Department of Technology and Aesthetics, Blekinge Institute of Technology, 37179 Karlskrona, Sweden.
Department of Physics, Czech Technical University, 11519 Prague 1, Czech Republic.
Sensors (Basel). 2019 Jan 29;19(3):568. doi: 10.3390/s19030568.
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.
我们视觉系统的进化过程研究表明，存在着变异性的空间排列；从中央凹的密集六边形到周边视网膜的稀疏圆形结构。今天的传感器空间排列是受到我们视觉系统的启发。然而，我们还没有超越刚性的矩形，并且在较小的范围内，只有六边形的传感器排列。即使在这种情况下，也需要直接评估矩形和六边形传感器排列之间的差异，即无需将一种排列转换为另一种排列。在本文中，我们提出了一种方法来创建一个通用空间，以处理任何空间排列，并评估它们之间的差异，例如，在矩形和六边形之间。这样的空间是通过实现离散 Weyl 群轨道函数变换的连续扩展来创建的，该变换将离散排列扩展到连续排列。通过比较两种不同的半像素移位方法和虚拟六边形方法，从每个矩形图像生成两种类型的生成六边形图像，来演示该空间的实现。在实验中，使用十种不同的 Perlin 噪声模式生成十种具有变曲率内容的纹理图像，添加到初始的 2D 高斯分布模式图像中。然后，从每个离散图像中获得通用空间，以评估原始矩形图像与其相应的六边形图像之间的差异。结果表明，该空间便于使用友好的工具来处理排列，并评估不同空间排列之间的变化，在实验中，与矩形图像相比，六边形图像显示出更丰富的强度变化、非线性行为和更大的动态范围。
