Fast interference detection between geometric models

We present efficient algorithms for interference detection between geometric models described by linear or curved boundaries and undergoing rigid motion. The set of models include surfaces described by rational spline patches or piecewise algebraic functions. In contrast to previous approaches, we first describe an efficient algorithm for interference detection between convex polytopes using coherence and local features. Then an extension using hierarchical representation to concave polytopes is presented. We apply these algorithms along with properties of input models, local and global algebraic methods for solving polynomial equations, and the geometric formulation of the problem to devise efficient algorithms for convex and nonconvex curved objects. Finally, a scheduling scheme to reduce the frequency of interference detection in large environments is described. These algorithms have been successfully implemented and we discuss their performance in various environments.     

Perturbation methods for interactive specular reflections

We describe an approach for interactively approximating specular reflections in arbitrary curved surfaces. The technique is applicable to any smooth implicitly defined reflecting surface that is equipped with a ray intersection procedure; it is also extremely efficient as it employs local perturbations to interpolate point samples analytically. After ray tracing a sparse set of reflection paths with respect to a given vantage point and static reflecting surfaces, the algorithm rapidly approximates reflections of arbitrary points in 3-space by expressing them as perturbations of nearby points with known reflections. The reflection of each new point is approximated to second-order accuracy by applying a closed-form perturbation formula to one or more nearby reflection paths. This formula is derived from the Taylor expansion of a reflection path and is based on first and second-order path derivatives. After preprocessing, the approach is fast enough to compute reflections of tessellated diffuse objects in arbitrary curved surfaces at interactive rates using standard graphics hardware. The resulting images are nearly indistinguishable from ray traced images that take several orders of magnitude longer to generate     

Detecting Symmetry in Grey Level Images: The Global Optimization Approach

The detection of significant local reflectional symmetry in grey level images is considered. Prior segmentation is not assumed, and it is intended that the results could be used for guiding visual attention and for providing side information to segmentation algorithms. A local measure of reflectional symmetry that transforms the symmetry detection problem to a global optimization problem is defined. Reflectional symmetry detection becomes equivalent to finding the global maximum of a complicated multimodal function parameterized by the location of the center of the supporting region, its size, and the orientation of the symmetry axis. Unlike previous approaches, time consuming exhaustive search is avoided. A global optimization algorithm for solving the problem is presented. It is related to genetic algorithms and to adaptive random search techniques. The efficiency of the suggested algorithm is experimentally demonstrated. Just one thousand evaluations of the local symmetry measure are typically needed in order to locate the dominant symmetry in natural test images.     

Symmetry detection by generalized complex (GC) moments: aclose-form solution

This paper presents a unified method for detecting both reflection-symmetry and rotation-symmetry of 2D images based on an identical set of features, i.e., the first three nonzero generalized complex (GC) moments. This method is theoretically guaranteed to detect all the axes of symmetries of every 2D image, if more nonzero GC moments are used in the feature set. Furthermore, we establish the relationship between reflectional symmetry and rotational symmetry in an image, which can be used to check the correctness of symmetry detection. This method has been demonstrated experimentally using more than 200 images     

Skeleton-based intrinsic symmetry detection on point clouds

We present a skeleton-based algorithm for intrinsic symmetry detection on imperfect 3D point cloud data. The data imperfections such as noise and incompleteness make it difficult to reliably compute geodesic distances, which play essential roles in existing intrinsic symmetry detection algorithms. In this paper, we leverage recent advances in curve skeleton extraction from point clouds for symmetry detection. Our method exploits the properties of curve skeletons, such as homotopy to the input shape, approximate isometry-invariance, and skeleton-to-surface mapping, for the detection task. Starting from a curve skeleton extracted from an input point cloud, we first compute symmetry electors, each of which is composed of a set of skeleton node pairs pruned with a cascade of symmetry filters. The electors are used to vote for symmetric node pairs indicating the symmetry map on the skeleton. A symmetry correspondence matrix (SCM) is constructed for the input point cloud through transferring the symmetry map from skeleton to point cloud. The final symmetry regions on the point cloud are detected via spectral analysis over the SCM. Experiments on raw point clouds, captured by a 3D scanner or the Microsoft Kinect, demonstrate the robustness of our algorithm. We also apply our method to repair incomplete scans based on the detected intrinsic symmetries.     

