Three-dimensional moment invariants

Recognition of three-dimensional objects independent of size, position, and orientation is an important and difficult problem of scene analysis. The use of three-dimensional moment invariants is proposed as a solution. The generalization of the results of two-dimensional moment invariants which had linked two-dimensional moments to binary quantics is done by linking three-dimensional moments to ternary quantics. The existence and number of nth order moments in two and three dimensions is explored. Algebraic invariants of several ternary forms under different orthogonal transformations are derived by using the invariant property of coefficients of ternary forms. The result is a set of three-dimensional moment invariants which are invariant under size, orientation, and position change. This property is highly significant in compressing the data which are needed in three-dimensional object recognition. Empirical examples are also given.     

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.     

Projective reconstruction and invariants from multiple images

This correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views, and the computation of projective invariants of these configurations from their images. A basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs. It is proven that once the epipolar geometry is known, the configurations of many geometric structures (for instance sets of points or lines) are determined up to a collineation of projective 3-space 𝒫³ by their projection in two independent images. This theorem is the key to a method for the computation of invariants of the geometry. Invariants of six points in 𝒫³ and of four lines in 𝒫³ are defined and discussed. An example with real images shows that they are effective in distinguishing different geometrical configurations. Since the fundamental matrix is a basic tool in the computation of these invariants, new methods of computing the fundamental matrix from seven-point correspondences in two images or six-point correspondences in three images are given     

基于不变矩的步态识别

提出了一种利用不变矩进行步态识别的方法。该方法把二维人体空间轮廓信号变换为一维不变矩信号,把人体的步态序列变换为不变矩矢量,对不变矩矢量进行规格化,然后根据规格化不变矩矢量进行步态识别。实验中,本文的方法取得很好的效果。     

基于不变矩特征和神经网络的步态识别

步态识别是利用人体步行的方式来识别人的身份.近年来,步态作为一种生物特征识别技术已引起越来越多人们的兴趣.本文提出了一种简单有效的步态识别算法,首先通过背景差方法得到运动人体轮廓,然后利用不变矩描述轮廓特征,最后用BP神经网络方法来进行模板匹配,实现人的身份识别.     

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.     

The revised fundamental theorem of moment invariants

A revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by M.K. Hu (1962), is presented. The correction affects neither similitude (scale) nor rotation invariants derived using the original theorem, but it does affect features invariant to general linear transformations. Four of the latter invariants were presented originally by Hu. These are revised to take the correction to the fundamental theorem into account. Furthermore, these four invariants are combined to yield three new invariants, which are additionally invariant to changes in the illumination of an image     

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。     

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 approximation-based approach to computing image moment invariants

A fast method for computing Hu’s image moment invariants is described. The invariants are found by approximation using generalized moments computed in a sliding window by a parallel recursive algorithm. The proposed method is shown to be computationally more efficient than direct computation. Vladislav V. Sergeev. Born 1951. Graduated from the Kuibyshev Aviation Institute (now, the Samara State Aerospace University) in 1974. Received doctoral degree (Dr. Sc. (Eng.)) in 1993. Head of Laboratory of Mathematical Methods of Image Processing, Image Processing Systems Institute, Russian Academy of Sciences. Scientific interests: digital signal processing, image analysis, pattern recognition, and geoinformatics. Author of more than 150 publications, including about 40 papers in journals, and a co-author of 2 monographs. Chair of the Volga-region Branch of the Russian Federation Association for Pattern Recognition and Image Analysis. Corresponding Member of the Russian Ecological Academy and the Russian Academy of Engineering, member of SPIE (The International Society for Optical Engineering), a winner of the Samara District Award for Science and Engineering. Ol’ga A. Titova. Born 1980. Graduated from the Samara State Aerospace University (SSAU) in 2002. Currently post-graduate student at the Chair of Geoinformatics, SSAU. Scientific interests: image analysis, pattern recognition, fast algorithms of digital image processing, and geoinformatics. Author of nine publications including three papers in journals. Member of the Russian Federation Association for Pattern Recognition and Image Analysis.     

Polar radius moment with application for affine invariants

Pattern Analysis and Applications - Image moment is an important technique for pattern recognition. But, invariants constructed with high-order moments are sensitive to noise. Only a few 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.     

Radial and angular moment invariants for image identification

Radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation, translation, reflection, and size changes without the aid of the theory of algebraic invariants. Hu's invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties.     

快速不变矩算法基于CUDA的并行实现

不变矩自提出以来被广泛应用于目标识别系统中进行特征描述,这需要能够实时计算不变矩值.虽然已经提出了许多不变矩的快速算法,但仍无法在单台PC机上实现不变矩的实时计算.分析了基于差分矩因子的不变矩快速算法的并行性,提出了一种基于统一计算架构(CUDA)的快速不变矩并行实现方法,并在NVIDIA Tesla C1060 GPU上实现.对所提出算法的计算性能与普通串行算法进行了对比分析.实验结果表明,所提出的并行计算方法极大地提高了不变矩的计算速度,可有效地用来进行实时特征提取.