7.2.3.2 Triangular, Hexagonal Grids, Geometry, Computations

Chapter Contents (Back)
Hexagonal. Digital Geometry.

Golay, M.J.E.,
Hexagonal Parallel Pattern Transformations,
TC(18), 1969, pp. 733-740. Hexagonal Representation. BibRef 6900

Golay, M.J.E.,
Topoglyphs,
TC(27), 1978, pp. 164-167. BibRef 7800

Preston, Jr., K.,
Feature Extraction by Golay Hexagonal Pattern Transforms,
TC(20), No. 9, September 1971, pp. 1007-1014. Hexagonal Representation. BibRef 7109

Luczak, E., Rosenfeld, A.,
Distance on a Hexagonal Grid,
TC(25), 1976, pp. 532-533. Hexagonal Grid. BibRef 7600

Siromoney, G.[Gift], Siromoney, R.[Rani],
Hexagonal arrays and rectangular blocks,
CGIP(5), No. 3, September 1976, pp. 353-381.
WWW Link. 0501
BibRef

Freeman, H.,
Algorithm for Generating a Digital Straight Line on a Triangular Grid,
TC(28), No. 2, February 1979, pp. 150-152. BibRef 7902

Subramanian, K.G.,
Hexagonal array grammars,
CGIP(10), No. 4, August 1979, pp. 388-394.
WWW Link. 0501
BibRef

Dersanambika, K.S., Krithivasan, K., Martin-Vide, C., Subramanian, K.G.,
Hexagonal Pattern Languages,
IWCIA04(52-64).
Springer DOI 0505
BibRef

Borgefors, G.[Gunilla],
Distance Transformations on Hexagonal Grids,
PRL(9), 1989, pp. 97-105. BibRef 8900

Bell, S.B.M., Holroyd, F.C., Mason, D.C.,
A Digital Geometry for Hexagonal Pixels,
IVC(7), No. 3, August 1989, pp. 194-204.
WWW Link. BibRef 8908

Staunton, R.C.,
The Design Of Hexagonal Sampling Structures for Image Digitization and Their Use with Local Operators,
IVC(7), No. 3, August 1989, pp. 162-166.
WWW Link. See also Analysis of Hexagonal Thinning Algorithms and Skeletal Shape Representation, An. BibRef 8908

Wuthrich, C.A., and Stucki, P.,
An Algorithmic Comparison Between Square- and Hexagonal-Based Grids,
GMIP(53), 1991, pp. 324-339. BibRef 9100

Her, I., Yuan, C.T.,
Resampling on a Pseudohexagonal Grid,
GMIP(56), No. 4, July 1994, pp. 336-347. BibRef 9407

Her, I.,
Geometric transformations on the hexagonal grid,
IP(4), No. 9, September 1995, pp. 1213-1222.
IEEE DOI 0402
BibRef

Mehnert, A.J.H.[Andrew J.H.], Jackway, P.T.[Paul T.],
On Computing the Exact Euclidean Distance Transform on Rectangular and Hexagonal Grids,
JMIV(11), No. 3, December 1999, pp. 223-230.
DOI Link BibRef 9912

Sheridan, P., Hintz, T., Alexander, D.,
Pseudo-invariant image transformations on a hexagonal lattice,
IVC(18), No. 11, August 2000, pp. 907-917.
WWW Link. 0006
BibRef

van de Ville, D.[Dimitri], Philips, W.[Wilfried], Lemahieu, I.[Ignace],
Least-squares spline resampling to a hexagonal lattice,
SP:IC(17), No. 5, May 2002, pp. 393-408.
WWW Link. 0206
BibRef

van de Ville, D., van de Walle, R., Philips, W., Lemahieu, I.,
Image resampling between orthogonal and hexagonal lattices,
ICIP02(III: 389-392).
IEEE DOI 0210
BibRef

Middleton, L., Sivaswamy, J.,
Hexagonal Image Processing: A Practical Approach,
Springer2004. ISBN 1-85233-914-4.
HTML Version. BibRef 0400