Efficient 3D reflection symmetry detection: A view-based approach

Symmetries exist in many 3D models while efficiently finding their symmetry planes is important and useful for many related applications. This paper presents a simple and efficient view-based reflection symmetry detection method based on the viewpoint entropy features of a set of sample views of a 3D model. Before symmetry detection, we align the 3D model based on the Continuous Principal Component Analysis (CPCA) method. To avoid the high computational load resulting from a directly combinatorial matching among the sample views, we develop a fast symmetry plane detection method by first generating a candidate symmetry plane based on a matching pair of sample views and then verifying whether the number of remaining matching pairs is within a minimum number. Experimental results and two related applications demonstrate better accuracy, efficiency, robustness and versatility of our algorithm than state-of-the-art approaches.     

Unified detection of skewed rotation,reflection and translation symmetries from affine invariant contour features

Symmetry detection is significant for object detection and recognition since symmetries are salient cues for distinguishing geometrical structures from cluttered backgrounds. This paper proposes a unified framework to detect rotation, reflection and translation symmetries simultaneously on unsegmented real-world images. The detection is performed based on affine invariant contour features, and is applicable under skewed imaging with distortions. Contours on a natural image are first matched to each other to find affine invariant matching pairs, which are then classified into three groups using a sign change criterion corresponding to the three types of symmetries. The three groups are used to vote for the corresponding symmetries: the voting for rotation utilizes a scheme of short line segments; the voting for reflection is based on a parameterization of axis equation, and the voting for translation uses a cascade-like approach. Experimental results of real-world images are provided with quantitative evaluations, validating that the proposed framework achieves desired performance.     

The second order local-image-structure solid

Characterization of second order local image structure by a 6D vector (or jet) of Gaussian derivative measurements is considered. We consider the affect on jets of a group of transformations-affine intensity-scaling, image rotation and reflection, and their compositions-that preserve intrinsic image structure. We show how this group stratifies the jet space into a system of orbits. Considering individual orbits as points, a 3D orbifold is defined. We propose a norm on jet space which we use to induce a metric on the orbifold. The metric tensor shows that the orbifold is intrinsically curved. To allow visualization of the orbifold and numerical computation with it, we present a mildly-distorting but volume-preserving embedding of it into euclidean 3-space. We call the resulting shape, which is like a flattened lemon, the second order local-image-structure solid. As an example use of the solid, we compute the distribution of local structures in noise and natural images. For noise images, analytical results are possible and they agree with the empirical results. For natural images, an excess of locally 1D structure is found.     

基于局部能量的对称性检测算法

目前大多数对称性检测算法都是基于亮度或梯度信息进行的．文中分析了对称性与相位之间的关系,提出一种基于局部能量的对称性检测方法,将对称性检测问题转化为能量分析．在频域中用log Gabor小波对原始图像进行滤波,在不同尺度下局部能量最大、相位为特定相位且保持一致的点,即为物体的对称点．文中的可行性分析、算法定义及其合理性为该算法奠定了理论基础．实验表明,该算法可以克服目前已有算法需要图像分割的局限性,即该算法可直接应用于原始图像,不需要图像的任何先验知识,不需进行分割等任何预处理,而且还可以同时检测多种对称性．     

