Accurate and speedy computation of image Legendre moments for computer vision applications

A novel algorithm that permits the fast and accurate computation of the Legendre image moments is introduced in this paper. The proposed algorithm is based on the block representation of an image and on a new image representation scheme, the Image Slice Representation (ISR) method. The ISR method decomposes a gray-scale image as an expansion of several two-level images of different intensities (slices) and thus enables the partial application of the well-known Image Block Representation (IBR) algorithm to each image component. Moreover, using the resulted set of image blocks, the Legendre moments’ computation can be accelerated through appropriate computation schemes. Extensive experiments prove that the proposed methodology exhibits high efficiency in calculating Legendre moments on gray-scale, but furthermore on binary images. The newly introduced algorithm is suitable for the computation of the Legendre moments for pattern recognition and computer vision applications, where the images consist of objects presented in a scene.     

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.     

Improved quality of reconstructed images using floating point arithmetic for moment calculation

Zernike moments which are superior to geometric moments because of their special properties of image reconstruction and immunity to noise, suffer from several discretization errors. These errors lead to poor quality of reconstructed image and wide variations in the numerical values of the moments. The predominant factor, as observed in this paper, is due to the discrete integer implementation of the steps involved in moment calculation. It is shown in this paper that by modifying the algorithms to include discrete float implementation, the quality of the reconstructed image improves significantly and the first-order moment becomes zero. Low-order Zernike moments have been found to be stable under linear transformations while the high-order moments have large variations. The large variations in high-order moments, however, do not greatly affect the quality of the reconstructed image, implying that they should be ignored when numerical values of moments are used as features. The 11 functions based on geometric moments have also been found to be stable under linear transformations and thus these can be used as features. Pixel level analysis of the images has been carried out to strengthen the results.     

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.     

SmartVisionApp: A framework for computer vision applications on mobile devices

In this paper a novel framework for the development of computer vision applications that exploit sensors available in mobile devices is presented. The framework is organized as a client–server application that combines mobile devices, network technologies and computer vision algorithms with the aim of performing object recognition starting from photos captured by a phone camera. The client module on the mobile device manages the image acquisition and the query formulation tasks, while the recognition module on the server executes the search on an existing database and sends back relevant information to the client. To show the effectiveness of the proposed solution, the implementation of two possible plug-ins for specific problems is described: landmark recognition and fashion shopping. Experiments on four different landmark datasets and one self-collected dataset of fashion accessories show that the system is efficient and robust in the presence of objects with different characteristics.     

A unified methodology for the efficient computation of discrete orthogonal image moments

A novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments. The computation scheme is mainly based on a new image representation method, the image slice representation (ISR) method, according to which an image can be expressed as the outcome of an appropriate combination of several non-overlapped intensity slices. This image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities, black or any other gray-level value. Therefore the image block representation can be effectively applied to describe the image in a more compact way. Once the image is partitioned into intensity blocks, the computation of the image moments can be accelerated, as the moments can be computed by using decoupled computation forms. The proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results, as has been concluded through a detailed experimental investigation.     

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.     

基于目标不变量的识别方法研究

一、引言不变量理论在80年代末引入计算机视觉领域,1991年召开了不变量在计算机视觉应用方面的国际研讨会。目前,对这一课题的研究引起了国内外学者的极大兴趣。视觉不变量理论的优点在于它对目标形状的描述不受目标物体的姿态、透视投影和摄像机内部参数的影响。同时它可以冗余地表示目标全局结构特征,当发生部分遮挡时,可以从剩余部分计算出表示全局的结构不变信息。     

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.     

The role of computer vision in prosthetic vision

The cost of vision loss worldwide has been estimated at nearly $3 trillion (http://www.amdalliance.org/cost-of-blindness.html). Non-preventable diseases cause a significant proportion of blindness in developed nations and will become more prevalent as people live longer. Prosthetic vision technologies including retinal implants will play an important therapeutic role. Retinal implants convert an input image stream to visual percepts via stimulation of the retina. This paper highlights some barriers to restoring functional human vision for current generation visual prosthetic devices that computer vision can help overcome. Such computer vision is interactive, aiming to restore function including visuo-motor tasks and recognition.     

A new class of Zernike moments for computer vision applications

A Modified Direct Method for the computation of the Zernike moments is presented in this paper. The presence of many factorial terms, in the direct method for computing the Zernike moments, makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of the present paper is that, by using Stirling’s Approximation formula for the factorial and by applying some suitable mathematical properties, a novel, factorial-free direct method can be developed. The resulted moments are not equal to those computed by the original direct method, but they are a sufficiently accurate approximation of them. Besides, their variability does not affect their ability to describe uniquely and distinguish the objects they represent. This is verified by pattern recognition simulation examples.     

