Calculating the perimeter of a plane figure from its discretized image

Cybernetics ◽  
1986 ◽  
Vol 22 (2) ◽  
pp. 149-155
Author(s):  
Yu. I. Petunin ◽  
G. A. Shul'deshov
Keyword(s):  
Plane Figure ◽  
Discretized Image

Algorithm to estimate the perimeter of a plane figure from its discretized image

1996 ◽  
Vol 32 (4) ◽  
pp. 546-553
Author(s):  
V. V. Rublev
Keyword(s):  
Plane Figure ◽  
Discretized Image

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Effect of the crystal plane figure on the catalytic performance of MnO2for the total oxidation of propane

CrystEngComm ◽  
2015 ◽  
Vol 17 (15) ◽  
pp. 3005-3014 ◽  
Author(s):  
Yujie Xie ◽  
Yanyan Yu ◽  
Xueqing Gong ◽  
Yun Guo ◽  
Yanglong Guo ◽  
...  
Keyword(s):  
Catalytic Performance ◽  
Crystal Plane ◽  
Plane Figure ◽  
Total Oxidation

scholarly journals Analogue Processing Methods for Synthesis Observations

1979 ◽  
Vol 49 ◽  
pp. 123-141
Author(s):  
T.W. Cole
Keyword(s):  
Light Intensity ◽  
Spatial Correlation ◽  
Aperture Synthesis ◽  
Conventional Imaging ◽  
Plane Figure ◽  
Output Plane ◽  
Processing Methods

In aperture synthesis the formation of an image involves the two steps of spatial correlation across an aperture and transformation to the image. This is closely related to conventional imaging with a lens (Cole, 1977a), which Abbé interpreted as two successive transformations at the surfaces of the lens. With the simple lens the image is the light intensity in the output plane (Figure 1(a)). In aperture synthesis (Figure 1(b)) the image is the transform of the correlation but no detection takes place. The image corresponds to the ‘light’ amplitude rather than intensity.

A multisheet plane figure and its medial axis

2011 ◽  
Vol 55 (12) ◽  
pp. 34-43 ◽  
Author(s):  
I. S. Mekhedov
Keyword(s):  
Medial Axis ◽  
Plane Figure

Drawing for Teachers of Solid Geometry

1925 ◽  
Vol 18 (1) ◽  
pp. 37-45
Author(s):  
John W. Bradshaw
Keyword(s):  
Descriptive Geometry ◽  
Analytic Geometry ◽  
Plane Figure ◽  
Space Object ◽  
Simple Matter ◽  
Solid Geometry ◽  
Frame Work ◽  
Mutual Relations ◽  
Straight Lines ◽  
Coordinate Geometry

To meet the difficulty that one unaided picture does not suffice to reconstruct the space object, the engineer commonly avails himself of two or more pictures, plan, elevation, profile, which he places side by side. To discuss the mutual relations of these and to solve problems in space by means of constructions on these plane figures is the object of technical descriptive geometry as usually treated in the text books. This is really only a branch of descriptive geometry, which, broadly defined, includes every attempt to represent a space figure by a plane figure in which straight lines are represented by straight lines. We are here interested not in the method of the engineer but in another branch of descriptive geometry called axonometry. We can make out with one picture if we'll put into it something familiar, something that wo shall agree represents a cube; or, what amounts to the same thing, if we'll introduce axes into the figure. We make use, then, of the frame-work of solid analytic geometry or coordinate geometry of space. Without presupposing any knowledge of this branch of mathematics, it is a simple matter to explain the fundamental notions on which it rests, as far as they are needed for our purpose.

scholarly journals Kinematical Theorems

1885 ◽  
Vol 4 ◽  
pp. 38-45
Author(s):  
William Harvey
Keyword(s):  
Plane Figure ◽  
Straight Line

§1. Figure 30. Let AB be any straight line in the plane figure, A′B the position of the same line after a displacement, the point A moving to A′ and B to B′. Since the position of a plane figure in its plane is determined, when the position of a straight line rigidly attached to it is determined, the motion of the plane figure is determined if we determine the motion of the straight line AB.

scholarly journals Efficient N-Dimensional surface estimation using Crofton formula and run-length encoding

2012 ◽  
Author(s):  
Gaetan Lehmann ◽  
David Legland
Keyword(s):  
Run Length ◽  
Surface Estimation ◽  
Crofton Formula ◽  
Two Parameters ◽  
Discretized Image ◽  
Dimensional Surface

Unlike the measure of the area in 2D or of the volume in 3D, the perimeter and the surface are not easily measurable in a discretized image. In this article we describe a method based on the Crofton formula to measure those two parameters in a discritized image. The accuracy of the method is discussed and tested on several known objects. An algorithm based on the run-length encoding of binary objects is presented and compared to other approaches. An implementation is provided and integrated in the LabelObject/LabelMap framework contributed earlier by the authors.

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