Sub-optimal solutions to track detection problem using graph theoretic concepts

This paper demonstrates how the problem of tracking targets, which appear as either straight or curved lines in two-dimensional display images (or data images) can be formulated in terms of a directed weighted graph model and how dynamic programming techniques can be efficiently applied to reach an optimal or sub-optimal solution. In general, track detection algorithms providing optimal solutions have good detective ability, but most of them suffer from the inability to detect discontinuous lines or to resolve efficiently pairs of crossing lines. A sub-optimal solution is provided that efficiently overcomes these weaknesses. We focus on modeling the track detection problem in terms of a graph, formulating fast sequential/parallel sub-optimal track detection algorithms and testing them on simulated data in order to show their detective ability. Moreover, we specify the conditions under which sub-optimal algorithms can perform at least as well as their corresponding optimal algorithms. This is significant for the track detection problem where fast, accurate and real-time detection is considered a necessity.     

从阴影恢复形状的径向基函数反射模型研究

目的 为解决传统阴影恢复形状（SFS）算法由于光源方向初始信息估计不准确,恢复的物体表面过于光滑,3维表面形状误差较大等问题,建立了基于径向基函数神经网络的反射模型,并对传统的神经网络进行了改进。方法 建立的基于径向基函数（SFS）神经网络的从阴影恢复形状反射模型代替了传统方法中采用的理想朗伯体表面反射模型。该模型利用径向基函数优秀的局部映射和函数逼近能力来处理SFS问题,通过网络训练过程中的权值代替物体所受到的初始光源信息,解决了传统算法在进行计算时,必须已知光源参数的限制。在该网络模型中添加自适应学习率算法,加速网络的收敛和训练速度。结果 针对SFS问题处理的两幅经典合成图像以及两幅实际图像进行了实验,实验结果表明,改进后的算法在3维视觉效果和3维形状信息的恢复方面都明显优于传统算法。归一化后的3维高度误差结果相比传统算法缩小了60%以上,而且同时适用合成图像和实际图像;自适应学习率的加入,使得网络的训练速度大大加快,对一幅128×128像素的图像,运算速度提升了50%。结论 本文针对SFS问题建立了基于RBF神经网络的从阴影恢复形状反射模型,利用网络模型中的参数代替SFS问题中的初始光源信息,通过最优化方法求解SFS问题。并针对传统的神经网络固定学习率造成网络收敛速度慢,容易陷入局部极小值的问题,加入了自适应学习率算法。实验结果表明,改进后的算法在处理该SFS问题时表现了优秀的性能,适用范围更广,收敛速度更快。     

Scene-consistent detection of feature points in video sequences

Detection of feature points in images is an important preprocessing stage for many algorithms in Computer Vision. We address the problem of detection of feature points in video sequences of 3D scenes, which could be mainly used for obtaining scene correspondence. The main feature we use is the zero crossing of the intensity gradient argument. We analytically show that this local feature corresponds to specific constraints on the local 3D geometry of the scene, thus ensuring that the detected points are based on real 3D features. We present a robust algorithm that tracks the detected points along a video sequence, and suggest some criteria for quantitative evaluation of such algorithms. These criteria serve in a comparison of the suggested operator with four other feature trackers. The suggested criteria are generic and could serve other researchers as well for performance evaluation of stable point detectors.     

Lambertian reflectance and linear subspaces

We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. We also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. We apply these algorithms to perform face recognition by finding the 3D model that best matches a 2D query image.     

Symmetry and Orbit Detection via Lie‐Algebra Voting

In this paper, we formulate an automatic approach to the detection of partial, local, and global symmetries and orbits in arbitrary 3D datasets. We improve upon existing voting‐based symmetry detection techniques by leveraging the Lie group structure of geometric transformations. In particular, we introduce a logarithmic mapping that ensures that orbits are mapped to linear subspaces, hence unifying and extending many existing mappings in a single Lie‐algebra voting formulation. Compared to previous work, our resulting method offers significantly improved robustness as it guarantees that our symmetry detection of an input model is frame, scale, and reflection invariant. As a consequence, we demonstrate that our approach efficiently and reliably discovers symmetries and orbits of geometric datasets without requiring heavy parameter tuning.     

