| Image feature extraction,as one of the most important research topics in the field of computer vision,pattern analysis and image engineering,has become a research focus under the background of industrial 4.0.As a global descriptor(feature-extraction method),image moments can effectively represent image shape features,and the invariance of image moments(invariant moments)is very important for image analysis,classification and recognition,due to it satisfies the geometric transformation invariance of rotation,scale stretching,and translation,and also illumination invariance.In recent years,because the kernel functions of orthogonal moments satisfy the orthogonality,the moments are independent of each other,there is no information redundancy,and they have a certain anti noise ability,therefore,they become the main focus of image moments.Especially,Radial orthogonal moments based on polar coordinates are the preferred descriptors for geometric invariance feature extraction because of their rotation invariance inherently.However,the existing orthogonal moments,especially radial orthogonal moments,still have the following shortcomings:(1)Most of orthogonal moments are composed of higher-order polynomials with high computational complexity,due to the existence of factorial operations.(2)The polynomials of radial orthogonal moments are usually obtained by transformation of orthogonal polynomials in Cartesian coordinate system.In order to satisfy the orthogonality in polar coordinates,this deformation results in numerical instability of image moments constructed at the image origin.(3)The existing orthogonal moments,whether lower-or higher-order moments,are constructed by the same orthogonal polynomial,which lacks flexibility.Therefore,the lower-order moments are insufficient to represent the image features,and the higher-order moments are instable and sensitive to noise.(4)The traditional orthogonal moments can only describe the global features of an image,but have not capability of constructing local features.(5)Most of the fractional-order orthogonal moments proposed recently are aimed at gray-scale images,and little investigation of color images.(6)Compared with the existing orthogonal moment methods,the performance of the proposed fractional-order orthogonal moment methods is not improved obviously.In order to solve the problems aforementioned,this paper will focus on the theory and application research of semi-orthogonal moment and fractional-order color image moment algorithms.The main research contents and innovations are as follows:(1)A class of semi-orthogonal image moments based on exponential function is proposed,named semi-orthogonal exponent-Fourier moments(SO-EFMs),which is mainly used in image reconstruction and geometric invariance recognition.Compared with classical exponent-Fourier moments(EFMs),the kernel function of SO-EFMs is composed of piecewise semi-orthogonal exponential function,which eliminates numerical instability and has better image description capability in lower-or higher-order moments.In addition,compared with the traditional Zernike moments(ZMs)and orthogonal Fourier-Mellion moments(OFMMs),the polynomial of SOEFMs does not have the factorial operation,which effectively reduces the time complexity.Finally,in the light of the characteristics of SOEFMs,we can realize the fast and accurate algorithm of proposed moments by FFT algorithm,and we design a rotation and scaling invariant recognition method based on logpolar coordinates,and also a translation invariance method based on image projection is proposed,which can be applied into geometric invariant recognition.(2)A general semi-orthogonal image moment model is proposed.Inspired by the main idea of SOEFMs,the corresponding general semi-orthogonal image moment model can be established in Cartesian coordinate system and polar coordinate space,respectively.The time-frequency characteristics,global feature extraction,local feature extraction,anti-noise ability and rotation invariance of general semi-orthogonal image moment model are studied and analyzed by semi-orthogonal image moments and semi-orthogonal radial image moments using triangular functions,respectively.(3)To reduce storage space and improve the practicability of image moments,a class of semi-orthogonal image moments based on Walsh function system is proposed.The kernel function of the proposed moments is composed of binary orthogonal base,which contains only + 1 and – 1,and its operation is convenient to hardware processing and the time consuming of image feature extraction can be accelerated.Walsh function system is composed of a complete set of discontinuous binary function system.Therefore,compared with the traditional moments based on continuous polynomials,it can effectively overcome the Gibbs image noise.Theoretical and experimental results show that the proposed method has obvious advantages in image reconstruction and anti-noise ability.(4)A color image analysis and geometric invariance recognition algorithm based on fractional-order generalized Laguerre moments is proposed using combining fractionalorder theory with quaternion method,furthermore,a general fractional-order color image moment is constructed in this paper.The constructed color image moments break through the drawbacks of graying the color image or processing its three primary color channelsseparately in traditional color image feature extraction.Compared with traditional methods,the constructed general fractional-order color image moments can improve the accuracy of image feature extraction to a certain extent.In addition,on the basis of fractional-order theory,we take on the challenge of defining a fractional-order image moments,which can capture local image features.And it can realize the feature analysis and extraction of the region of interest(ROI) of an image.Finally,the linear combination of geometric moment invariants can be used to construct the geometric invariance of the quaternion fractional order Laguerre moments,which can be applied to the field of color image geometric invariant object recognition. |
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