Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engine...Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.展开更多
A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample ...A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.展开更多
This paper is a study on texture analysis of Computer Tomography (CT) liver images using orthogonal moment features. Orthogonal moments are used as image feature representation in many applications like invariant patt...This paper is a study on texture analysis of Computer Tomography (CT) liver images using orthogonal moment features. Orthogonal moments are used as image feature representation in many applications like invariant pattern recognition of images. Orthogonal moments are proposed here for the diagnosis of any abnormalities on the CT images. The objective of the proposed work is to carry out the comparative study of the performance of orthogonal moments like Zernike, Racah and Legendre moments for the detection of abnormal tissue on CT liver images. The Region of Interest (ROI) based segmentation and watershed segmentation are applied to the input image and the features are extracted with the orthogonal moments and analyses are made with the combination of orthogonal moment with segmentation that provides better accuracy while detecting the tumor. This computational model is tested with many inputs and the performance of the orthogonal moments with segmentation for the texture analysis of CT scan images is computed and compared.展开更多
In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely...In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments(SFFMs and WFFMs),which are orthogonal in polar coordinates.The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one.Therefore,it provides the possibility of avoiding calculating high order polynomials,and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost.Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs,but compared with traditional orthogonal moments(e.g.,BFMs,OFMs and ZMs)in polar coordinates,the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.展开更多
A method to estimate the probabilistic density function （PDF） of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial（SCOP） combined with sample moments （the origin moments） was use...A method to estimate the probabilistic density function （PDF） of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial（SCOP） combined with sample moments （the origin moments） was used to approximate the PDF of parameters. X^2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme value Ⅰ , gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.展开更多
文摘为了有效地利用伪Zernike矩进行图像分析和模式识别,针对传统伪Zernike矩快速计算方法在计算伪Zernike矩时复杂度大的问题,提出一种改进的伪Zernike矩快速计算方法.该方法利用C lenshaw递推公式实现了伪Zernike矩多项式求和的快速计算.初步实验结果表明:在计算指定阶伪Zernike矩时,文中方法比传统伪Zernike矩快速计算方法需要更少的CPU时间;在人脸特征的提取及识别方面,文中方法的识别率比传统的主成分分析方法约高5%,而特征提取需要的平均时间为1.2 s.
文摘Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.
文摘A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.
文摘This paper is a study on texture analysis of Computer Tomography (CT) liver images using orthogonal moment features. Orthogonal moments are used as image feature representation in many applications like invariant pattern recognition of images. Orthogonal moments are proposed here for the diagnosis of any abnormalities on the CT images. The objective of the proposed work is to carry out the comparative study of the performance of orthogonal moments like Zernike, Racah and Legendre moments for the detection of abnormal tissue on CT liver images. The Region of Interest (ROI) based segmentation and watershed segmentation are applied to the input image and the features are extracted with the orthogonal moments and analyses are made with the combination of orthogonal moment with segmentation that provides better accuracy while detecting the tumor. This computational model is tested with many inputs and the performance of the orthogonal moments with segmentation for the texture analysis of CT scan images is computed and compared.
基金supported by the National Natural Science Foundation of China(61572092,61702403)the Fundamental Research Funds for the Central Universities(JB170308,JBF180301)+2 种基金the Project Funded by China Postdoctoral Science Foundation(2018M633473)the Basic Research Project of Weinan Science and Technology Bureau(ZDYF-JCYJ-17)the Project of Shaanxi Provincial Supports Discipline(Mathematics)
文摘In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments(SFFMs and WFFMs),which are orthogonal in polar coordinates.The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one.Therefore,it provides the possibility of avoiding calculating high order polynomials,and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost.Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs,but compared with traditional orthogonal moments(e.g.,BFMs,OFMs and ZMs)in polar coordinates,the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.
基金Projects(50490274 , 10472134 , 50404010) supported by the National Natural Science Foundation of China project(2002CB412703) supported by the Key Fundamental Research and Development Programof China
文摘A method to estimate the probabilistic density function （PDF） of shear strength parameters was proposed. The second Chebyshev orthogonal polynomial（SCOP） combined with sample moments （the origin moments） was used to approximate the PDF of parameters. X^2 test was adopted to verify the availability of the method. It is distribution-free because no classical theoretical distributions were assumed in advance and the inference result provides a universal form of probability density curves. Six most commonly-used theoretical distributions named normal, lognormal, extreme value Ⅰ , gama, beta and Weibull distributions were used to verify SCOP method. An example from the observed data of cohesion c of a kind of silt clay was presented for illustrative purpose. The results show that the acceptance levels in SCOP are all smaller than those in the classical finite comparative method and the SCOP function is more accurate and effective in the reliability analysis of geotechnical engineering.
