The study of the evolution process of our visual system indicates the existence of variational spatial arrangement; from densely hexagonal in the fovea to a sparse circular structure in the peripheral retina. Today's sensor spatial arrangement is inspired by our visual system. However, we have not come further than rigid rectangular and, on a minor scale, hexagonal sensor arrangements. Even in this situation, there is a need for directly assessing differences between the rectangular and hexagonal sensor arrangements, i.e., without the conversion of one arrangement to another. In this paper, we propose a method to create a common space for addressing any spatial arrangements and assessing the differences among them, e.g., between the rectangular and hexagonal. Such a space is created by implementing a continuous extension of discrete Weyl Group orbit function transform which extends a discrete arrangement to a continuous one. The implementation of the space is demonstrated by comparing two types of generated hexagonal images from each rectangular image with two different methods of the half-pixel shifting method and virtual hexagonal method. In the experiment, a group of ten texture images were generated with variational curviness content using ten different Perlin noise patterns, adding to an initial 2D Gaussian distribution pattern image. Then, the common space was obtained from each of the discrete images to assess the differences between the original rectangular image and its corresponding hexagonal image. The results show that the space facilitates a usage friendly tool to address an arrangement and assess the changes between different spatial arrangements by which, in the experiment, the hexagonal images show richer intensity variation, nonlinear behavior, and larger dynamic range in comparison to the rectangular images.

Department of Physics Czech Technical University 11519 Prague 1 Czech Republic

Department of Technology and Aesthetics Blekinge Institute of Technology 37179 Karlskrona Sweden

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Mead C. Neuromorphic electronic systems. Proc. IEEE. 1990;78:1629–1636. doi: 10.1109/5.58356. DOI

Lamb T.D. Evolution of phototransduction, vertebrate photoreceptors and retina. Prog. Retinal Eye Res. 2013;36:52–119. doi: 10.1016/j.preteyeres.2013.06.001. PubMed DOI

Wen W., Khatibi S. Back to basics: Towards novel computation and arrangement of spatial sensory in images. Acta Polytech. 2016;56:409–416. doi: 10.14311/AP.2016.56.0409. DOI

Luczak E., Rosenfeld A. Distance on a hexagonal grid. IEEE Trans. Comput. 1976;25:532–533. doi: 10.1109/TC.1976.1674642. DOI

Wüthrich C.A., Stucki P. An algorithmic comparison between square- and hexagonal-based grids. CVGIP Graph. Models Image Process. 1991;53:324–339. doi: 10.1016/1049-9652(91)90036-J. DOI

Snyder W.E., Qi H., Sander W.A. Coordinate system for hexagonal pixels; Proceedings of the Medical Imaging 1999: Image Processing; San Diego, CA, USA. 20–26 February 1999; pp. 716–728.

Her I. A symmetrical coordinate frame on the hexagonal grid for computer graphics and vision. J. Mech. Des. 1993;115:447–449. doi: 10.1115/1.2919210. DOI

Her I., Yuan C.-T. Resampling on a pseudohexagonal grid. CVGIP Graph. Models Image Process. 1994;56:336–347. doi: 10.1006/cgip.1994.1030. DOI

Her I. Geometric transformations on the hexagonal grid. IEEE Trans. Image Process. 1995;4:1213–1222. doi: 10.1109/83.413166. PubMed DOI

Nagy B. Finding shortest path with neighbourhood sequences in triangular grids; Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis (ISPA 2001); Pula, Croatia. 19–21 June 2001; pp. 55–60.

Sheridan P. Ph.D. Thesis. University of Technology Sydney; Sydney, Australia: 1996. Spiral Architecture for Machine Vision.

He X. Ph.D. Thesis. University of Technology Sydney; Sydney, Australia: 1999. 2D-Object Recognition with Spiral Architecture.

Middleton L., Sivaswamy J. Edge detection in a hexagonal-image processing framework. Image Vis. Comput. 2001;19:1071–1081. doi: 10.1016/S0262-8856(01)00067-1. DOI

Middleton L., Sivaswamy J. Framework for practical hexagonal-image processing. J. Electron. Imaging. 2002;11:104–115.

Wu Q., He S., Hintz T. Virtual Spiral Architecture; Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications; Las Vegas, NV, USA. 21–24 June 2004.

He S., Hintz T., Wu Q., Wang H., Jia W. A new simulation of Spiral Architecture; Proceedings of the International Conference on Image Processing, Computer Vision and Pattern Recognition; Las Vegas, NV, USA. 26–29 June 2006.

Wen W., Khatibi S. Novel Software-Based Method to Widen Dynamic Range of CCD Sensor Images; Proceedings of the International Conference on Image and Graphics; Tianjin, China. 13–16 August 2015; pp. 572–583.

Wen W., Khatibi S. The Impact of Curviness on Four Different Image Sensor Forms and Structures. Sensors. 2018;18:429. doi: 10.3390/s18020429. PubMed DOI PMC

He X., Jia W. Hexagonal Structure for Intelligent Vision; Proceedings of the 2005 International Conference on Information and Communication Technologies; Karachi, Pakistan. 27–28 August 2005; pp. 52–64.

Horn B. Robot Vision. MIT Press; Cambridge, MA, USA: 1986.

Perlin K. An image synthesizer. ACM SIGGRAPH Comput. Graph. 1985;19:287–296. doi: 10.1145/325165.325247. DOI

Parberry I. Amortized noise. J. Comput. Graph. Tech. 2014;3:31–47.

Asharindavida F., Hundewale N., Aljahdali S. Study on hexagonal grid in image processing; Proceedings of the 2012 International Conference on Information and Knowledge Management; Kuala Lumpur, Malaysia. 24–26 July 2012.