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On approximating Euclidean metrics by digital distances in 2D and 3D

J. Mukherjee, P.P. Das, M. Aswatha Kumar, B.N. Chatterji
2000 Pattern Recognition Letters  
First we show that the vertices of the digital circles (spheres) for octagonal distances can be suitably approximated as a function of the number of neighborhood types used in the sequence.  ...  octagonal distances.  ...  Acknowledgements The comments of the anonymous reviewers for improving the paper in its ®nal form are gratefully acknowledged.  ... 
doi:10.1016/s0167-8655(00)00022-2 fatcat:otcdlou4xbflrpapiz3qfsi3ji

Best simple octagonal distances in digital geometry

P.P Das
1992 Journal of Approximation Theory  
distances in 2-D digital geometry.  ...  A subclass of general octagonal distances defined by neighbourhood sequences [2] have been characterized here which have a strikingly simple closed functional form. These are called simple distances.  ...  The octagonal distance for digital pictures was introduced in digital geometry by Pfaltz and Rosenfeld in [4] when they proved that an alternating use of cityblock and chessboard motions defines a new  ... 
doi:10.1016/0021-9045(92)90090-b fatcat:ca6hy6vmmndcbcby5dh5kz55be

Distance transformations in arbitrary dimensions

Gunilla Borgefors
1984 Computer Vision Graphics and Image Processing  
In many applications of digital picture processing, distances from certain feature elements to the nonfeature elements must be computed.  ...  The comparison with Euclidean distance is given as upper limits for the difference between the Euclidean distance and the computed distances.  ...  INTRODUCTION In many applications of digital picture processing it is essential to measure the distance between elements.  ... 
doi:10.1016/0734-189x(84)90035-5 fatcat:g5cswcggcfcillbtkxm73vs75y

Euclidean distance mapping

Per-Erik Danielsson
1980 Computer Graphics and Image Processing  
The map indicates, for each pixel in the objects (or the background) of the originally binary picture, the shortest distance to the nearest pixel in the background (or the objects).  ...  Based on a two-component descriptor, a distance label for each point, it is shown that Euclidean distance maps can be generated by effective sequential algorithms.  ...  SEQUENTIAL OCTAGONAL MAPPING As was mentioned in the introduction, octagonal distances and octagonal propagation are almost standard procedures in picture processing.  ... 
doi:10.1016/0146-664x(80)90054-4 fatcat:pw7pdyi5xfendcwyru7jndltmm

Page 1072 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
N. (6-IITKH-EL) Octagonal distances for digital pictures. Inform. Sci. 50 (1990), no. 2, 123-150.  ...  Summary: “The set of distances obtained by combining the city- 68 COMPUTER SCIENCE 1072 block and the chessboard motions is studied as a generalization of the octagonal distance for digital pictures.  ... 

DIGITAL PHOTOGRAMMETRY FOR THE GEOMETRICAL ANALYSIS OF THE UMBRELLA-SHAPED DOME IN BAIA (NAPLES)

L. Aliberti, M. Á. Alonso-Rodríguez
2018 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
This paper is focused on the use of photogrammetric measurement techniques for the valorization of architectural and archaeological heritage.  ...  Currently half part of the octagonal room annexed to the Temple of Mercury in Baia is underwater. Moreover the level of water may grow due to the characteristic movement of the soil in this area.  ...  The results obtained with the difficult conditions of the data collection in the octagonal room are an example of the great versatility of the digital photogrammetry with structure for motion method.  ... 
doi:10.5194/isprs-archives-xlii-2-23-2018 fatcat:ooiouwjgwrhzbhayqt4gtdsapy

High-Capacity Embedding Method Based on Double-Layer Octagon-Shaped Shell Matrix

Chin-Feng Lee, Jau-Ji Shen, Somya Agrawal, Yen-Hsi Li
2021 Symmetry  
This paper proposes a data hiding scheme based on a double-layer octagon-shaped shell matrix.  ...  Compared to previous octagon-shaped data hiding methods, the proposed method embeds a total of 7 bits in each pixel pair, reaching an embedding capacity of 3.5 bits per pixel (bpp).  ...  For each sub-stream , convert the first 2 bits into a 4-ary digit and the last 5 bits into a 32-ary digit , viz., || where "||" denotes the string concatenation operator.  ... 
doi:10.3390/sym13040583 fatcat:jgyit663ozd4no3iephuvre33i

Understanding Digital Cardwall Usage

Stevenson Gossage, Judith M. Brown, Robert Biddle
2015 2015 Agile Conference  
We identify issues to address in the design of digital Cardwalls.  ...  We conducted field studies of 8 Agile teams using digital Cardwalls, and performed qualitative data analysis to understand patterns of usages and user needs.  ...  We also thank the Natural Sciences and Engineering Research Council of Canada for funding through the SurfNet Strategic Research Network.  ... 
doi:10.1109/agile.2015.16 dblp:conf/agiledc/GossageBB15 fatcat:abcg2qznt5d6zozdyjekqo554m

