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

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. BibRef

Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.], Gardiner, B.[Bryan],
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
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:Jul 15, 2017 at 20:56:55