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Способ динамической реконструкции размеров и формы трехмерных объектов по размерам их проекционных изображений.
The main object of this paper consists in solving of the inverse problem of optical tomography through the development of a method of dynamical statistical spatial-temporal reconstruction of sizes and shape of moving three-dimensional objects with the usage of their projected images.
The newness of the given method consists in dynamical, few view, spatial-temporal reconstruction of sizes and shape not of a convex three-dimensional object itself, but its adequate approximation represented as a three-dimensional image of the ellipsoid of general form. Along with this, the geometrical sizes of a three-dimensional object are specified by numerical values of the axes of this three-dimensional image of ellipsoid and the average projected diameter of the image (D), and the shape factor (K) is specified by the ratio of the maximum and minimum overall dimensions (axes) of the image of the approximating ellipsoid.
The contours of three discrete, two-dimensional projected images of an object are specified as the optimal form of the primary geometrical information by a simulation modeling method. In this case, their spatial orientation is their mutual orthogonality. Their maximum and minimum overall dimensions are chosen as the optimal basic geometrical characteristics of projected images (the most informative characteristics according to the method of maximal entropy).
The mathematical model of object reconstruction is defined by the functional dependences of linear sizes of three mutually orthogonal axis of the approximating ellipsoid to the maximum and minimum dimensions of its three projected images.
In the result of statistical studies it is determined that the relative error of computing of the average projected diameter of an object is about 0.25% (at the reliability of PD = 0.7 and K = 1,3 relative units). The relative error of computing of form factor of an object is from 2.3% (PK = 0.7 and K = 1.3 relative units) to 0.6% (with PK = 0.96 and K = 1.05 relative units), and the total control time of object sizes and object shape does not exceed 10 Ms.
Thus, the proposed method of dynamic reconstruction has a new combination of characteristics of accuracy, reliability and performance. It has been successfully employed for a high performance, manufacturing, televisional size and form control for elements of the nuclear fuel and can be applied for remote control of various moving convex objects in real-time.