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Digital distance functions on three-dimensional grids

Robin Strand, Benedek Nagy, Gunilla Borgefors
2011 Theoretical Computer Science  
Digital distance functions are defined on the cubic, face-centered cubic, bodycentered cubic, honeycomb, and diamond grids.  ...  In this paper, we examine five different three-dimensional grids suited for image processing.  ...  Three-dimensional grids and neighborhood relations The main motivation for this work is to allow image processing on non-standard, three-dimensional grids.  ... 
doi:10.1016/j.tcs.2010.10.027 fatcat:hcmtewywbzh7dablkjadpdxfpe

Neighborhood Sequences on nD Hexagonal/Face-Centered-Cubic Grids [chapter]

Benedek Nagy, Robin Strand
2009 Lecture Notes in Computer Science  
In this paper, we define distance functions based on neighborhood sequences on these, higher dimensional generalizations of the hexagonal grid.  ...  The two-dimensional hexagonal grid and the three-dimensional face-centered cubic grid can be described by intersecting Z 3 and Z 4 with a (hyper)plane.  ...  This grid is called A n−1 in [3] . We will present some digital distance functions on these grids.  ... 
doi:10.1007/978-3-642-10210-3_8 fatcat:ijioqg26gzhgtf6dwzdw6abbvq

Application of Three-dimensional Design Software in Transmission Lines

Kejian Ni, Xinming Yu, Yuanhao Chen, Yinhe Lin, Xin Ye, Ming Xie, A. Safuan Bin A. Rashid, A. Liu
2021 E3S Web of Conferences  
The digitization of power grid projects is a development requirement in the era of big data, as well as an inevitable requirement for the State Grid Corporation of China to build digital power grids and  ...  Three-dimensional design establishes three-dimensional models of ground conductors, insulators, and fittings through line electrical majors, and completes line poles and towers in a three-dimensional scene  ...  The three-dimensional digital software has a positive effect on design optimization.  ... 
doi:10.1051/e3sconf/202128301049 fatcat:psuxyestp5hdfb3qhviiwiis6a

Searching for Topological Symmetry in Data Haystack [article]

Kallol Roy and Anh Tong and Jaesik Choi
2016 arXiv   pre-print
The three grid moves are legal transformations as they preserve the statistical distribution of hamming distances in each grid block.  ...  To compute the symmetry in a grid structure, we introduce three legal grid moves (i) Commutation (ii) Cyclic Permutation (iii) Stabilization on sets of local grid squares, grid blocks.  ...  We define three grid moves (i) Commutation (ii) Cyclic Permutation (iii) Stabilization on grid blocks, consisting of a finite number of local grid squares.  ... 
arXiv:1603.03703v1 fatcat:d5llsb2rk5euznu2fmngw3gsdu

Two-Dimensional Configurations of Unidimensional Stimulus Sets in Nonmetric Multidimensional Scaling

Mark L. Davison, Marsha Hearn
1989 Applied Psychological Measurement  
of the function mapping psychological dissimilarity, represented as distance in the scaling model, onto the observed response scale.  ...  In simulated unidimensional data scaled in two dimensions, stimuli formed a C-shaped configuration when the monotone function relating distances to dissimilarity data was negatively accelerating.  ...  The basic grid can be seen in Figure 6a , and the curvature of the grid into a bowl shape in three dimensions can be seen in Figure 6b .  ... 
doi:10.1177/014662168901300401 fatcat:yp5qxt4abrfktbklwhjeavp42m

Neighborhood Sequences in the Diamond Grid – Algorithms with Four Neighbors [chapter]

Benedek Nagy, Robin Strand
2009 Lecture Notes in Computer Science  
In this paper the diamond grid is considered, that is the three-dimensional grid of Carbon atoms in the diamond crystal.  ...  In digital image processing digital distances are useful; distances based on neighborhood sequences are widely used.  ...  One disadvantage with these distance functions is that the rotational dependency is high.  ... 
doi:10.1007/978-3-642-10210-3_9 fatcat:tegcfhrrwrbnhjufxymvzyu5au

Consistent digital rays

Jinhee Chun, Matias Korman, Martin Nöllenburg, Takeshi Tokuyama
2008 Proceedings of the twenty-fourth annual symposium on Computational geometry - SCG '08  
Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p.  ...  We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight Θ(log n) bound in the n × n grid.  ...  Digital mountain approximation Consider a [0, 1]-valued function f on P, which we call a pixel image function.  ... 
doi:10.1145/1377676.1377737 dblp:conf/compgeom/ChunKNT08 fatcat:phwiu4agibbn7kfoifzffbu4c4

