Fuzzy Three-Dimensional Voronoi Diagram and its Application to Geographical Data Analysis

2012 ◽  
Vol 16 (2) ◽  
pp. 191-198
Author(s):  
Mian Dai ◽  
◽  
Fangyan Dong ◽  
Kaoru Hirota
Keyword(s):  
Voronoi Diagram ◽  
Three Dimensional ◽  
Spatial Relation ◽  
Spatial Relations ◽  
Mountainous Area ◽  
Two Dimensional ◽  
Spatial Direction ◽  
Geographical Data ◽  
Direction Relations ◽  
Complex Boundaries

A concept of fuzzy three-dimensional Voronoi Diagram is presented for spatial relations analysis of real world three-dimensional geographical data, where it is an extension of well known two-dimensional Voronoi Diagram to three-dimensional representation with uncertain spatial relation information in terms of fuzzy set. It makes possible to analyze quantitatively complex boundaries of geographically intricate areas, to give human friendly fuzzy explanation of determining three-dimensional directions, and to express uncertain spatial relations by precise unified fuzzy description. It is applied to decide spatial direction relations of artificial geographicalmountain data, which includes 8 spatial directions with at most 60 relative direction relations, and it leads to detect threedimensional directions whereas the expression of traditional 4 directions and 12 relative directions indicate two-dimensional directions only. The proposed concept aims to discriminate neighbors’ class relations and spatial-temporal changes of specially appointed objects, and also aims to be a tool to achieve the intellective extraction and analysis of geographical data of a mountainous area located in northeast China.

scholarly journals Dimensionality Expressed by Caseendings and Spatial Prepositions

2002 ◽  
pp. 7-15
Author(s):  
Géza Andrássy ◽  
László Imre Komlósi
Keyword(s):  
Native Speakers ◽  
Three Dimensional ◽  
Spatial Relation ◽  
Spatial Relations ◽  
Two Dimensional ◽  
Closed Set ◽  
Spatial Prepositions ◽  
Clear Cut ◽  
Nominal Phrase ◽  
Hungarian Case

The purpose of this essay is to investigate some of the uses of English prepositions and Hungarian case endings employed to express spatial relations. The observation of invariant mistakes Hungarian native speakers learning English make initiated the investigation. The questions raised are: (a) where do the two systems match and where do mismatches lie, (b) how do language users perceive the world, and (c) do speakers observe spatial relations as two-dimensional or three-dimensional cognitive models? Do different languages see the same thing as either three-dimensional, or two-dimensional?Abondolo (1988) gives an adequate morphological analysis of ten Hungarian case-endings (inessive, illative, elative, superessive, delative, sublative adessive, ablative, allative and terminative) used in spatial reference, which give a closed set in references made to factors, such as (1) location which can be broken down as interior vs. exterior location with the latter being further analysable as superficial and proximal, and (2) orientation which can be analysed as zero orientation (position), source and goal. In addition to those in this list, two other case endings (genetive/dative and locative) are also used for expressing spatial relations but the last is only a variant of the inessive and superessive case-endings and is only used with place-names. The set is closed in the sense that the same item is meant to refer to the same sort of spatial relation in every case. Language textbooks, c.f. Benkő (1972) seem to suggest a neat match between the above Hungarian case endings and their English prepositional counterparts, e.g. London-ban (inessive) = in London.The picture, however, is far from being so clear-cut. The data, which were taken from various dictionaries and textbooks, show that the choices of both the prepositions and the case endings listed above depend on how the speaker considers factors (1) and (2) and that proximity is very important. Instead of a one-to-one match between the prepositions and the case endings, we rather find that the above case endings will match a dual, and in some cases a tripartite system of prepositions with the correspondences found in the two languages, which yield the following chart: We suggest that languages may view or map the same physical entities in different ways, for example along surface vs. volume or goal vs. passage, etc.Furthermore, we also find it possible that it is the language specific, inherent coding of the nominal phrase that decides – in many cases – upon the choice of prepositions and case endings.

scholarly journals Detection of Symmetry and Repetition in One and Two Objects

2009 ◽  
Vol 56 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Arno Koning ◽  
Johan Wagemans
Keyword(s):  
Three Dimensional ◽  
Intrinsic Property ◽  
Spatial Relations ◽  
Two Dimensional ◽  
Single Object ◽  
Ground Segmentation ◽  
Matching Strategy ◽  
The One

Symmetry is usually easier to detect within a single object than in two objects (one-object advantage), while the reverse is true for repetition (two-objects advantage). This interaction between regularity and number of objects could reflect an intrinsic property of encoding spatial relations within and across objects or it could reflect a matching strategy. To test this, regularities between two contours (belonging to a single object or two objects) had to be detected in two experiments. Projected three-dimensional (3-D) objects rotated in depth were used to disambiguate figure-ground segmentation and to make matching based on simple translations of the two-dimensional (2-D) contours unlikely. Experiment 1 showed the expected interaction between regularity and number of objects. Experiment 2 used two-objects displays only and prevented a matching strategy by also switching the positions of the two objects. Nevertheless, symmetry was never detected more easily than repetition in these two-objects displays. We conclude that structural coding, not matching strategies, underlies the one-object advantage for symmetry and the two-objects advantage for repetition.

