Model-Based Object Recognition Using Geometric Invariants of Points and Lines

In this paper, we derive new geometric invariants for structured 3D points and lines from single image under projective transform, and we propose a novel model-based 3D object recognition algorithm using them. Based on the matrix representation of the transformation between space features (points and lines) and the corresponding projected image features, new geometric invariants are derived via the determinant ratio technique. First, an invariant for six points on two adjacent planes is derived, which is shown to be equivalent to Zhu's result [1], but in simpler formulation. Then, two new geometric invariants for structured lines are investigated: one for five lines on two adjacent planes and the other for six lines on four planes. By using the derived invariants, a novel 3D object recognition algorithm is developed, in which a hashing technique with thresholds and multiple invariants for a model are employed to overcome the over-invariant and false alarm problems. Simulation results on real images show that the derived invariants remain stable even in a noisy environment, and the proposed 3D object recognition algorithm is quite robust and accurate.     

Stable Algebraic Surfaces for 3D Object Representation

Linear fitting techniques by implicit algebraic models usually suffer from global stability problems. Ridge regression regularization can be used to improve the stability of algebraic surface fits. In this paper a Euclidean Invariant 3D ridge regression matrix is developed and applied to a particular linear algebraic surface fitting method. Utilization of such a regularization in fitting process makes it possible to globally stabilize 3D object fits with surfaces of any degree. Robustness to noise and moderate levels of occlusion has also been enhanced significantly. Experimental results are presented to verify the improvements in global stability and robustness of the resulting fits.

基于隐含多项式曲线欧氏不变量物体识别

目标物体的识别和匹配在计算机视觉、图像视频压缩与传输中都有重要应用。隐含多项式曲线对物体有良好的描述能力,用它识别和匹配目标物体是很有效的。文章给出了任意次隐含多项式曲线欧氏几何不变量的计算方法,理论证明这些不变量是完全独立的并且是完备的。文中的实验证明基于这些欧氏不变量能较好地识别发生欧氏变换的目标物体。     

Invariants of Families of Coplanar Conics and Their Applications to Object Recognition

This paper presents mutual invariants of families ofcoplanar conics. These invariants are compared with the use ofinvariants of two conics and a case is presented where the proposedinvariants have a greater discriminating power than the previouslyused invariants. The use of invariants for two conics is extended toany number of coplanar conics. A lambda-matrix is associated witheach family of coplanar conics. The use of lambda-matrices isextended from the single variable polynomial to multi-variablepolynomials. The Segre characteristic and other invariants of thelambda-matrix are used as invariants of the family of conics.     

Recognizing 3D Objects Using Tactile Sensing and Curve Invariants

A general paradigm for recognizing 3D objects is offered, and applied to some geometric primitives (spheres, cylinders, cones, and tori). The assumption is that a curve on the surface, or a pair of intersecting curves, was measured with high accuracy (for instance, by a sensory robot). Differential invariants of the curve(s) are then used to recognize the surface. The motivation is twofold: the output of some devices is not surface range data, but such curves. Also, a considerable speedup is obtained by using curve data, as opposed to surface data which usually contains a much higher number of points.We survey global, algebraic methods for recognizing surfaces, and point out their limitations. After introducing some notions from differential geometry and elimination theory, the differential and semi-differential approaches to the problem are described, and novel invariants which are based on the curve's curvature and torsion are derived.     

基于帧间差分法和不变矩特征的运动目标检测与识别

针对视频监视的复杂背景,提出了一种基于帧间差分法和不变矩特征的运动目标检测与识别方法.在运动目标检测算法中,首先对定义的像素区域进行数据分析,然后通过帧间的数据差异产生运动信号,捕捉到场景中的运动目标.在目标识剐方法中,首先提取运动目标区域的不变矩特征,并对其矢量进行标准化,然后利用遗传小波神经网络作为模式识别器,实现运动目标的自动识别.为验证该方法及网络模型的泛化能力,在Matalb7.0中对模型进行了仿真.     

基于不变矩的实时人形识别研究

介绍了一种实时人形识别方法,使用这个方法,可以自动监测进入摄像机镜头拍摄范围内的物体,并识别其是否是人类,其主要步骤包括,首先预处理其中包括含一除背景之外的其它物体的图像,然后提取其7个不变矩,利用贝叶斯分类器作主要手段对不变矩进行分类,最后采用辅助手段修正分类结果,识别该物体的形状是否为人形,从而判断出是否有人类经过.     

