scholarly journals RESTORATION OF THE INNER STYRUCTURE OF AN OBJECT FROM INTEGRAL DATA ON CONES

2019 ◽  
Vol 2 (3) ◽  
pp. 116-121
Author(s):  
Akbar Begmatov
Keyword(s):  
Internal Structure ◽  
Inversion Formula ◽  
Three Dimensional ◽  
Stability Estimates ◽  
Dimensional Object ◽  
And Inversion ◽  
Integral Data

We consider the problem of determining the internal structure of the three-dimensional object from integral data obtained by tomografic scanning using a cone scheme over a family of right circular cones. Stability estimates are proven and inversion formula is obtained.

scholarly journals PROBES, POPULATIONS, SAMPLES, MEASUREMENTS AND RELATIONS IN STEREOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 1 ◽  
Author(s):  
Robert T Dehoff
Keyword(s):  
Internal Structure ◽  
Three Dimensional ◽  
Sample Design ◽  
Typical Problem ◽  
Three Dimensional Objects ◽  
Summary Paper ◽  
Unbiased Estimates ◽  
Dimensional Object ◽  
Almost All ◽  
Simple Count

This summary paper provides an overview of the content of stereology. The typical problem at hand centers around some three dimensional object that has an internal structure that determines its function, performance, or response. To understand and quantify the geometry of that structure it is necessary to probe it with geometric entities: points, lines, planes volumes, etc. Meaningful results are obtained only if the set of probes chosen for use in the assessment is drawn uniformly from the population of such probes for the structure as a whole. This requires an understanding of the population of each kind of probe. Interaction of the probes with the structure produce geometric events which are the focus of stereological measurements. In almost all applications the measurement that is made is a simple count of the number of these events. Rigorous application of these requirements for sample design produce unbiased estimates of geometric properties of features in the structure no matter how complex are the features or what their arrangement in space. It is this assumption-free characteristic of the methodology that makes it a powerful tool for characterizing the internal structure of three dimensional objects.

scholarly journals Approximation of discontinuous functions of three variables by discontinuous interpolation splines

2021 ◽  
pp. 99-104
Author(s):  
Iuliia Pershyna
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Computed Tomography ◽  
Internal Structure ◽  
Approximation Method ◽  
Three Dimensional ◽  
Discontinuous Functions ◽  
The One ◽  
Dimensional Object ◽  
Special Case

In this paper, discontinuous interpolation splines of three variables are constructed and a method for reconstructing of the discontinuous internal structure of a three-dimensional body by constructed splines is proposed. It is believed that a three-dimensional object, which is described by a function of three variables with discontinuities of the first kind on a given grid of nodes, is completely covered by a system of parallelepipeds. The experimental data are the one-sided value of the discontinuous function in a given grid of nodes. In the article, theorems on interpolation properties and the error of the constructed discontinuous structures are formulated and proved. Moreover, the constructed discontinuous interpolation splines include, as a special case, classical continuous splines. The developed approximation method can be applied in three-dimensional mathematical modeling of discontinuous processes, including in computed tomography.

scholarly journals Basic Stereology

2003 ◽  
Vol 11 (1) ◽  
pp. 12-17 ◽  
Author(s):  
John M. Basgen
Keyword(s):  
Mr Imaging ◽  
Internal Structure ◽  
Three Dimensional ◽  
Quantitative Information ◽  
Two Dimensional ◽  
Two Dimensional Image ◽  
Three Dimensional Objects ◽  
Different Types ◽  
Dimensional Object ◽  
Two Dimensional Images

Many us who use microscopes are interested in the internal structure or components of three-dimensional objects. Often we must section these objects to observe these internal components. For many years, microtomes have been used to make physical sections, but in recent years confocal microscopes, MR imaging, CT scanners, and even standard optical microscopes have been used to obtain “optical” sections. Two-dimensional images of these different types of sections can be used to extract three-dimensional quantitative information about the objects and their internal components, The sectioning process reduces the observed dimensions of the object and components. With apologies to Rene Magritte, the structure portrayed in Figure 1 is not a three-dimensional glomerulus but a two-dimensional profile of a glomerulus. In most cases, interest is on the structure of the three-dimensional object and not the structure in the two-dimensional image. Thus, care must be taken when obtaining and interpreting data from two-dimensional images.

Reconstruction of Objects from their Projections Using Orthogonal Functions

1973 ◽  
Vol 31 ◽  
pp. 268-269
Author(s):  
Elrnar Zeitler
Keyword(s):  
Unit Area ◽  
Three Dimensional ◽  
One Dimension ◽  
Spatial Density ◽  
Dimensional Representation ◽  
Orthogonal Functions ◽  
Object A ◽  
Plane Normal ◽  
Dimensional Object ◽  
Spatial Density Distribution

Considering any finite three-dimensional object, a “projection” is here defined as a two-dimensional representation of the object's mass per unit area on a plane normal to a given projection axis, here taken as they-axis. Since the object can be seen as being built from parallel, thin slices, the relation between object structure and its projection can be reduced by one dimension. It is assumed that an electron microscope equipped with a tilting stage records the projectionWhere the object has a spatial density distribution p(r,ϕ) within a limiting radius taken to be unity, and the stage is tilted by an angle 9 with respect to the x-axis of the recording plane.

X-ray microtomography

1988 ◽  
Vol 46 ◽  
pp. 998-999
Author(s):  
H.W. Deckman ◽  
B.F. Flannery ◽  
J.H. Dunsmuir ◽  
K.D' Amico
Keyword(s):  
Computed Tomography ◽  
Internal Structure ◽  
Imaging Technique ◽  
Three Dimensional ◽  
Tissue Structure ◽  
Individual Element ◽  
X Ray ◽  
Non Invasive ◽  
Panoramic Imaging ◽  
Three Dimensional Images

We have developed a new X-ray microscope which produces complete three dimensional images of samples. The microscope operates by performing X-ray tomography with unprecedented resolution. Tomography is a non-invasive imaging technique that creates maps of the internal structure of samples from measurement of the attenuation of penetrating radiation. As conventionally practiced in medical Computed Tomography (CT), radiologists produce maps of bone and tissue structure in several planar sections that reveal features with 1mm resolution and 1% contrast. Microtomography extends the capability of CT in several ways. First, the resolution which approaches one micron, is one thousand times higher than that of the medical CT. Second, our approach acquires and analyses the data in a panoramic imaging format that directly produces three-dimensional maps in a series of contiguous stacked planes. Typical maps available today consist of three hundred planar sections each containing 512x512 pixels. Finally, and perhaps of most import scientifically, microtomography using a synchrotron X-ray source, allows us to generate maps of individual element.

Three-Dimensional In Vivo Kinematics of the Subtalar Joint During Dorsi-Plantarflexion and Inversion-Eversion

2009 ◽  
Vol 30 (05) ◽  
pp. 432-438 ◽  
Author(s):  
Akira Goto ◽  
Hisao Moritomo ◽  
Tomonobu Itohara ◽  
Tetsu Watanabe ◽  
Kazuomi Sugamoto
Keyword(s):  
Subtalar Joint ◽  
Three Dimensional ◽  
In Vivo Kinematics ◽  
And Inversion
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