This paper deals with a theoretical possibility of a new visualizing measurement method based on a fast 2D model reconstruction utilizing a few projection data. A theory of least squares syped 2D model reconstruction by means of cutting singular value decomposition is discussed, utilizing projection data of a few directions for a smooth 2D spampled density distribution model which satisfies the condition of the sampling theorem. First it is shown that we can set up a linear equation system which corresponds to the parallel penetrating X beams. Next in advance by means of singular value decomposition and cutting small singular value down, we get a constant matrix for the linear equation system. Last we can fast calculate a good 2D image with the least squares error in the reconstruction by only one multiplication of matrix. The results of computer simulation with the fast 2D reconstruction algorithm are presented. Key words : Fast 2D Model Reconstruction, Sampling Theorem, Smooth 2D Sampled Density Distribution Model, Cutting Singular Value Decomposition
This paper is concerned with a theoretical possibility of a new visualizing measurement method based on an optimum 3D reconstruction from a few selected projections. A theory of optimum 3D reconstruction by a linear programming is discussed, utilizing a few projections for sampled 3D smooth-density-distribution model which satisfies the condition of the 3D sampling theorem. First by use of the sampling theorem, it is shown that we can set up simultaneous simple equations which corresponds to the case of the parallel beams. Then we solve the simultaneous simple equations by means of linear programming algorithm, and we can get an optimum 3D density distribution images with minimum error in the reconstruction. The results of computer simulation with the algorithm are presented.
A simplified visualization system for measuring airflow patterns in clean rooms was developed. A tracer of distilled-water droplets with several micron diameter was radiated by a red-colored fluorescent light. The scattered light by the tracer was separated from all lights. And the scattered light was amplified and recorded by a video camera built-in real-time image processing. And this system enables us to visualize the airflow patterns in which there was an obscure contrast between the tracer and the background illumination. The two-dimensional visualized images were converted into digital image-data, and processed numerically with an image pattern tracking method. The accuracy of the calculated vectors was influenced by the image-contrast. The effect of image-contrast on the accuracy was investigated by processing several images of different contrast. And the air-velocity measured with the image processing was compared with that measured with a laser doppler velocimeter. From these analyzed results, it was concluded that the image of emphasized contrast enables to calculated exact vectors, air-velocity measured with image processing almost agreed with that measured with a laser doppler velocimeter, and the method was very useful for quantitative evaluation of various airflow patterns in clean rooms.