Consistent Digital Rays

Jinhee Chun, Matias Korman, Martin Nöllenburg, Takeshi Tokuyama
2009 Discrete & Computational Geometry  
Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p.  ...  We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight Θ(log n) bound in the n × n grid.  ...  The authors thank János Pach for his stimulating discussion on this topic, especially on the problem of the lower distance bound.  ... 
doi:10.1007/s00454-009-9166-2 fatcat:q5ybfdc75ng2ddf34aiaw5ch6u

Path-based distance functions in n-dimensional generalizations of the face- and body-centered cubic grids

Robin Strand, Benedek Nagy
2009 Discrete Applied Mathematics  
Path-based distance functions are defined on n-dimensional generalizations of the facecentered cubic and body-centered cubic grids. The distance functions use both weights and neighborhood sequences.  ...  For the three-dimensional case, we introduce four different error functions which are used to find the optimal weights and neighborhood sequences that can be used to define the distance functions with  ...  The research is supported by Digital geometry with applications in image processing in three dimensions (DIGAVIP) at Centre for Image Analysis, Uppsala University.  ... 
doi:10.1016/j.dam.2009.02.008 fatcat:2l4pbpvvczdk3fcrxeoeyymr6i

On the Accuracy of First-Order Numerical Derivatives in Multidimensional Digital Waveguide Mesh Topologies

H. Hachabiboglu, B. Gunel, A.M. Kondoz
2008 IEEE Signal Processing Letters  
This letter discusses the accuracy of first-order approximations to numerical derivatives on more general unstructured mesh topologies.  ...  Index Terms-Acoustic signal processing, acoustical modeling, digital waveguides, finite difference methods, multidimensional sampling, numerical derivatives.  ...  Välimäki and three anonymous reviewers for their feedback and constructive comments.  ... 
doi:10.1109/lsp.2007.911162 fatcat:ed2covpl3reblk6pchmzmzymhm


Valentin E. Brimkov, Reneta P. Barneva, Petra Wiederhold
2011 Theoretical Computer Science  
They also show that any cycle of the integer grid contains an inscribed square with integer vertices. Finally, they provide an O(n 2 ) algorithm to find inscribed squares in simple digital curves.  ...  As a result of a rigorous reviewing process, typically by three referees per paper, 11 works were eventually accepted for publication.  ...  In the paper ''Digital Distance Functions on Three-Dimensional Grids'', the authors Robin Strand, Benedek Nagy, and Gunilla Borgefors define distance functions on the cubic, face-centered cubic, body-centered  ... 
doi:10.1016/j.tcs.2010.12.001 fatcat:gakq33in7zghtphdoei3zztgaa

Page 1460 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
For two-dimensional im- ages, it is obtained as the ‘ridge’ of a ‘medial function’ defined on (2+ 1)-dimensional scale space.  ...  A statistical analysis is performed separately for the three common distance concepts, namely, the Euclidean, city-block, and chessboard distance.  ... 

Efficient computation paths for the systematic analysis of sensitivities

Paolo Greppi, Elisabetta Arato
2013 Computer Physics Communications  
A systematic sensitivity analysis requires computing the model on all points of a multi-dimensional grid covering the domain of interest, defined by the ranges of variability of the inputs.  ...  The problem of choosing a better order can be translated geometrically into finding Hamiltonian paths on certain grid graphs.  ...  graph on a small two-dimensional grid Dense grid graph on a small two-dimensional grid Square two-dimensional spiral LIBPF™ Lexicographical ordering on a three-dimensional grid having three steps in each  ... 
doi:10.1016/j.cpc.2012.08.018 fatcat:n5hihw3qgvhm3c4nxurwdpn4aq

Connectivity preserving digitization of blurred binary images in 2D and 3D

Peer Stelldinger, Ullrich Köthe
2006 Computers & graphics  
Now we extend this result to other common sampling grids in the two and even in the three dimensional space, including hexagonal, bcc and fcc grids.  ...  In some previous work we showed that certain shapes can be digitized topologically correctly with a square grid when some blurring with an arbitrary non-negative radially symmetric point spread function  ...  In this paper we extend these results to other types of sampling grids, namely hexagonal and triangular grids and even three dimensional grids like cubic, bcc and fcc ones.  ... 
doi:10.1016/j.cag.2005.10.012 fatcat:zmurvv4qqra57hiuzurahww354


2017 International Journal of Engineering and Geosciences  
Triangulation with Linear interpolation, Nearest Neighbor, Invers Distance to a Power, Local Polynomial and Minimum Curvature).  ...  The main objective of the study was to examine accuracies of DEMs (Digital Elevation Models) with different topographical structures generated by using the Unmanned Aerial Vehicle (UAV) point clouds.  ...  One of these methods, LIDAR systems, has become a preferred method for Digital Elevation Model preparation thanks to its three dimensional information gathering capability, which is very effective for  ... 
doi:10.26833/ijeg.329717 fatcat:xz5iulqvsvgq3ltacccqlbn2wa
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