Vince, A.,
Indexing the aperture 3 hexagonal discrete global grid,
JVCIR(17), No. 6, December 2006, pp. 1227-1236.
WWW Link. 0711
Discrete global grid; Spherical tessellation; Hexagonal tessellation BibRef

Nagy, B.[Benedek],
Distances with neighbourhood sequences in cubic and triangular grids,
PRL(28), No. 1, 1 January 2007, pp. 99-109.
WWW Link. 0611
BibRef
Earlier:
A Comparison Among Distances Based on Neighborhood Sequences in Regular Grids,
SCIA05(1027-1036).
Springer DOI 0506
BibRef
Earlier:
Calculating Distance with Neighborhood Sequences in the Hexagonal Grid,
IWCIA04(98).
Springer DOI 0505
Digital geometry; Distance functions; Neighbourhood sequences; Cubic grid; Triangular grid; Discrete geometry; Computational geometry See also Connection between Z n and Generalized Triangular Grids, A. BibRef

Kovács, G.[Gergely], Nagy, B.[Benedek], Vizvári, B.[Béla],
On Weighted Distances on the Khalimsky Grid,
DGCI16(372-384).
WWW Link. 1606
BibRef

Nagy, B.[Benedek],
Weighted Distances on a Triangular Grid,
IWCIA14(37-50).
Springer DOI 1405
BibRef
Earlier:
Cellular Topology on the Triangular Grid,
IWCIA12(143-153).
Springer DOI 1211
BibRef

Puschel, M., Rotteler, M.,
Algebraic Signal Processing Theory: 2-D Spatial Hexagonal Lattice,
IP(16), No. 6, June 2007, pp. 1506-1521.
IEEE DOI 0706
BibRef

Condat, L.[Laurent], van de Ville, D.[Dimitri], Forster-Heinlein, B.[Brigitte],
Reversible, Fast, and High-Quality Grid Conversions,
IP(17), No. 5, May 2008, pp. 679-693.
IEEE DOI 0804
BibRef
Earlier: A1, A3, A2:
H2O: Reversible Hexagonal-Orthogonal Grid Conversion by 1-D Filtering,
ICIP07(II: 73-76).
IEEE DOI 0709
BibRef

Condat, L., van de Ville, D., Unser, M.,
Efficient Reconstruction of Hexagonally Sampled Data using Three-Directional Box-Splines,
ICIP06(697-700).
IEEE DOI 0610
BibRef

Condat, L., van de Ville, D., Blu, T.,
Hexagonal Versus Orthogonal Lattices: A New Comparison Using Approximation Theory,
ICIP05(III: 1116-1119).
IEEE DOI 0512
BibRef

Jiang, Q.,
FIR Filter Banks for Hexagonal Data Processing,
IP(17), No. 9, September 2008, pp. 1512-1521.
IEEE DOI 0810
BibRef

Shima, T.[Tetsuo], Saito, S.[Suguru], Nakajima, M.[Masayuki],
Design and Evaluation of More Accurate Gradient Operators on Hexagonal Lattices,
PAMI(32), No. 6, June 2010, pp. 961-973.
IEEE DOI 1004
human eye is hexagonal (more than square lattice). Derived gradients perform better than those on square lattice. BibRef

Veni, S., Narayanankutty, K.A.,
Vision-based hexagonal image processing using Hex-Gabor,
SIViP(8), No. 2, February 2014, pp. 317-326.
WWW Link. 1402
BibRef

Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.], Suganthan, S.[Shanmugalingam],
Multi-scale edge detection on range and intensity images,
PR(44), No. 4, April 2011, pp. 821-838.
Elsevier DOI 1101
Range; Intensity; Scale BibRef

Gardiner, B.[Bryan], Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.],
Multiscale Edge Detection Using a Finite Element Framework for Hexagonal Pixel-Based Images,
IP(25), No. 4, April 2016, pp. 1849-1861.
IEEE DOI 1604
BibRef
Earlier:
Fast Edge Map Pyramids for Hexagonal Image Structures,
IMVIP09(41-46).
IEEE DOI 0909
BibRef
And:
Fast Multiscale Operator Development for Hexagonal Images,
DAGM09(282-291).
Springer DOI 0909
BibRef
Earlier:
Multi-scale Feature Extraction in a Sub-pixel Virtual Hexagonal Environment,
IMVIP08(111-116).
IEEE DOI 0809
BibRef
Earlier:
A Design Procedure for Gradient Operators on Hexagonal Images,
IMVIP07(47-54).
IEEE DOI 0709
See also Improving angular error by near-circular operator design. See also Gradient operators for feature extraction and characterisation in range images. BibRef

Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.], Gardiner, B.[Bryan],
Tri-directional gradient operators for hexagonal image processing,
JVCIR(38), No. 1, 2016, pp. 614-626.
Elsevier DOI 1605
BibRef
And:
Fast low-level multi-scale feature extraction for hexagonal images,
MVA17(342-345)
DOI Link 1708
BibRef
Earlier:
Integral Spiral Image for Fast Hexagonal Image Processing,
CIAP13(II:532-541).
Springer DOI 1309
BibRef
Earlier:
Design of Feature Extraction Operators for Use on Biologically Motivated Hexagonal Image Structures,
MVA09(178-).
PDF File. 0905
BibRef
And:
Processing Hexagonal Images in a Virtual Environment,
CIAP09(920-928).
Springer DOI 0909
Computer architecture, Convolution, Feature extraction, Indexes, Machine vision, Organizations, Spirals Hexagonal image processing See also Adaptive Technique for Accurate Feature Extraction from Regular and Irregular Image Data, An. BibRef


Kardos, P.[Péter], Palágyi, K.[Kálmán],
Unified Characterization of P-Simple Points in Triangular, Square, and Hexagonal Grids,
CompIMAGE16(79-88).
Springer DOI 1704
BibRef

Li, X., Gardiner, B., Coleman, S.A.,
Square to hexagonal lattice conversion based on one-dimensional interpolation,
IPTA16(1-6)
IEEE DOI 1703
image sampling BibRef

Nagy, B.[Benedek],
Number of Words Characterizing Digital Balls on the Triangular Tiling,
DGCI16(31-44).
WWW Link. 1606
BibRef

Comic, L.[Lidija], Nagy, B.[Benedek],
A Combinatorial 4-Coordinate System for the Diamond Grid,
ISMM15(585-596).
Springer DOI 1506
BibRef

Mujahed, H.[Hamzeh], Nagy, B.[Benedek],
Wiener Index on Lines of Unit Cells of the Body-Centered Cubic Grid,
ISMM15(597-606).
Springer DOI 1506
BibRef

Lalitha, D., Rangarajan, K., Thomas, D.G.,
Petri Net Generating Hexagonal Arrays,
IWCIA11(235-247).
Springer DOI 1105
BibRef

Shima, T.[Tetsuo], Sugimoto, S.[Shigeki], Okutomi, M.[Masatoshi],
Comparison of image alignment on hexagonal and square lattices,
ICIP10(141-144).
IEEE DOI 1009
BibRef

Shidfar, S.[Shaadi], Ion, A.[Adina], Ktorides, L.[Lazaros], Colchester, A.[Alan],
Hexagonal pixels for improved low level segmentation,
BMVCWS10(xx-yy).
HTML Version. 1009
BibRef

He, X.J.[Xiang-Jian], Li, J.M.[Jian-Min], Hintz, T.[Tom],
Comparison of Image Conversions Between Square Structure and Hexagonal Structure,
ACIVS07(262-273).
Springer DOI 0708
BibRef

He, X.J.[Xiang-Jian], Wang, H.Q.[Hua-Qing], Hur, N.H.[Nam-Ho], Jia, W.J.[Wen-Jing], Wu, Q.A.[Qi-Ang], Kim, J.W.[Jin-Woong], Hintz, T.,
Uniformly Partitioning Images on Virtual Hexagonal Structure,
ICARCV06(1-6).
IEEE DOI 0612
BibRef

Gillespie, W., Mori, S., and Suen, C.Y.,
Representation and Traversal of Images in the Hexagonal Field,
CVWS82(35-37). BibRef 8200

Chapter on 2-D Feature Analysis, Extraction and Representations, Shape, Skeletons, Texture continues in
Digital Topology .


Last update:Nov 18, 2017 at 20:56:18