基于不变矩的实时人形监测与识别系统

介绍了一种实时监视系统，该系统可以捕获正在进入摄像机镜头的物体，并识别其是否是人类．所采用的主要方法是，预处理其中包含了除背景之外的其它物体的图像，即，去掉背景图像，并得到该物体的形状图像，然后提取其七个不变矩，利用贝叶斯分类器做主要手段对不变矩进行分类，另外采用辅助手段修正分类结果，识别该物体的形状是否为人形，从而判断出是否有人类经过．     

使用范围数据的三维物体的识别

本文所使用的系统有二个工作阶段。在知识阶段,含有单个物体的景物每次一个地示给系统,景物的范围数据可利用范围测距仪获得。根据区域特性和各区域间的关系建立每一景物的描述并将这种描述存储作为物体的模型。在识别阶段,以与知识阶段同样的方式对未知景物的特征进行描述,然后把这一描述和物体模型匹配,结果可实现成堆物体按顺序地逐个识别。为提高匹配效率,可把数据驱动和模型驱动搜索过程紧密结合。实验结果表明,这一方法是很有希望的。     

Partially Occluded Object Recognition Using Statistical Models

In this paper, we present a new Bayesian framework for partially occluded object recognition based on matching extracted local features on a one-to-one basis with object features. We introduce two different statistical models for occlusion: one model assumes that each feature in the model can be occluded independent of whether any other features are occluded, whereas the second model uses spatially correlated occlusion to represent the extent of occlusion. Using these models, the object recognition problem reduces to finding the object hypothesis with largest generalized likelihood. We develop fast algorithms for finding the optimal one-to-one correspondence between scene features and object features to compute the generalized likelihoods under both models. We conduct experiments illustrating the differences between the two occlusion models using different quantitative metrics. We also evaluate the recognition performance of our algorithms using examples extracted from object silhouettes and synthetic aperture radar imagery, and illustrate the performance advantages of our approach over alternative algorithms.     

Planar Numerical Signature Theory Applied to Object Recognition

Geometric invariants play a crucial role in the field of object recognition where the objects of interest are affected by a group of transformations. However, designing robust algorithms that are tolerant to noise and image occlusion remains an open problem. In particular, numerical signature-invariants in terms of joint invariants, as an approximation to the differential signature-invariants, suffer instability, bias, noise and indeterminacy in the resulting signatures. This paper addresses some of these issues in respect of planar signatures. To improve the stability in the Euclidean case, we replace Heron’s formula by the “accurate area” and then we demonstrate that the proposed algorithm is, not only numerically stable but is also, in terms of mean square error, a closer approximation (by at least a factor of three) compared with the original formulation of Calabi. To reduce noise in the resulting curves “the n-difference technique” and “the m-mean signature method” are introduced and we show that these methods are capable of minimizing noise by more than 90 %. The n-difference technique can also be applied to eliminate indeterminacy in the outputs. For the equiaffine case, we improve and extend the required formulation for the implementation of Signature theory for any planar meshes with a general position property. Moreover, we introduce a general formulation for the full conic sections to determine an equiaffine-invariant numerical approximation to the equiaffine arc length, measured along the given curve between any two points of the mesh. Finally, we demonstrate the discriminative power of the concept of discrete signature analysis for distinguishing normal and abnormal regions in the medical imaging domain.     

共形几何代数与几何不变量的代数运算

几何不变量的使用是计算机视觉和图形学的一个重要手段.发现一个不变量后,如何找到它与其他不变量的关系,是实际应用中的一个重要问题,这种关系的探讨主要依靠在不变量层次上的代数运算.文中介绍了共形几何代数中的基本、高级和有理不变量如何在几何问题中自然出现,它们之间如何进行代数运算,以及如何通过不变量的化简,自然地得到几何条件的充分必要化和几何定理的完全化.几何定理的机器证明作为几何定理完全化的副产品,被发展成几何定理的关系定量化,这种量化的几何还原就是几何定理的自然推广.几何不变量之间的几何关系的计算是这些技术的一个具体应用.     

基于遗传算法的运动物体实时识别

文章提出了一种应用遗传算法对一个已知几何模型的运动目标物体的位置与方向进行识别的方法,这种对运动目标的识别可以用于机器人手臂实时视觉伺服控制中。文章以一个三角形的物体为目标,对所提出的方法进行了仿真试验,结果证实了这种识别方法的有效性。     

Parameter Estimation for Optimal Object Recognition: Theory and Application

Object recognition systems involve parameters such as thresholds, bounds and weights. These parameters have to be tuned before the system can perform successfully. A common practice is to choose such parameters manually on an ad hoc basis, which is a disadvantage. This paper presents a novel theory of parameter estimation for optimization-based object recognition where the optimal solution is defined as the global minimum of an energy function. The theory is based on supervised learning from examples. Correctness and instability are established as criteria for evaluating the estimated parameters. A correct estimate enables the labeling implied in each exemplary configuration to be encoded in a unique global energy minimum. The instability is the ease with which the minimum is replaced by a non-exemplary configuration after a perturbation. The optimal estimate minimizes the instability. Algorithms are presented for computing correct and minimal-instability estimates. The theory is applied to the parameter estimation for MRF-based recognition and promising results are obtained.     

