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A method of general moments for orienting 2D projections of unknown 3D objects

✍ Scribed by David B. Salzman

Publisher
Elsevier Science
Year
1989
Weight
74 KB
Volume
48
Category
Article
ISSN
0734-189X

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✦ Synopsis

We develop a technique using general moments to find the orientations of 2D planar orthographic projections of 3D objects, even if the 3D object has a completely unknown structure. The technique should open new classes of biological materials for ultrastructural analysis, through molecular scale transmission electron microscopy reconstruction applications where the original 3D object's structure is unknown. In machine vision applications where the full 3D structure is known, the technique provides a fast and computationally efficient way to orient projections. The techm'que can also be used to orient 1D line projections of 2D unknown objects.

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The theory of the multidimensional filter diagonalization method (FDM) described in the previous paper (V. A. Mandelshtam, 2000, J. Magn. Reson. 144, 343-356 (2000)) is applied to NMR time signals with up to four independent time variables. Direct projections of the multidimensional time signals pro