The reconstruction of binary patterns from their projections
Communications of the ACM
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Shape from Equal Thickness Contours
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Recursive Methods for Matrix Inversion in Pattern Recognition Environments
IEEE Transactions on Computers
Some Properties of Image-Processing Operations on Projection Sets Obtained from Digital Pictures
IEEE Transactions on Computers
Research of the image reconstruction from incomplete projection data based on the homotopy mapping
CAR'10 Proceedings of the 2nd international Asia conference on Informatics in control, automation and robotics - Volume 3
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In this paper we will present two methods for the reronstruction of a two-dimensional picture from its one-dimensional projections at various angles. The first method is recursive, and the second is nonrecursive. Both of these methods have potential applications in picture transmission, and offer valuable insight into the more general problem of reconstruction of three-dimensional objects from their two-dimensional projections. We will illustrate the numerical details of each method by considering the reconstruction of a picture discretized on a 32 X 32 grid, and compare their relative merits. These two methods will also be compared with other methods suggested in the literature.