基于几何矩的字母手势识别算法

提出了一种基于提取字母手势的统计特征的方法,计算各手势图像的几何矩,以形成特征空间,并将之应用到手势识别中去。该算法具有旋转、缩放、及平移不变性的特点,并取得了较好的实验效果。     

Recognition of Symmetrical Images Using Affine Moment Invariants in both Frequency and Spatial Domains

: In this paper, a new set of affine moment invariants is proposed in the frequency domain. By thresholding the magnitude of the Discrete Fourier Transform (DFT) of affine transformation-related images, new images which are also related by affine transformation are constructed. Then some affine invariant features in the frequency domain are obtained from the reconstructed images. Experimental results are given to show that the new affine invariants are less sensitive to noise and the recognition rate is increased when using both the available spatial domain and the proposed frequency domain affine moment invariants. Received: 10 October 2000, Received in revised form: 25 July 2001, Accepted: 25 July 2001     

Classical Invariants and 2-descent on Elliptic Curves

The classical theory of invariants of binary quartics is applied to the problem of determining the group of rational points of an elliptic curve defined over a field K by 2-descent. The results lead to some simplifications to the method first presented in Birch and Swinnerton-Dyer (1963), and can be applied to give a more efficient algorithm for determining Mordell–Weil groups over Q, as well as being more readily extended to other number fields. In this paper we mainly restrict ourselves to general theory, valid over arbitrary fields of characteristic neither 2 nor 3.     

A Computational Learning Theory of Active Object Recognition Under Uncertainty

We present some theoretical results related to the problem of actively searching a 3D scene to determine the positions of one or more pre-specified objects. We investigate the effects that input noise, occlusion, and the VC-dimensions of the related representation classes have in terms of localizing all objects present in the search region, under finite computational resources and a search cost constraint. We present a number of bounds relating the noise-rate of low level feature detection to the VC-dimension of an object representable by an architecture satisfying the given computational constraints. We prove that under certain conditions, the corresponding classes of object localization and recognition problems are efficiently learnable in the presence of noise and under a purposive learning strategy, as there exists a polynomial upper bound on the minimum number of examples necessary to correctly localize the targets under the given models of uncertainty. We also use these arguments to show that passive approaches to the same problem do not necessarily guarantee that the problem is efficiently learnable. Under this formulation, we prove the existence of a number of emergent relations between the object detection noise-rate, the scene representation length, the object class complexity, and the representation class complexity, which demonstrate that selective attention is not only necessary due to computational complexity constraints, but it is also necessary as a noise-suppression mechanism and as a mechanism for efficient object class learning. These results concretely demonstrate the advantages of active, purposive and attentive approaches for solving complex vision problems.     

采用多曲线拟合的柔性体建模仿真方法

提出了一种多曲线拟合的数学建模方法,用于在仿真中快速建立柔性物体受力的形变模型。该方法根据柔性体的形变特性将其外形轮廓分为多个部分;然后使用不同的简单曲线拟合各部分轮廓的形状,并通过改变拟合曲线的参数使得曲线形状改变,以此定量仿真出轮廓的受力形变;最后将曲线拼接起来构成物体的整体形变模型。文中讨论了常见的方体和板块体在挤压、拉伸和扭转这三种非常普遍受力下的形变特性,并使用多曲线拟合方法建立了形变模型。多曲线拟合方法虽然在表现精度上存在一定误差,但建模形式简单、计算速度快,为仿真中表现速度与表达精度的矛盾提供了一种有效的解决手段。     

隐式二次代数曲线插值

目前,二次参数曲线在曲线曲面造型中应用非常广泛,起着至关重要的作用,因此对二次曲线的性质和应用的研究仍十分有意义。本文首先综述近年来有关二次曲线的研究,对各种方法的优缺点进行了客观的评价。然后根据三次代数曲线的构造方法,提出一种新的二次曲线的构造方法,该方法通过几何量如控制点和切线来控制二次代数曲线的形状。文章在理论上对曲线的一系列性质进行了详细说明。