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.     

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.     

3-D moment forms: their construction and application to objectidentification and positioning

The 3-D moment method is applied to object identification and positioning. A general theory of deriving 3-D moments invariants is proposed. The notion of complex moments is introduced. Complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3-D rotations. The application of the 3-D moment method to motion estimation is also discussed. Using group-theoretic techniques, various invariant scalars are extracted from compounds of complex moments via Clebsch-Gordon expansion. Twelve moment invariants consisting of the second-order and third-order moments are explicitly derived. Based on a perturbation formula, it is shown that the second-order moment invariants can be used to predict whether the estimation using noisy data is reliable or not. The new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach. Vectors consisting of the third-order moments can be derived in a similar manner     

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.     

Illumination Invariant Recognition of Three-Dimensional Texture in Color Images

In this paper, illumination-affine invariant methods are presented based on affine moment normalization techniques, Zernike moments, and multiband correlation functions. The methods are suitable for the illumination invariant recognition of 3D color texture. Complex valued moments (i.e., Zernike moments) and affine moment normalization are used in the derivation of illumination affine invariants where the real valued affine moment invariants fail to provide affine invariants that are independent of illumination changes. Three different moment normalization methods have been used, two of which are based on affine moment normalization technique and the third is based on reducing the affine transformation to a Euclidian transform. It is shown that for a change of illumination and orientation, the affinely normalized Zernike moment matrices are related by a linear transform. Experimental results are obtained in two tests: the first is used with textures of outdoor scenes while the second is performed on the well-known CURET texture database. Both tests show high recognition efficiency of the proposed recognition methods.     

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     

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.     

统一Hu矩及在电视图像目标识别中的应用

分析了在离散状态下比例因子对不变矩特征的影响,扩展了Hu提出的基于区域的不变矩和Chen提出的基于边界的不变矩,构造了一种新的不变矩,统一了基于区域和边界的矩不变量公式,并满足离散状态下的比例不变性,比传统的不变矩更具一般性。将其应用到电视图像目标识别中,仿真结果表明,不变矩不变性好,识别率高,实时性好,具有一定的应用前景。     

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。     

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.     

Novel moment invariants for improved classification performance in computer vision applications

A novel set of moment invariants based on the Krawtchouk moments are introduced in this paper. These moment invariants are computed over a finite number of image intensity slices, extracted by applying an innovative image representation scheme, the image slice representation (ISR) method. Based on this technique an image is decomposed to a several non-overlapped intensity slices, which can be considered as binary slices of certain intensity. This image representation gives the advantage to accelerate the computation of image's moments since the image can be described in a number of homogenous rectangular blocks, which permits the simplification of the computation formulas. The moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image, in recognizing the pattern under processing. The proposed moment invariants are exhaustively tested in several well known computer vision datasets, regarding their rotation, scaling and translation (RST) invariant recognition performance, by resulting to remarkable outcomes.     

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.     

Hu修正不变矩在零水印中的应用

文章提出了一种使用修正后的Hu新增不变矩零水印算法。该算法融合Hu不变矩及其新增的几个不变矩的特征矢量,提出了一种基于Hu修正不变矩的零水印算法。该方法保持了原有Hu矩的平移、尺度、旋转不变性,比原有的Hu不变矩包含了更多的细节信息用于更全面地描述图像。通过对该算法进行了一系列加噪、滤波以及JPEG压缩等仿真实验,结果表明该算法对常规的信号处理和几何攻击在鲁棒性上比原始7个Hu不变矩都有一定的提高。     

基于颜色不变量的多相机目标匹配方法

针对监控系统中存在复杂光照变化的问题,提出一种基于颜色不变量的多相机目标匹配方法。将人体目标分为头部、躯干和腿部,在导数空间和色度空间中,利用高斯光谱模型提取位于边缘和区域的颜色不变量,通过矩函数得到与平移、旋转和尺度变换无关的矩不变量,用描述子进行目标匹配。实验结果表明,该方法能适应场景中复杂的光照环境变化,以及低分辨率特征不充分等情况,并能获得较高的目标匹配正确率。     

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.     

Color Subspaces as Photometric Invariants

Complex reflectance phenomena such as specular reflections confound many vision problems since they produce image ‘features’ that do not correspond directly to intrinsic surface properties such as shape and spectral reflectance. A common approach to mitigate these effects is to explore functions of an image that are invariant to these photometric events. In this paper we describe a class of such invariants that result from exploiting color information in images of dichromatic surfaces. These invariants are derived from illuminant-dependent ‘subspaces’ of RGB color space, and they enable the application of Lambertian-based vision techniques to a broad class of specular, non-Lambertian scenes. Using implementations of recent algorithms taken from the literature, we demonstrate the practical utility of these invariants for a wide variety of applications, including stereo, shape from shading, photometric stereo, material-based segmentation, and motion estimation.     

光照鲁棒的抗模糊新组合不变矩图像匹配方法

基于特征的传统图像匹配方法对环境光照变化和模糊噪声适应性较差,针对该问题文中提出了一种新组合不变矩。在Hu不变矩的基础上,重新组合构造出三个新组合不变矩并将其应用到图像匹配中。实验结果表明,这种新组合不变矩具有很好的光照鲁棒性和模糊不变性,能够有效地解决受光照变化和模糊噪声共同影响造成的匹配率下降问题;在保证高精度的前提下,匹配效率大大提高。该不变矩作为图像特征的描述形式进行图像匹配是有效可行的,具有良好的参考价值。