Neuropsychological Functioning in Unilateral Cerebellar Damage

Thérèse Botez-Marquard, Jean Léveillé, M.I. Botez
1994 Canadian Journal of Neurological Sciences  
Ottawa-Wechsler January 1991 May 1993 Norms Global IQ* Verbal IQ* Performance IQ* Information Comprehension Digit span Arithmetic Similarities Picture arrangement Picture completion Block  ...  The second assessment shows a significant improvement of performance IQ (115), particularly the picture arrangement (logical judgment of sequences in familiar situations) and digit symbol subtests.  ... 
doi:10.1017/s0317167100040956 fatcat:7sbongs5pfeexfooojsycawlvu

New algebraic and geometric constructs arising from Fibonacci numbers

Fabio Caldarola, Gianfranco d'Atri, Mario Maiolo, Giuseppe Pirillo
2020 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
Such octagons, in some previous articles, have been given the name of Carboncettus octagons for historical reasons.  ...  Fibonacci numbers are the basis of a new geometric construction that leads to the definition of a family {C n : n ∈ N} of octagons that come very close to the regular octagon.  ...  6 as follows: Note that for W 8 we have written 30 more digits (177) than for the previous words: The reason for this will be clear later.  ... 
doi:10.1007/s00500-020-05256-1 fatcat:bnfkz7gkpfafvd6fsvbojpeq5q

Classification of Geometric Forms in Mosaics Using Deep Neural Network

Mridul Ghosh, Sk Md Obaidullah, Francesco Gherardini, Maria Zdimalova
2021 Journal of Imaging  
the dataset for testing the CNN-based approach.  ...  As a case study, a Roman mosaic is considered, which is digitally reconstructed by close-range photogrammetry based on standard photos.  ...  In [53] , Falomir et al. presented a mathematical method for calculating a likeness score among qualitative assessments of item structure, color and dimension in digitized pictures.  ... 
doi:10.3390/jimaging7080149 pmid:34460785 fatcat:3g2q6r4xuve2vhbgtzhoqyqwpu

VIRTUAL AND PHYSICAL RECOMPOSITION OF FRAGMENTED ECCLESIASTICAL FRESCOES USING A PHOTOGRAMMETRIC APPROACH

D. Abate, S. Hermon, I. Eliades
2016 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
Two of these are exceptional for their artistic and historic value: the story of the Tree of Jesse (a pictorial genealogy of the Virgin) located on the southern wall of the octagon, and the Last Judgment  ...  These were digitally documented through high-resolution ortophotos.  ...  ACKNOWLEDGEMENTS The authors would like to thank Marina Faka and Panayotis Kyriacou of STARC of the Cyprus Institute for the support given during the photogrammetric field survey at the Byzantine Museum  ... 
doi:10.5194/isprs-archives-xli-b5-153-2016 fatcat:rkgalsn5uvfifhh3hcydgfe2wy

Novel Method For The Analysis Of Printed Circuit Images

Jon R. Mandeville, Andrew G. Tescher
1984 Applications of Digital Image Processing VII  
use an analog subsystem for part handling and image acquisition and a digital subsystem for image analysis and overall system control.  ...  With an appropriate sequence of expansion steps it is possible to achieve the discrete octagonal expansion as illustrated in Fig. 2 and Fig. 3(a) and (b) .  ...  We use the distance measure implied by octagonal expansion.  ... 
doi:10.1117/12.944849 fatcat:joz46rwybjhbtai5i6up6pm3um

Novel method for analysis of printed circuit images

Jon R. Mandeville
1985 IBM Journal of Research and Development  
use an analog subsystem for part handling and image acquisition and a digital subsystem for image analysis and overall system control.  ...  With an appropriate sequence of expansion steps it is possible to achieve the discrete octagonal expansion as illustrated in Fig. 2 and Fig. 3(a) and (b) .  ...  We use the distance measure implied by octagonal expansion.  ... 
doi:10.1147/rd.291.0073 fatcat:hxehdmbe2fecbdc42wbruaho7m

Data Hiding Method Based on 3D Magic Cube

Chin-Feng Lee, Jau-Ji Shen, Somya Agrawal, Ying-Xiang Wang, Yen-Hsi Lee
2020 IEEE Access  
Rule 2: If M (p i , p i+1 ) is an edge digit included in at least one octagon, then M (q i , q i+1 ) is one of the digits in all octagons that are adjacent.  ...  The pixels were modified according to the rules below: Rule 1: If M (p i , p i+1 ) is a digit that is located in an octagon, then M (q i , q i+1 ) is one of the digits in this octagon.  ... 
doi:10.1109/access.2020.2975385 fatcat:klprfjf63rd5xfzwyrliwpgdo4
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