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 Version. 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 Version. 0501
BibRef

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

Borgefors, G.,
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 Version. 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 Version. 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 Link 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.
WWW Version. 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 Version. 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 Version. 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 Abstract. 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 Version. 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 Version. 0611
BibRef
Earlier:
A Comparison Among Distances Based on Neighborhood Sequences in Regular Grids,
SCIA05(1027-1036).
Springer DOI Link 0506
BibRef
Earlier:
Calculating Distance with Neighborhood Sequences in the Hexagonal Grid,
IWCIA04(98).
WWW Version. 0505
Digital geometry; Distance functions; Neighbourhood sequences; Cubic grid; Triangular grid; Discrete geometry; Computational geometry 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 Link 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 Link 0804
BibRef
Earlier: A1, A3, A2:
H2O: Reversible Hexagonal-Orthogonal Grid Conversion by 1-D Filtering,
ICIP07(II: 73-76).
IEEE DOI Link 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 Link 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 Link 0512
BibRef

Jiang, Q.,
FIR Filter Banks for Hexagonal Data Processing,
IP(17), No. 9, September 2008, pp. 1512-1521.
IEEE DOI Link 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 Link 1004
human eye is hexagonal (more than square lattice). Derived gradients perform better than those on square lattice. BibRef


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

Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.], Gardiner, B.[Bryan],
Design of Feature Extraction Operators for Use on Biologically Motivated Hexagonal Image Structures,
MVA09(178-).
PDF Version. 0905
BibRef

Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.], Gardiner, B.[Bryan],
Processing Hexagonal Images in a Virtual Environment,
CIAP09(920-928).
Springer DOI Link 0909
See also Adaptive Technique for Accurate Feature Extraction from Regular and Irregular Image Data, An. BibRef

Gardiner, B.[Bryan], Coleman, S.A.[Sonya A.], Scotney, B.W.[Bryan W.],
Fast Edge Map Pyramids for Hexagonal Image Structures,
IMVIP09(41-46).
IEEE DOI Link 0909
BibRef
And:
Fast Multiscale Operator Development for Hexagonal Images,
DAGM09(282-291).
Springer DOI Link 0909
BibRef
Earlier:
Multi-scale Feature Extraction in a Sub-pixel Virtual Hexagonal Environment,
IMVIP08(111-116).
IEEE DOI Link 0809
BibRef
Earlier:
A Design Procedure for Gradient Operators on Hexagonal Images,
IMVIP07(47-54).
IEEE DOI Link 0709
See also Improving angular error by near-circular operator design. 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 Link 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 Link 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:Feb 8, 2012 at 11:25:05