Hexagonal structure for intelligent vision

Using hexagonal grids to represent digital images have been studied for more than 40 years. Increased processing capabilities of graphic devices and recent improvements in CCD technology have made hexagonal sampling attractive for practical applications and brought new interests on this topic. The hexagonal structure is considered to be preferable to the rectangular structure due to its higher sampling efficiency, consistent connectivity and higher angular resolution and is even proved to be superior to square structure in many applications. Since there is no mature hardware for hexagonal-based image capture and display, square to hexagonal image conversion has to be done before hexagonal-based image processing. Although hexagonal image representation and storage has not yet come to a standard, experiments based on existing hexagonal coordinate systems have never ceased. In this paper, we firstly introduced general reasons that hexagonally sampled images are chosen for research. Then, typical hexagonal coordinates and addressing schemes, as well as hexagonal based image processing and applications, are fully reviewed. © 2005 IEEE

End-to-end analysis of hexagonal vs rectangular sampling in digital imaging systems

The purpose of this study was to compare two common methods for image sampling in digital image processing: hexagonal sampling and rectangular sampling. The two methods differ primarily in the arrangement of the sample points on the image focal plane. In order to quantitatively compare the two sampling methods, a mathematical model of an idealized digital imaging system was used to develop a set of mean-squared-error fidelity loss metrics. The noiseless continuous/discrete/continuous end-to-end digital imaging system model consisted of four independent components: an input scene, an image formation point spread function, a sampling function, and a reconstruction function. The metrics measured the amount of fidelity lost by an image due to image formation, sampling and reconstruction, and the combined loss for the entire system

Approximation of the Euclidean distance by Chamfer distances

Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon "small" neighborhoods still outperforms it e.g. in terms of computation time. In this paper we determine the best possible maximum relative error of chamfer distances under various boundary conditions. In each case some best approximating sequences are explicitly given. Further, because of possible practical interest, we give all best approximating sequences in case of small (i.e. 5x5 and 7x7) neighborhoods

Template Lattices for a Cross-Correlation Search for Gravitational Waves from Scorpius X-1

We describe the application of the lattice covering problem to the placement of templates in a search for continuous gravitational waves from the low-mass X-Ray binary Scorpius X-1. Efficient placement of templates to cover the parameter space at a given maximum mismatch is an application of the sphere covering problem, for which an implementation is available in the LatticeTiling software library. In the case of Sco X-1, potential correlations, in both the prior uncertainty and the mismatch metric, between the orbital period and orbital phase, lead to complications in the efficient construction of the lattice. We define a shearing coordinate transformation which simultaneously minimizes both of these sources of correlation, and allows us to take advantage of the small prior orbital period uncertainty. The resulting lattices have a factor of about 3 fewer templates than the corresponding parameter space grids constructed by the prior straightforward method, allowing a more sensitive search at the same computing cost and maximum mismatch.Comment: 21 pages, 8 figure

Elliptical Distance Transforms And Object Splitting

The classical morphological method to separate fused objects in binary images is to use the watershed transform on the complement of the distance transform of the binary image. This method assumes roughly disk-like objects and cannot separate objects when they are fused together beyond a certain point. In this paper we revisit the issue by assuming that fused objects are unions of ellipses rather than mere disks. The problem is recast in terms of finding the constituent primary grains given a boolean model of ellipses. To this end, we modify the well-known pseudo-Euclidean distance transform algorithm to generate arbitrary elliptical distance transforms to reduce the dimension of the problem and we present a goodness-of-fit measure that allows us to select ellipses. The results of the methods are given on both synthetic sample boolean models and real data