The Research on the Reasoning Model of Combining Directional and Topological Relationships in 3D Space

2011 ◽  
Vol 58-60 ◽  
pp. 256-261
Author(s):  
Wei Jie Gu ◽  
Yong Shan Liu
Keyword(s):  
Matrix Model ◽  
Spatial Relation ◽  
Spatial Relations ◽  
Reference Object ◽  
3D Space ◽  
Topological Relationships ◽  
Interior Boundary ◽  
Direction Relations

The spatial relations usually consist of topological, directional and measurement relations. It is not accurate to using single spatial relation to describe spatial scene. Double projections and interior-division matrix model in 3D space is proposed by dividing the reference object within interior rectangle box. The expression of direction relations is combined with interior, boundary and exterior direction relations. 11 transforming rules are proposed by the constraint between directional and topological relationships. Finally, the model is evaluated by Roop K.Goyal’s five required properties and the result shows the satisfaction.

scholarly journals The Existence of a Convex Polyhedron with Respect to the Constrained Vertex Norms

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 645
Author(s):  
Supanut Chaidee ◽  
Kokichi Sugihara
Keyword(s):  
Voronoi Diagram ◽  
Convex Polyhedron ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Two Dimensional

Given a set of constrained vertex norms, we proved the existence of a convex configuration with respect to the set of distinct constrained vertex norms in the two-dimensional case when the constrained vertex norms are distinct or repeated for, at most, four points. However, we proved that there always exists a convex configuration in the three-dimensional case. In the application, we can imply the existence of the non-empty spherical Laguerre Voronoi diagram.

Communicating Spatial Relations Using Online Chat

2018 ◽  
pp. 233-282
Author(s):  
Theodor Wyeld
Keyword(s):  
Qualitative Analysis ◽  
Coordinate System ◽  
Qualitative Methodology ◽  
Three Dimensional ◽  
Spatial Relations ◽  
Two Dimensional ◽  
Online Chat ◽  
Spatial Expressions ◽  
Block Construction ◽  
Spatial Terms

The block construction exercises described in this chapter were used to investigate how spatial communication about the manipulation of objects in virtual, physical, and graphical space is communicated using online text. Where this study differs from previous research in the area is in its use of a qualitative methodology to investigate how these types of interactions are structured, communicated, and interpreted via text-based media. What emerges from the qualitative analysis is new insights over the previous quantitative investigations. More particularly, this mode of investigation has revealed the apparent superior efficacy of the fragmenting of three-dimensional spatial arrangements into two-dimensional planar representations using a simple ABC123 grid-wise coordinate system. The spatial terms used by participants in their textual communications are filtered according to Lefebvre's thirdspace and deictic spatial expressions.

scholarly journals Interpretation of Spatial Relationships by Objects Tracking in a Complex Streaming Video

2021 ◽  
Vol 15 (2) ◽  
pp. 245-257
Author(s):  
Noralhuda Alabid
Keyword(s):  
Three Dimensional ◽  
Spatial Relationship ◽  
Object Oriented ◽  
Spatial Relation ◽  
Spatial Relations ◽  
Three Dimensions ◽  
Spatial Relationships ◽  
Time Varying ◽  
Relationship Types ◽  
The Right

By interpreting spatial relations among objects, many applications such as video surveillance, robotics, and scene understanding systems can be utilized efficiently for different purposes. The vast majority of known models for spatial relationships are carried out with an image. However, due to the advance in technology, a three-dimensional scene became available. For our knowledge, most of the interpreted spatial relations were defined between silent objects in images. A technique for determining the dynamic spatial relation between a moving object and another silent one in a time varying scene is presented here. The spatial relationships were determined by using motion-based object tracking along with hypergraph object-oriented model. Defining the spatial relationship types between a single silent object and a moving human body has applied based on two strategies; determining each object with a bounding box, then comparing the locations of these boxes by applying certain conditional rules. This study identifies some of the spatial relationships in three dimensions of streaming frames, which has carried out by establishing a highly accurate and efficient proposed algorithm. The following relations have been studied; (“direct in front of”, “in front of on the Right/Left”, “direct behind of”, “behind of on the Right/Left”, “to the Right”, “to the Left”, “On”, “Under”, Besides, and “Besides on to the Right/Left”). The experimental results, which have been obtained based on actual indoor streaming frames, show effectiveness and reliable execution of our system

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

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