Feature Extraction Based on Wavelet Moments and Moment Invariants in Machine Vision Systems (original) (raw)
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This paper addresses bivariate orthogonal polynomials, which are a tensor product of two different orthogonal polynomials in one variable. These bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments. Some elementary properties of the proposed continuous Chebyshev-Gegenbauer moments (CGM), Gegenbauer-Legendre moments (GLM), and Chebyshev-Legendre moments (CLM), as well as the discrete Tchebichef-Krawtchouk moments (TKM), Tchebichef-Hahn moments (THM), Krawtchouk-Hahn moments (KHM) are presented. We also detail the application of the corresponding moments describing the noise-free and noisy images. Specifically, the local information of an image can be flexibly emphasized by adjusting parameters in bivariate orthogonal polynomials. The global extraction capability is also demonstrated by reconstructing an image using these bivariate polynomials as the kernels for a reversible image transform. Comparisons with the known moments are performed, and the results show that the proposed moments are useful in the field of image analysis. Furthermore, the study investigates invariant pattern recognition using the proposed three moment invariants that are independent of rotation, scale and translation, and an example is given of using the proposed moment invariants as pattern features for a texture classification application.
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2001
Image feature representation techniques using orthogonal moment functions have been used in many applications such as invariant pattern recognition, object identification and image reconstruction. Legendre and Zernike moments are very popular in this class, owing to their feature representation capability with a minimal information redundancy measure. This paper presents a comparative analysis between these moments and a new set of discrete orthogonal moments based on Tchebichef polynomials. The implementation aspects of orthogonal moments are discussed, and experimental results using both binary and gray-level images are included to show the advantages of discrete orthogonal moments over continuous moments.
Orthogonal Image Moment Invariants
IGI Global eBooks, 2013
This chapter focuses on the usage of image orthogonal moments as discrimination features in pattern recognition applications and discusses their main properties. Initially, the ability of the moments to carry information of an image with minimum redundancy is studied, while their capability to enclose distinctive information that uniquely describes the image's content is also examined. Along these directions, the computational formulas of the most representative moment families will be defined analytically and the form of the corresponding moment invariants in each case will be derived. Appropriate experiments have taken place in order to investigate the description capabilities of each moment family, by applying them in several benchmark problems.
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IEEE Transactions on Image Processing, 2001
This paper introduces a new set of orthogonal moment functions based on the discrete Tchebichef polynomials. The Tchebichef moments can be effectively used as pattern features in the analysis of two-dimensional images. The implementation of moments proposed in this paper does not involve any numerical approximation, since the basis set is orthogonal in the discrete domain of the image coordinate space. This property makes Tchebichef moments superior to the conventional orthogonal moments such as Legendre moments and Zernike moments, in terms of preserving the analytical properties needed to ensure information redundancy in a moment set. The paper also details the various computational aspects of Tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction.
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1996
To select a set of appropriate n umerical attributes of features from the i n terested objects for the purpose of classi cation has been among t he f u ndamental problems in the d e s i g n o f a n i m agery pattern recognition system. One o f t he s o lutions, the utilization of moments for object characterization has received considerable attentions in recent y ears. In this research, the n ew techniques derived to increase the accuracy and t he e ciency in moment computing are addressed. Based on these developments, the signi cant improvement o n i m age reconstructions via Legendre moments a n d Zernike moments h as been achieved. The e ect of image noise on image reconstruction, the a utomatic selection of the o ptimal order of moments f o r image reconstruction from noisy image, and t he usage of moments a s i m age features for character recognition are analyzed as well. v Many p e o ple have p r o vided advice, support, and encouragement t o t he a uthor, during theresearch w h i c h l e d t o t his thesis. Iwould like t o express my h eartfelt a p preciation to: My supervisor, Prof. Dr. Miroslaw Pawlak, for his generous support and i n tellectual guidance throughout m y y ears as a graduate s t udent his insightful advice, clear vision, many suggestions, and e n dless e orts t o b e a vailable for many e d ucational discussions, were invaluable Prof. Dr. David Erbach, whose friendship and encouragement w ere invaluable and k ept me t hinking t hat t here really was a light a t t he e n d o f t he t unnel, and w h o provided many v aluable comments on drafts o f t his thesis my committee members, Prof. Dr. Richard Gordon and P r o f. Dr. Waldemar Lehn, for valuable insights a n d suggestions which h ave signi cantly improved this thesis in both structure and contents my External Examiner, Prof. Dr. Adam Krzyzak, for his critical comments a n d constructive suggestions on this thesis my wife, Dr. Ming Y ang, who s h ared with t he pains and h appiness during t he course of this work her endless support, sacri ce, and u nderstanding k ept me going through it all and n ally, m y parents, Li Bofan and Liao Cuichuan, who rst taught m e t he importance of education. vi Contents Abstract v Acknowledgements vi List of Figures xiv List of Tables xiv List of Symbols xv Bibliography 104 A 112 ix List of Figures 2.1 Moments projections onto x and y axes.
Image analysis by krawtchouk moments
IEEE Transactions on Image Processing, 2003
In this paper, a new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal information redundancy. No numerical approximation is involved in deriving the moments, since the weighted Krawtchouk polynomials are discrete. These properties make the Krawtchouk moments well suited as pattern features in the analysis of two-dimensional images. It is shown that the Krawtchouk moments can be employed to extract local features of an image, unlike other orthogonal moments, which generally capture the global features. The computational aspects of the moments using the recursive and symmetry properties are discussed. The theoretical framework is validated by an experiment on image reconstruction using Krawtchouk moments and the results are compared to that of Zernike, Pseudo-Zernike, Legendre, and Tchebichef moments. Krawtchouk moment invariants is constructed using a linear combination of geometric moment invariants and an object recognition experiment shows Krawtchouk moment invariants perform significantly better than Hu's moment invariants in both noise-free and noisy conditions.
Computation Strategies of Orthogonal Image Moments: A Comparative Study
This paper discusses possible computation schemes that have been introduced in the past and cope with the efficient computation of the orthogonal image moments. An exhaustive comparative study of these alternatives is performed in order to investigate the conditions under which each scheme ensures high computation rates, for several test images. The present study aims to discover the properties and the behaviour of the different methodologies and it serves as a reference point in the field of moment's computation. Some useful conclusions are drawn regarding the applicability and the usefulness of the computation strategies in comparison and efficient hybrid methods are proposed to better utilize their advantages.
Transactions on Machine Learning and Artificial Intelligence
This paper present an improved reconstruction algorithm of the multigray level images based on overlapping block method using exact continuous moments computation: Legendre , Zernike, Pseudo Zernike and Gegenbauer moments. We solve the artifact issue caused by unitary block reconstruction which affects the visual image quality. This method aim to ensure high accuracy and low computation time, using only small finite number of moments. Our approaches aims to introduce these moments in the field of data compression and local feature extraction for pattern recognition. Experimental results show the superiority of our proposed approaches over the existing methods.
Novel moment invariants for improved classification performance in computer vision applications
Pattern Recognition, 2010
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 ISR (Image Slice Representation) 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 RST (Rotation, Scaling and Translation) invariant recognition performance, by resulting to remarkable outcomes.