基于组合不变矩和神经网络的三维物体识别

在三维物体识别系统中,提出将三维物体的Hu不变矩和仿射不变矩两者的低阶矩组合作为三维物体的特征,结合改进的BP神经网络应用于三维物体的分类识别。理论分析和仿真实验表明组合这两种矩特征进行物体识别,性能优于单独使用Hu不变矩,如果进一步对这两种组合的矩特征进行主成分分析处理,可显著提高系统识别性能,并减少网络的训练时间。     

Quasi-Invariant Parameterisations and Matching of Curves in Images

In this paper, we investigate quasi-invariance on a smooth manifold, and show that there exist quasi-invariant parameterisations which are not exactly invariant but approximately invariant under group transformations and do not require high order derivatives. The affine quasi-invariant parameterisation is investigated in more detail and exploited for defining general affine semi-local invariants from second order derivatives only. The new invariants are implemented and used for matching curve segments under general affine motions and extracting symmetry axes of objects with 3D bilateral symmetry.     

基于协方差矩阵的仿射不变量

为了对仿射变形的物体进行有效和正确的识别,构造了一种新的仿射不变量.构造的主要过程是：先计算图像的协方差矩阵,接着计算该矩阵的特征值和特征向量,再构造出一组同心椭圆,这些椭圆以图像质心为中心,以两个特征向量为长、短轴,且轴长和两个特征值的平方根成正比,进而利用图像紧化原理和仿射变换的有关性质推导出一组仿射不变量.文中将仿射不变量用于模式识别,获得很高的识别率.     

Determination of blur and affine combined invariants by normalization

The determination of invariant characteristics is an important problem in pattern recognition. In many situations, images to be processed are usually subjected to geometric distortion and/or blur degradation. In this paper, we introduce an approach to derive blur and affine combined invariants (BAI). Firstly, we normalize the image to a standard form by using blur invariant moments as normalization constraints. Then, we construct the blur and affine combined invariants at the standard form. Using the method proposed in this paper, a set of blur and affine combined invariant features can be obtained easily and effectively. Several experimental results are presented to illustrate the performance of the invariants for simultaneously affine deformed and blur degraded images.     

Affine moment invariants generated by graph method

The paper presents a general method of an automatic deriving affine moment invariants of any weights and orders. The method is based on representation of the invariants by graphs. We propose an algorithm for eliminating reducible and dependent invariants. This method represents a systematic approach to the generation of all relevant moment features for recognition of affinely distorted objects. We also show the difference between pseudoinvariants and true invariants.     

An automatic method for generating affine moment invariants

Affine moment invariants are important if one wants to recognize the surface of a plane in three dimensions when the orientation of the plane is not known beforehand and only two-dimensional information is available. The notion of generating function is introduced as a simple and straightforward way to derive various affine invariants. By this notion, we can get the explicit construction of much more affine moment invariants. Based on this conclusion, a large set of invariant polynomials can be generated automatically and immediately by the algorithm we have designed. These new affine moment invariants can be applied to recognize the image. Approaches in this paper will improve the practicability of affine invariants in object recognition applications.     

基于几何不变量的图像特征识别

图像的特征识别是图像处理和识别中的一个重要问题，几何不变量作为特征的特征值在很多领域已经得到了广泛的应用。实际中，普遍采用在仿射变换及射影变换下保持不变的仿射、射影不变量作为特征值。本文根据具体图像的特点，利用4类仿射和射影不变量构成特征的特征值空间，依据4步识别策略来识别图像中的特征点，从而完成识别任务。实验表明，这4类不变量能够较好地识别出实际图像中的特征。     

Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment

This paper outlines a new geometric parameterization of 2D curves where parameterization is in terms of geometric invariants and parameters that determine intrinsic coordinate systems. This new approach handles two fundamental problems: single-computation alignment, and recognition of 2D shapes under Euclidean or affine transformations. The approach is model-based: every shape is first fitted by a quartic represented by a fourth degree 2D polynomial. Based on the decomposition of this equation into three covariant conics, we are able, in both the Euclidean and the affine cases, to define a unique intrinsic coordinate system for non-singular bounded quartics that incorporates usable alignment information contained in the polynomial representation, a complete set of geometric invariants, and thus an associated canonical form for a quartic. This representation permits shape recognition based on 11 Euclidean invariants, or 8 affine invariants. This is illustrated in experiments with real data sets.     