A collaborative representation based projections method for feature extraction

In graph embedding based methods, we usually need to manually choose the nearest neighbors and then compute the edge weights using the nearest neighbors via L2 norm (e.g. LLE). It is difficult and unstable to manually choose the nearest neighbors in high dimensional space. So how to automatically construct a graph is very important. In this paper, first, we give a L2-graph like L1-graph. L2-graph calculates the edge weights using the total samples, avoiding manually choosing the nearest neighbors; second, a L2-graph based feature extraction method is presented, called collaborative representation based projections (CRP). Like SPP, CRP aims to preserve the collaborative representation based reconstruction relationship of data. CRP utilizes a L2 norm graph to characterize the local compactness information. CRP maximizes the ratio between the total separability information and the local compactness information to seek the optimal projection matrix. CRP is much faster than SPP since CRP calculates the objective function with L2 norm while SPP calculate the objective function with L1 norm. Experimental results on FERET, AR, Yale face databases and the PolyU finger-knuckle-print database demonstrate that CRP works well in feature extraction and leads to a good recognition performance.     

遥感图像小型目标的识别方法

提出使用特征提取的方法来识别遥感图像中的小目标。介绍了不变矩法和高阶累积量法两种用于目标识别方法的原理和如何构造它们的不变特征集的过程。在论述了这两种不变特征集的构造方法的基础上，对遥感图像采用多元识别方法。实验结果证明：经过图像预处理后，采用不变矩法和高阶累积量法进行多元搜索有很高的准确度。     

Combined pattern search optimization of feature extraction and classification parameters in facial recognition

Constantly, the assumption is made that there is an independent contribution of the individual feature extraction and classifier parameters to the recognition performance. In our approach, the problems of feature extraction and classifier design are viewed together as a single matter of estimating the optimal parameters from limited data. We propose, for the problem of facial recognition, a combination between an Interest Operator based feature extraction technique and a k-NN statistical classifier having the parameters determined using a pattern search based optimization technique. This approach enables us to achieve both higher classification accuracy and faster processing time.     

Toward designing intelligent PDEs for computer vision: An optimal control approach

Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing a PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we consider designing PDEs for various problems arising in computer vision and image processing in a lazy manner: learning PDEs from training data via an optimal control approach. We first propose a general intelligent PDE system which holds the basic translational and rotational invariance rule for most vision problems. By introducing a PDE-constrained optimal control framework, it is possible to use the training data resulting from multiple ways (ground truth, results from other methods, and manual results from humans) to learn PDEs for different computer vision tasks. The proposed optimal control based training framework aims at learning a PDE-based regressor to approximate the unknown (and usually nonlinear) mapping of different vision tasks. The experimental results show that the learnt PDEs can solve different vision problems reasonably well. In particular, we can obtain PDEs not only for problems that traditional PDEs work well but also for problems that PDE-based methods have never been tried before, due to the difficulty in describing those problems in a mathematical way.     

Radial shifted Legendre moments for image analysis and invariant image recognition

The rotation, scaling and translation invariant property of image moments has a high significance in image recognition. Legendre moments as a classical orthogonal moment have been widely used in image analysis and recognition. Since Legendre moments are defined in Cartesian coordinate, the rotation invariance is difficult to achieve. In this paper, we first derive two types of transformed Legendre polynomial: substituted and weighted radial shifted Legendre polynomials. Based on these two types of polynomials, two radial orthogonal moments, named substituted radial shifted Legendre moments and weighted radial shifted Legendre moments (SRSLMs and WRSLMs) are proposed. The proposed moments are orthogonal in polar coordinate domain and can be thought as generalized and orthogonalized complex moments. They have better image reconstruction performance, lower information redundancy and higher noise robustness than the existing radial orthogonal moments. At last, a mathematical framework for obtaining the rotation, scaling and translation invariants of these two types of radial shifted Legendre moments is provided. Theoretical and experimental results show the superiority of the proposed methods in terms of image reconstruction capability and invariant recognition accuracy under both noisy and noise-free conditions.     

Feature extraction for texture classification

We address the problem of texture classification. Random walks are simulated for plane domains $\text{A}$ bounded by absorbing boundaries Γ, and the absorption distributions are estimated. Measurements derived from the above distributions are the features used for texture classification. Experiments using such a model have been performed and the results showed a rate of accuracy of 89.7% for a data set consisting of one hundred and twenty-eight textured images equally distributed among thirty-two classes of textures.