Image Reconstruction from Multiscale Critical Points

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

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Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051669 ◽

1974 ◽

Vol 32 ◽

pp. 330-331

Author(s):

R. A. Crowther

Keyword(s):

Image Reconstruction ◽

Finite Number ◽

Density Distribution ◽

Electron Micrographs ◽

Mathematical Problem ◽

Three Dimensional ◽

Ideal Case ◽

Dimensional Image ◽

General Object ◽

The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

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Three dimensional deblurring of transmitted-light brightfield micrographs

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100148654 ◽

1993 ◽

Vol 51 ◽

pp. 564-565

Author(s):

Santosh Bhattacharyya

Keyword(s):

Image Reconstruction ◽

Three Dimensional ◽

Transmitted Light ◽

Reconstruction Algorithms ◽

3D Image Reconstruction ◽

Structural Details ◽

Spread Function ◽

Early Testing ◽

Linearized Model ◽

Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

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