Projective invariants of co-moments of 2D images

Functions of moments of 2D images that are invariant under some changes are important in image analysis and pattern recognition. One of the most basic changes to a 2D image is geometric change. Two images of the same plane taken from different viewpoints are related by a projective transformation. Unfortunately, it is well known that geometric moment invariants for projective transformations do not exist in general. Yet if we generalize the standard definition of the geometric moments and utilize some additional information from the images, certain type of projective invariants of 2D images can be derived. This paper first defines co-moment as a moment-like function of image that contains two reference points. Then a set of functions of co-moments that is invariant under general projective transformations is derived. The invariants are simple and in explicit form. Experimental results validated the mathematical derivations.     

Invariants of six points and projective reconstruction from threeuncalibrated images

There are three projective invariants of a set of six points in general position in space. It is well known that these invariants cannot be recovered from one image, however an invariant relationship does exist between space invariants and image invariants. This invariant relationship is first derived for a single image. Then this invariant relationship is used to derive the space invariants, when multiple images are available. This paper establishes that the minimum number of images for computing these invariants is three, and the computation of invariants of six points from three images can have as many as three solutions. Algorithms are presented for computing these invariants in closed form. The accuracy and stability with respect to image noise, selection of the triplets of images and distance between viewing positions are studied both through real and simulated images. Applications of these invariants are also presented. Both the results of Faugeras (1992) and Hartley et al. (1992) for projective reconstruction and Sturm's method (1869) for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points     

Implicit Moment Invariants

The use of traditional moment invariants in object recognition is limited to simple geometric transforms, such as rotation, scaling and affine transformation of the image. This paper introduces so-called implicit moment invariants. Implicit invariants measure the similarity between two images factorized by admissible image deformations. For many types of image deformations traditional invariants do not exist but implicit invariants can be used as features for object recognition. In the paper we present implicit moment invariants with respect to polynomial transform of spatial coordinates, describe their stable and efficient implementation by means of orthogonal moments, and demonstrate their performance in artificial as well as real experiments.     

Algebraic and geometric tools to compute projective and permutationinvariants

Studies the computation of projective invariants in pairs of images from uncalibrated cameras and presents a detailed study of the projective and permutation invariants for configurations of points and/or lines. Two basic computational approaches are given, one algebraic and one geometric. In each case, invariants are computed in projective space or directly from image measurements. Finally, we develop combinations of those projective invariants which are insensitive to permutations of the geometric primitives of each of the basic configurations     

基于Radon变换的水声图像矩特征提取与分类

成像声纳采集的水声图像分析是自动水下潜器研究中的一个重要课题,该文提出了一种基于图像边缘Radon变换的水声图像矩特征提取和分类方法。使用一种形态学边缘提取算子和细化算法提取二维图像中目标的轮廓,构造目标轮廓在 Radon变换空间的平移、比例和旋转矩不变量,应用于3类水下物体的分类中,实验仿真结果表明该方法在运算速度上优于Hu’s不变矩和图像目标面Radon投影空间不变矩,具有很好的性能和较高的实用价值。     

Pattern recognition with moment invariants: A comparative study and new results

Moment invariants have been proposed as pattern sensitive features in classification and recognition applications. In this paper, the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data: handwritten numerals and aircrafts.

The authors also present a detailed study of Zernike and pseudo Zernike moment invariants including a new procedure for deriving the moment invariants. In addition, the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants.

Based on a comprehensive study with both handwritten numerals and aircraft data, the authors show that the new method of deriving Zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise.     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

计算射影与排列不变量的新方法

给出了一种表示和计算离散有限点集的射影与排列不变量的简单有效方法.该不变量在计算机视觉、模式识别中有重要应用.首先导出了射影直线上4个点的基于一种对称函数的射影与排列不变量,该不变量等于这4个点的某个原始交比值,具有计算量低,不丢失分辨力等优点.然后根据这个简单的对称函数,结合基本的多项式对称函数,推导出了平面上5个点的两个函数无关的射影与排列不变量,以及空间中6个点的3个函数无关的射影与排列不变量.     

