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。     

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.     

Projectively invariant decomposition and recognition of planar shapes

An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented. by ellipses. The method is invariant to projective transformations of the shape, and thus the conic primitives can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and it is based on finding ellipses with four points of contact to the given shape. The cross ratio computed from the four points on the ellipse can then be used as a projectively invariant index. It is demonstrated that a given shape has a unique parameter-free decomposition into a finite set of ellipses with unit cross ratio. For a given shape, each pair of ellipses can be used to compute two independent projective invariants. The set of invariants computed for each ellipse pair can be used as indexes to a hash table from which model hypothesis can be generated Examples of shape decomposition and recognition are given for synthetic shapes and shapes extracted from grey level images of real objects using edge detection.     

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.     

基于小波矩不变量的海上目标识别

针对识别海上目标时不同目标相似性大的特点,将不变矩理论与小波分析相结合,本文引入一种基于小波矩不变量的特征提取法,并且为得到一组局部最优特征组而提出一种结合DB Index准则的特征选择法。在仿真实验中,将小波矩不变量与Hu矩、Zernike矩进行了比较。实验表明,小波矩不变量具有更好的识别效果。     

Moment invariants for recognition under changing viewpoint and illumination

Generalised color moments combine shape and color information and put them on an equal footing. Rational expressions of such moments can be designed, that are invariant under both geometric deformations and photometric changes. These generalised color moment invariants are effective features for recognition under changing viewpoint and illumination. The paper gives a systematic overview of such moment invariants for several combinations of deformations and photometric changes. Their validity and potential is corroborated through a series of experiments. Both the cases of indoor and outdoor images are considered, as illumination changes tend to differ between these circumstances. Although the generalised color moment invariants are extracted from planar surface patches, it is argued that invariant neighbourhoods offer a concept through which they can also be used to deal with 3D objects and scenes.     

Orthogonal variant moments features in image analysis

Moments are statistical measures used to obtain relevant information about a certain object under study (e.g., signals, images or waveforms), e.g., to describe the shape of an object to be recognized by a pattern recognition system. Invariant moments (e.g., the Hu invariant set) are a special kind of these statistical measures designed to remain constant after some transformations, such as object rotation, scaling, translation, or image illumination changes, in order to, e.g., improve the reliability of a pattern recognition system. The classical moment invariants methodology is based on the determination of a set of transformations (or perturbations) for which the system must remain unaltered. Although very well established, the classical moment invariants theory has been mainly used for processing single static images (i.e. snapshots) and the use of image moments to analyze images sequences or video, from a dynamic point of view, has not been sufficiently explored and is a subject of much interest nowadays. In this paper, we propose the use of variant moments as an alternative to the classical approach. This approach presents clear differences compared to the classical moment invariants approach, that in specific domains have important advantages. The difference between the classical invariant and the proposed variant approach is mainly (but not solely) conceptual: invariants are sensitive to any image change or perturbation for which they are not invariant, so any unexpected perturbation will affect the measurements (i.e. is subject to uncertainty); on the contrary, a variant moment is designed to be sensitive to a specific perturbation, i.e., to measure a transformation, not to be invariant to it, and thus if the specific perturbation occurs it will be measured; hence any unexpected disturbance will not affect the objective of the measurement confronting thus uncertainty. Furthermore, given the fact that the proposed variant moments are orthogonal (i.e. uncorrelated) it is possible to considerably reduce the total inherent uncertainty. The presented approach has been applied to interesting open problems in computer vision such as shape analysis, image segmentation, tracking object deformations and object motion tracking, obtaining encouraging results and proving the effectiveness of the proposed approach.     

Model-based invariants for 3-D vision

Invariance under a group of 3-D transformations seems a desirable component of an efficient 3-D shape representation. We propose representations which are invariant under weak perspective to either rigid or linear 3-D transformations, and we show how they can be computed efficiently from a sequence of images with a linear and incremental algorithm. We show simulated results with perspective projection and noise, and the results of model acquisition from a real sequence of images. The use of linear computation, together with the integration through time of invariant representations, offers improved robustness and stability. Using these invariant representations, we derive model-based projective invariant functions of general 3-D objects. We discuss the use of the model-based invariants with existing recognition strategies: alignment without transformation, and constant time indexing from 2-D images of general 3-D objects.     

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     

基于步态能量图和不变矩的身份识别算法

分析步态能量图即具有作为静态的外观特征,又包含了识别的动力学有用信息,同时证明了步态能量图对噪声的不敏感性。文章提出了一种基于步态能量图和不变矩的身份识别算法,介绍了不变矩的基本理论以及Hu提出的七个不变矩,利用图像不变矩的平移、尺度和旋转不变特性,从原始的步态能量图中提取不变矩特征作为步态能量图的输入特征向量,运用不变矩的最小距离分类器的模式匹配进行步态特征分类。最后在CASIA步态数据库上对所提出的算法和其他新的步态识别方法相比较。实验结果表明,提出的算法是一种有效的步态识别方法。     

Combined blur and affine moment invariants and their use in pattern recognition

The paper is devoted to the recognition of objects and patterns deformed by imaging geometry as well as by unknown blurring. We introduce a new class of features invariant simultaneously to blurring with a centrosymmetric PSF and to affine transformation. As we prove in the paper, they can be constructed by combining affine moment invariants and blur invariants derived earlier. Combined invariants allow to recognize objects in the degraded scene without any restoration.     

Moment invariants for the analysis of 2D flow fields

We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.     

基于结构矩不变量的形状相似性比较

在传统的几何矩定义的基础上进行扩展,给出了结构矩的定义和计算。其实质是对原有几何矩定义中的密度函数经过变换得到新的密度函数。在此基础上定义的不变矩突出或者扩大了形状之间的差别,因而使形状相似性的比较建立在更为可靠的基础上。基于平方变换的实验表明,与传统的几何矩相比结构矩方法具有更好的效果。     

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．     

Geometric and illumination invariants for object recognition

We propose invariant formulations that can potentially be combined into a single system. In particular, we describe a framework for computing invariant features which are insensitive to rigid motion, affine transform, changes of parameterization and scene illumination, perspective transform, and view point change. This is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively. The formulations are widely applicable to many popular basis representations, such as wavelets, short-time Fourier analysis, and splines. Exploiting formulations that examine information about shape and color at different resolution levels, the new approach is neither strictly global nor local. It enables a quasi-localized, hierarchical shape analysis which is rarely found in other known invariant techniques, such as global invariants. Furthermore, it does not require estimating high-order derivatives in computing invariants (unlike local invariants), whence is more robust. We provide results of numerous experiments on both synthetic and real data to demonstrate the validity and flexibility of the proposed framework