一种新的统计仿射不变量

本文在充分分析了现有各种仿射不变量的基础上，提出了一种新的统计仿射不变量，它对于发生尺度变化、旋转、扭曲和平移的目标具有不变性。实验结果表明，相对于传统的仿射不变量，在目标轮廓分割不完整或噪声污染的情况下，仍能够保持较高的稳健性，同时克服了基于轮廓的小波方法和傅立叶级数等方法对目标轮廓出现缺陷时的不足，
，在图像目标识别中具有实用价值。     

The Classical Theory of Invariants and Object Recognition Using Algebraic Curve and Surfaces

Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. In this paper, we explore the findings of the classical theory of invariants for the calculation of algebraic invariants of implicit curves and surfaces, a theory largely disregarded in the computer vision community by a shadow of skepticism. Here, the symbolic method of the classical theory is described, and its results are extended and implemented as an algorithm for computing algebraic invariants of projective, affine, and Euclidean transformations. A list of some affine invariants of 4th degree implicit polynomials generated by the proposed algorithm is presented along with the corresponding symbolic representations, and their use in recognizing objects represented by implicit polynomials is illustrated through experiments. An affine invariant fitting algorithm is also proposed and the performance is studied.     

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     

基于分数阶矩的仿射不变特征提取

仿射不变的特征提取在目标识别和配准中起关键作用, 图像矩是提取仿射不变特征的重要方法, 高阶矩对噪声较敏感, 实际中仅有几个由整数阶矩构造的仿射不变量可用. 本文引入分数阶矩, 它由变形累次积分定义, 不仅充分利用仿射变换映直线为直线这一特性,而且能方便地消除仿射变换前后极角因子的影响. 利用分数阶矩给出了仿射不变量的构造, 传统矩构造的不变量仅是这种构造的特例. 实验结果表明低次矩构造的不变量一般有较好的抗噪性能.     

一种基于目标边界的不变特征提取方法

提出了一种基于目标边界的不变特征提取方法。导出了用物体角点坐标表示的低阶边界矩的闭合形式,构造了基于边界矩的仿射变换不变量。该方法只需要对物体角点进行简单的代数运算,因此,该方法简单明了,计算量很小。实验结果证明了该方法的有效性。     

Model-Based Recognition of 3D Curves From One View

It is well known that there are no geometric invariants of a projection from 3D to 2D. However, given some modeling assumptions about the 3D object, such invariants can be found. The modeling assumptions should be sufficiently strong to enable us to find such invariants, but not stronger than necessary. In this paper we find such modeling assumptions for general 3D curves under affine projection. We show, for example, that if one of the two affine curvatures is known along the 3D curve, the other can be found from the curve's 2D image. We can also derive the point correspondence between the curve and its image. We also deal with point sets and direction vectors.     

Extension of Moment Features’ Invariance to Blur

Moment invariants are features calculated on an image, which do not change their values after a transformation of the image. This paper focuses on the so called combined invariants, which obey additional requirement of invariance to image blurring. Our first contribution is a review of achievements most relevant to the derivation of algebraic, moment and combined invariants. The review explains and develops parallels between the moment and the blur invariants. Gradually, it reveals new properties, simplifying construction of the combined invariants, but having more general extent. Resulting substitution rules for easy construction of the combined invariants from other invariants are thus the main results of this paper. All the conclusions can be understood without knowledge of the tensor calculus. This paper addresses construction of the combined invariants in arbitrary dimension.

利用仿射几何的仿射不变特征提取方法

提出一种新的基于仿射几何的仿射不变特征提取方法,适合于目标的识别和图像的匹配。算法分3步执行：首先,提取区域的质心和扩展质心,质心和扩展质心的连线把目标区域分割成两部分,再分别计算两部分区域的质心,如此迭代,直到提取出满足要求的质心个数;然后,依次计算四边形的面积,其中四边形的顶点分别为其连线分割目标区域的两个质心和两个分割区域的质心;最后,依次计算各个四边形的面积比,得到仿射不变特征矢量; 另外,仿射变换的参数也可以通过计算提取的质心坐标得到。实验表明,提取的不变特征矢量稳健性好、计算速度快、分类精度高。     

基于不变矩的人形"头肩像"识别技术

针对实时监控识别人形的要求,提出了一种基于矩不变量的分级识别人形“头肩像”技术。首先从视频帧序列中,采用差分的方法分割出活动目标,对活动目标进行预处理后,根据活动目标轮廓的最小外接矩形宽高比,所定义的轮廓描述符和仿射不变矩,依据所选择的分级差别策略,由实验得出的经验数值,判断运动动目标是人形“头肩像”“正面”还是“侧面”。实验结果表明本方法具有快速,适应性强的特点。     

主轴方法和矩方法相融合的三维物体归一化的识别

针对主轴方法和矩方法各自的特点,提出将这两种方法相融合的物体归一化和识别的新 思想.首先推导出主轴唯一性判别准则,有效地解决了物体取向的归一化问题,然后推导出 了对物体平移、取向和比例变化归一化的3-D不变矩.最后提出由二阶、三阶3-D不变矩组 成的判别向量和识别判据.对12个三维物体进行归一化和识别的实验结果验证了本文方法 的有效性.