Approximate Symmetry Detection in Partial 3D Meshes

Symmetry is a common characteristic in natural and man‐made objects. Its ubiquitous nature can be exploited to facilitate the analysis and processing of computational representations of real objects. In particular, in computer graphics, the detection of symmetries in 3D geometry has enabled a number of applications in modeling and reconstruction. However, the problem of symmetry detection in incomplete geometry remains a challenging task. In this paper, we propose a vote‐based approach to detect symmetry in 3D shapes, with special interest in models with large missing parts. Our algorithm generates a set of candidate symmetries by matching local maxima of a surface function based on the heat diffusion in local domains, which guarantee robustness to missing data. In order to deal with local perturbations, we propose a multi‐scale surface function that is useful to select a set of distinctive points over which the approximate symmetries are defined. In addition, we introduce a vote‐based scheme that is aware of the partiality, and therefore reduces the number of false positive votes for the candidate symmetries. We show the effectiveness of our method in a varied set of 3D shapes and different levels of partiality. Furthermore, we show the applicability of our algorithm in the repair and completion of challenging reassembled objects in the context of cultural heritage.     

Deformed Lattice Detection in Real-World Images Using Mean-Shift Belief Propagation

We propose a novel and robust computational framework for automatic detection of deformed 2D wallpaper patterns in real-world images. The theory of 2D crystallographic groups provides a sound and natural correspondence between the underlying lattice of a deformed wallpaper pattern and a degree-4 graphical model. We start the discovery process with unsupervised clustering of interest points and voting for consistent lattice unit proposals. The proposed lattice basis vectors and pattern element contribute to the pairwise compatibility and joint compatibility (observation model) functions in a Markov Random Field (MRF). Thus, we formulate the 2D lattice detection as a spatial, multitarget tracking problem, solved within an MRF framework using a novel and efficient Mean-Shift Belief Propagation (MSBP) method. Iterative detection and growth of the deformed lattice are interleaved with regularized thin-plate spline (TPS) warping, which rectifies the current deformed lattice into a regular one to ensure stability of the MRF model in the next round of lattice recovery. We provide quantitative comparisons of our proposed method with existing algorithms on a diverse set of 261 real-world photos to demonstrate significant advances in accuracy and speed over the state of the art in automatic discovery of regularity in real images.     

Data‐Driven Sparse Priors of 3D Shapes

We present a sparse optimization framework for extracting sparse shape priors from a collection of 3D models. Shape priors are defined as point‐set neighborhoods sampled from shape surfaces which convey important information encompassing normals and local shape characterization. A 3D shape model can be considered to be formed with a set of 3D local shape priors, while most of them are likely to have similar geometry. Our key observation is that the local priors extracted from a family of 3D shapes lie in a very low‐dimensional manifold. Consequently, a compact and informative subset of priors can be learned to efficiently encode all shapes of the same family. A comprehensive library of local shape priors is first built with the given collection of 3D models of the same family. We then formulate a global, sparse optimization problem which enforces selecting representative priors while minimizing the reconstruction error. To solve the optimization problem, we design an efficient solver based on the Augmented Lagrangian Multipliers method (ALM). Extensive experiments exhibit the power of our data‐driven sparse priors in elegantly solving several high‐level shape analysis applications and geometry processing tasks, such as shape retrieval, style analysis and symmetry detection.     

Measuring Symmetry in Drawings of Graphs

Layout symmetry is an important and desired feature in graph drawing. While there is a substantial body of work in computer vision around the detection and measurement of symmetry in images, there has been little effort to define and validate meaningful measures of the symmetry of graph drawings. In this paper, we evaluate two algorithms that have been proposed for measuring graph drawing symmetry, comparing their judgments to those of human subjects, and investigating the use of stress as an alternative measure of symmetry. We discuss advantages and disadvantages of these measures, possible ways to improve them, and implications for the design of algorithms that optimize the symmetry in the layout.