enrolled samples to depress the distortion of the non-rigid regions. The gradient field works in the differential domain. According to the Poisson equation, a smooth deformed shape can be computed by a linear system. The second part of the model is the definition of a surface property that determines the deformation ability of different face regions. Unlike the target gradient fields that improve the similarity of intra-personal samples, the original topology and surface property can keep inter-personal samples sufficiently dissimilar. Our deformation model can be used to improve existing 3D face recognition methods. Experiments are carried out on FRGC and BU-3DFE databases. There are about 8–10% improvements obtained after applying this deformation model to the baseline ICP method. Compared with other deformation models, the experimental results show that our model has advantages on both recognition performance and computational efficiency.     

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.     

任意摆放的二次曲面体的三维重建

本文采用特征点匹配的方法,先由二维视力获取三维空间的点和曲线,然后经过一系列线性运算得出三维曲面。本算法可对任意二次曲面进行三维重建,不仅对曲面的空间摆放沿有限制,而且对曲面自身的对称性也无要求。因此,可将重建对象扩展为圆柱、椭圆柱、球、椭球、双曲面、抛物面等。本文给出的算例表明了算法的有效性。     

3-D reconstruction using mirror images based on a plane symmetryrecovering method

Three-dimensional reconstruction from a perspective 2D image using mirrors is addressed. The mirrors are used to form symmetrical relations between the direct image and mirror images. By finding correspondences between them, the 3D shape can be reconstructed by means of plane symmetry recovering method using the vanishing point. Two constraints are used in determining the correspondence. In the case where only one mirror is used, invisible parts both in the direct image and in the mirror image may still remain. Using multiple mirrors, however, occluded parts will decrease or disappear, and occlusion-free object reconstruction becomes possible     

Manipulation of CAD surface models with haptics based on shape control functions

With traditional two-dimensional based interfaces, many CAD surface models are difficult to design and edit due to their 3D nature. This paper discusses a technique for the deformation of CAD surface models with haptic interaction based on shape control functions. With the technique, designers can use a haptic interface to directly touch a native B-rep CAD model, and deform it in real-time by pushing, pulling and dragging its surfaces in a natural 3D environment. The deformation is governed by shape control functions. By using the shape functions, designers can specify the area of deformation, and also have greater controls on the shape of deformation. This technique is numerically efficient, and can deform complex surface models involving several thousand control points in real-time. The haptic-based deforming approach gives designers greater flexibility for the manipulation of complex CAD surfaces.     

Geodesic distance-weighted shape vector image diffusion

This paper presents a novel and efficient surface matching and visualization framework through the geodesic distance-weighted shape vector image diffusion. Based on conformal geometry, our approach can uniquely map a 3D surface to a canonical rectangular domain and encode the shape characteristics (e.g., mean curvatures and conformal factors) of the surface in the 2D domain to construct a geodesic distance-weighted shape vector image, where the distances between sampling pixels are not uniform but the actual geodesic distances on the manifold. Through the novel geodesic distance-weighted shape vector image diffusion presented in this paper, we can create a multiscale diffusion space, in which the cross-scale extrema can be detected as the robust geometric features for the matching and registration of surfaces. Therefore, statistical analysis and visualization of surface properties across subjects become readily available. The experiments on scanned surface models show that our method is very robust for feature extraction and surface matching even under noise and resolution change. We have also applied the framework on the real 3D human neocortical surfaces, and demonstrated the excellent performance of our approach in statistical analysis and integrated visualization of the multimodality volumetric data over the shape vector image.     

Defect detection in inhomogeneously textured sputtered surfaces using 3D Fourier image reconstruction

Texture analysis techniques have been used extensively for surface inspection, in which small defects that appear as local anomalies in textured surfaces must be detected. Traditional surface inspection methods are mainly concentrated on homogeneous textures. In this paper, we propose a 3D Fourier reconstruction scheme to tackle the problem of surface inspection on sputtered glass substrates that contain inhomogeneous textures. Such sputtered surfaces can be found in touch panels and liquid crystal displays (LCDs). Since an inhomogeneously textured surface does not have repetition, self-similarity properties in the image, a sequence of faultless images along with the inspection image are used to construct a 3D image so that the periodic patterns of the surface can be observed in the additional frame-axis. Bandreject filtering is used to eliminate frequency components associated with faultless textures in the spatial domain image, and the 3D inverse Fourier transform is then carried out to reconstruct the image. The resulting image can effectively remove background textures and distinctly preserve anomalies. This converts the difficult defect detection in complicated inhomogeneous textures into a simple thresholding in nontextured images. Experimental results from a number of sputtered glass surfaces have shown the efficacy of the proposed 3D Fourier image reconstruction scheme.     

On the shape of a set of points and lines in the plane

Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free‐form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the guided α‐shape: an extension of the well known α‐shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided α‐shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided α‐shape can be constructed in O((n + m) log (n + m)) time, from an input of n points and m guides. We apply guided α‐shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided α‐shapes of both synthetic and real data and show they are consistently better than α‐shapes for this application.     

Volumetric Shapes of Solids of Revolution from a Single-View Range Image

Many man-made objects such as industrial parts are partially constructed of surfaces of revolution, as well as planar surfaces. We have studied the problem of finding and recovering solids of revolution in range data which are potentially useful for modeling and recognizing 3D objects. We propose an approach to the problem which is based on the fact that at least one of two focal surfaces for a surface of revolution degenerates into the axis of rotation. First, by computing the surface normal and principal curvatures, the centers of principal curvature which construct the focal surfaces are obtained for each point in the range image. Then, using the Hough transform, the axes of rotation are detected by finding the centers of principal curvature which lie on straight lines in space. Finally, the solid of revolution is completely determined by estimating the radius function of cross-section along each rotational axis. The proposed method can be used even in situations where occlusion or truncation is a problem because it does not require the visibility of entire surfaces. Experiments have been successfully carried out with real range data obtained from laser rangefinders.