We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic ...We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.展开更多
X-ray image has been widely used in many fields such as medical diagnosis,industrial inspection,and so on.Unfortunately,due to the physical characteristics of X-ray and imaging system,distortion of the projected image...X-ray image has been widely used in many fields such as medical diagnosis,industrial inspection,and so on.Unfortunately,due to the physical characteristics of X-ray and imaging system,distortion of the projected image will happen,which restrict the application of X-ray image,especially in high accuracy fields.Distortion correction can be performed using algorithms that can be classified as global or local according to the method used,both having specific advantages and disadvantages.In this paper,a new global method based on support vector regression（SVR）machine for distortion correction is proposed.In order to test the presented method,a calibration phantom is specially designed for this purpose.A comparison of the proposed method with the traditional global distortion correction techniques is performed.The experimental results show that the proposed correction method performs better than the traditional global one.展开更多
文摘We derive for crystal optics in coordinate-invariant way the cone approximation of refraction vectors in the neighborhood of optic axes and determine its invariants and eigenvectors. It proved to describe an elliptic cone. The second invariant of the operator of the wave equation with respect to similarity transformations determines the special cases of degeneration including the optic axes where the polarization of the waves due to self-intersection of the dispersion surface is not uniquely determined. This second invariant is included in all investigations and it is taken into account in the illustrations. It is biquadratic in the refraction vectors and the corresponding forth-order surface in three-dimensional space splits in two separate shells and a non-rational product decomposition describing this is found. We give also a more general classification of all possible solutions of an equation with an arbitrary three-dimensional operator.
基金National Natural Science Foundation of China(No.61305118)
文摘X-ray image has been widely used in many fields such as medical diagnosis,industrial inspection,and so on.Unfortunately,due to the physical characteristics of X-ray and imaging system,distortion of the projected image will happen,which restrict the application of X-ray image,especially in high accuracy fields.Distortion correction can be performed using algorithms that can be classified as global or local according to the method used,both having specific advantages and disadvantages.In this paper,a new global method based on support vector regression（SVR）machine for distortion correction is proposed.In order to test the presented method,a calibration phantom is specially designed for this purpose.A comparison of the proposed method with the traditional global distortion correction techniques is performed.The experimental results show that the proposed correction method performs better than the traditional global one.
