Some Properties of Image-Processing Operations on Projection Sets Obtained from Digital Pictures

A projection of a digital picture (image) may be defined as an ordered set of values, each of which is the sum of the gray levels along a given path drawn through the picture. A projection set is at ordered set of projections of the picture. Given a projection set, reconstruction is achieved by operating on the projection set to produce either the original picture or an approximation to it.

[1]  Shi-Kuo Chang,et al.  The Reconstruction of Three-Dimensional Objects from Two Orthogonal Projections and its Application to Cardiac Cineangiography , 1973, IEEE Transactions on Computers.

[2]  Shi-Kuo Chang,et al.  The reconstruction of binary patterns from their projections , 1971, Commun. ACM.

[3]  D. DeRosier,et al.  The reconstruction of a three-dimensional structure from projections and its application to electron microscopy , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[4]  Yuan R. Wang,et al.  Characterization of Binary Patterns and Their Projections , 1975, IEEE Transactions on Computers.

[5]  G T Herman,et al.  ART: mathematics and applications. A report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques. , 1973, Journal of theoretical biology.

[6]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[7]  Yi-tzuu T. Chien.  Interactive pattern recognition , 1978 .

[8]  Y. T. Chien.  Interactive Pattern Recognition: Techniques and Systems , 1976, Computer.

[9]  G. N. Ramachandran,et al.  Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Richard Gordon,et al.  Reconstruction of pictures from their projections , 1971, CACM.

[11]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[12]  G T Herman,et al.  Resolution in reconstructing objects from electron micrographs. , 1971, Journal of theoretical biology.

[13]  D. J. De Rosier,et al.  Reconstruction of Three Dimensional Structures from Electron Micrographs , 1968, Nature.

[14]  Yang Wang,et al.  Three-dimensional object reconstruction from orthogonal projections , 1975, Pattern Recognit..

[15]  Gabor T. Herman,et al.  Three methods for reconstructing objects from x rays: A comparative study , 1973, Comput. Graph. Image Process..

[16]  A. Lent,et al.  ART: Mathematics and applications a report on the mathematical foundations and on the applicability to real data of the algebraic reconstruction techniques , 1973 .

[17]  H. Ryser.  Combinatorial Properties of Matrices of Zeros and Ones , 1957, Canadian Journal of Mathematics.

[18]  Y. T. Chien,et al.  Switching components and the ambiguity problem in the reconstruction of pictures from their projections , 1978, Pattern Recognit..

[19]  P. Gilbert.  Iterative methods for the three-dimensional reconstruction of an object from projections. , 1972, Journal of theoretical biology.

[20]  A. Klug,et al.  ART and science or conditions for three-dimensional reconstruction from electron microscope images. , 1971, Journal of theoretical biology.

[21]  Rangasami L. Kashyap,et al.  Picture Reconstruction from Projections , 1975, IEEE Transactions on Computers.

[22]  J. E. Rowe,et al.  ART is science being a defense of algebraic reconstruction techniques for three-dimensional electron microscopy. , 1971, Journal of theoretical biology.