基于投影变换的声纳图像特征提取与识别

用投影变换的方法进行了成像声纳采集的水声图像特征提取与识别。阐述了Radon与扇束投影变换的特点与关系,并提出了一种基于图像边缘Radon变换的水声图像矩特征提取和识别方法。首先使用一种形态学边缘提取算子和细化算法提取二维图像中目标的轮廓,构造目标轮廓在 Radon变换空间的平移、比例和旋转矩不变量,并应用于三类水下物体的分类识别中,实验仿真结果表明该方法在运算速度上优于Hu’s不变矩和图像目标面Radon投影空间不变矩,具有很好的性能和较高的实用价值。     

基于改进小波矩特征的快速无损图像描述算法

为了更有效地利用小波矩不变量算法来快速无损地计算图像特征值, 提出了一种融合Mallat算法的无损采样的新型小波矩不变量算法. 在此基础之上, 结合傅里叶变换的原理及特点, 提出了基于频率幅值谱与小波矩不变量的特征提取方法. 并将改进的小波矩不变量算法与传统使用三次B样条矩的小波矩、Hu矩进行了比较. 实验表明, 改进的小波矩不变量在比传统小波矩不变量算法性能几乎没有损失的情况下, 大大加快了小波矩不变量的计算速度, 并且基于频率幅值谱的小波矩有更强的抗噪性.     

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。     

Hu不变矩的构造与推广

为了更简洁高效地构造指定要求的不变矩,并判断矩组信息冗余性,推导了实复矩反演关系公式并提出了Hu不变矩构造定理。不变矩多项式和不变矩多项式空间概念的引入,可以赋予不变矩多项式空间代数结构特征。结合组合计数定理,列出了工程上非常实用且没有信息冗余的全部3阶4次不变矩,这是对7个经典Hu不变矩的推广。实验表明,与Hu不变矩的代数不变量构造方法和三角函数系构造方法相比,该构造方法更简洁高效且具有一般性,也更适合判断矩组信息冗余。所构造新不变矩具有较好的鲁棒性,用于图像描述取得了较好效果。     

Texture discrimination by projective invariants

We investigate the use of projective invariants for discriminating textured surfaces under projective transformation. A theorem is presented which shows that statistics of cross ratios of groups of four collinear points are a projective invariant. The distance between normalized vectors is used as the similarity measure for texture discrimination.     

Recognitive aspects of moment invariants

Moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance. The notion of complex moments is introduced as a simple and straightforward way to derive moment invariants. Through this relation, properties of complex moments are used to characterize moment invariants. Aspects of information loss, suppression, and redundancy encountered in moment invariants are investigated and significant results are derived. The behavior of moment invariants in the presence of additive noise is also described.     

图像不变矩的推广

该文提出了一种快速有效的推导不变矩的方法——三角函数生成法，建立了一种不变矩空间，总结出不变矩的一般构造规律，导出了5个新的不变矩表达式C8～C12其它高阶不变矩表达形式也可采用类似的构造方案．在此基础上还得出多种高阶不变矩的表达通式，讨论了不变矩的反射变换特性．并在实验中给出了离散情况下一些图像不变矩的稳定性比较．利用扩充后的不变矩特征集能更准确地对图像进行分类和识别．     

基于Tchebichef不变距的图形识别

论文提出一种新的基于Tchebichef不变距的图形识别方法,Tchebichef不变距通过对图像进行大小归一化、平移处理以及旋转处理并结合Tchebichef正交距得到;利用提出的Tchebichef不变距作为特征进行图形的识别,和采用Hu不变距以及Zernike不变矩的识别方法相比,无论是在无噪声还是在有噪声的情况下都有更高的识别精度;仿真试验证实了本方法的可行性。     

一种由未定标图象估计三维射影不变量的新算法

本文提出了一种由未定标图象估计三维射不变量的新算法。实验结果表明了本算法的有效性。     

基于不变矩的高分辨率遥感图像建筑物提取方法

为了有效地对图像进行特征提取, 利用不变矩算法对IKONOS和WorldView两种高分辨率遥感图像的城市建筑物地区进行提取。首先将图像数据经过Canny边缘检测和标记分水岭分割, 然后在此基础上分别利用胡氏不变矩和仿射不变矩对图像进行特征提取; 最后通过实验结果的评价可以证明在建筑物的特征提取上, 仿射不变矩比胡氏不变矩的提取效果更加显著, 进而也证明了利用不变矩算法对高分辨率遥感图像建筑物特征提取这一方法是可行且有效的。