Image Transformation on Hexagonal Structure Based on Conversion between 1D and 2D Coordinates

Ye, Y; He, S; Li, J; Jia, W; Wu, Q

Image Transformation on Hexagonal Structure Based on Conversion between 1D and 2D Coordinates

Ye, Y He, S

Li, J Jia, W

Wu, Q

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Publisher:: Springer
Publication Type:: Chapter
Citation:: Rough Sets and Knowledge Technology, 2009, 1, pp. 571 - 578
Issue Date:: 2009-01

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Field	Value	Language
dc.contributor.author	Ye, Y	en_US
dc.contributor.author	He, S https://orcid.org/0000-0001-8962-540X	en_US
dc.contributor.author	Li, J	en_US
dc.contributor.author	Jia, W https://orcid.org/0000-0002-0940-3338	en_US
dc.contributor.author	Wu, Q https://orcid.org/0000-0001-5641-2483	en_US
dc.contributor.editor	Wen, P	en_US
dc.contributor.editor	Li, Y	en_US
dc.contributor.editor	Polkowski, L	en_US
dc.contributor.editor	Yao, Y	en_US
dc.contributor.editor	Tsumoto, S	en_US
dc.contributor.editor	Wang, G	en_US
dc.date.issued	2009-01	en_US
dc.identifier.citation	Rough Sets and Knowledge Technology, 2009, 1, pp. 571 - 578	en_US
dc.identifier.isbn	978-3-642-02961-5	en_US
dc.identifier.uri	http://hdl.handle.net/10453/7838
dc.description.abstract	Spiral Architecture, a hexagonal image structure is a novel and powerful approach to machine vision system. The pixels on Spiral architecture are geometrically arranged using a 1D (Spiral) addressing scheme in an ascending order along a spiral-like curve. Spiral addition and Spiral multiplication are defined based on the Spiral addresses on Spiral Architecture. These two fundamental operations result in fast and easy translation, rotation and separation on images, and hence play very important roles for image processing on Spiral Architecture. Moreover, 2D coordinates according to rows and columns defined on Spiral Structure provide a good mapping to the ordinary 2D coordinates defined on the common square image structure. Therefore, how to convert the 1D Spiral addresses from and to the 2D coordinates on Spiral Architecture has become very important to apply the theory developed on a hexagonal image structure for image processing (e.g., rotation). In this paper, we perform a fast way to correctly locate any hexagonal pixel when its Spiral address is known, and compute the Spiral address of any hexagonal pixel when its location is known. As an illustration of the use of conversions, we demonstrate the accurate image translation and rotation using experimental results.	en_US
dc.publisher	Springer	en_US
dc.relation.ispartof	Rough Sets and Knowledge Technology	en_US
dc.relation.isbasedon	10.1007/978-3-642-02962-2	en_US
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in Rough Sets and Knowledge Technology. The final authenticated version is available online at: https://dx.doi.org/10.1007/978-3-642-02962-2.	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Image Transformation on Hexagonal Structure Based on Conversion between 1D and 2D Coordinates	en_US
dc.type	Chapter
utslib.location	Berlin, Germany	en_US
utslib.for	080106 Image Processing	en_US
utslib.for	080104 Computer Vision	en_US
utslib.for	080109 Pattern Recognition and Data Mining	en_US
utslib.citation.edition	1	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CRIN - Realtime Information Networks
pubs.organisational-group	/University of Technology Sydney/Strength - GBDTC - Global Big Data Technologies
pubs.organisational-group	/University of Technology Sydney/Strength - INEXT - Innovation in IT Services and Applications
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.edition	1	en_US
pubs.place-of-publication	Berlin, Germany	en_US

Abstract:

Spiral Architecture, a hexagonal image structure is a novel and powerful approach to machine vision system. The pixels on Spiral architecture are geometrically arranged using a 1D (Spiral) addressing scheme in an ascending order along a spiral-like curve. Spiral addition and Spiral multiplication are defined based on the Spiral addresses on Spiral Architecture. These two fundamental operations result in fast and easy translation, rotation and separation on images, and hence play very important roles for image processing on Spiral Architecture. Moreover, 2D coordinates according to rows and columns defined on Spiral Structure provide a good mapping to the ordinary 2D coordinates defined on the common square image structure. Therefore, how to convert the 1D Spiral addresses from and to the 2D coordinates on Spiral Architecture has become very important to apply the theory developed on a hexagonal image structure for image processing (e.g., rotation). In this paper, we perform a fast way to correctly locate any hexagonal pixel when its Spiral address is known, and compute the Spiral address of any hexagonal pixel when its location is known. As an illustration of the use of conversions, we demonstrate the accurate image translation and rotation using experimental results.

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http://hdl.handle.net/10453/7838