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The current camera has made a huge progress in the sensor resolution and the lowluminance performance. However, we are still far from having an optimal camera as powerful as our eye is. The study of the evolution process of our visual system indicates attention to two major issues: the form and the density of the sensor. High contrast and optimal s...
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... we propose hexagonal computational for the image processing operation using directly the orbit domain. The flow chart of such a hexagonal computation for typical operations is shown in Figure 6. A hexagonal image, generated by the proposed method in § 3.1, is transformed to an orbit domain using the hexagonal grid related to the image. ...
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... two filter kernels, con- structed in the spatial domain, are transformed to the orbit domain using the same hexagonal grid related to the image. The process of the convolution in the orbit domain is a multiplication operation, shown as X in the middle dash box in Figure 6. According to the convolution theory in the orbit domain, the multiple convolutions can be combined to one by multiplication operations, which implies that all the image process- ing operations remain in the orbit domain and use the same hexagonal grid. ...
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Citations
... Some of the obstacles in developing new sensor arrangements are the difficulty in manufacturing, the cost, and rigidity of hardware components. The virtual deformation of the sensor arrangement [3] provides new possibilities for overcoming such obstacles. We need strong arguments to convince the involved partners in sensor development to implement the virtual deformation ideas. ...
... The new pseudo hexagonal grid is derived from a usual 2D grid by shifting each even row a half pixel to the right and leaving odd rows unattached, or of course any similar translation. The virtual Half-pixel Shift Enriched image (HS_E) is generated from the original enriched image [3] which has a square arrangement. ...
... Figure 14 shows the mean (a) and variance (b) of ratio values of ten corresponding pixel sets between each SQ and to Hex_E image. The mean (a) shows the nonlinear relation between SQ to Hex_E which was previously shown in [3,18]. The mean (a) also shows that the relation between to Hex_E is similar to the relation between SQ to Hex_E and behaves in a nonlinear manner. ...
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.
... The results show the dynamic range is widened and tonal level is extended. (b) The grid and pixel are hexagonal and square respectively and there is no or fixed gap in [29], where the hexagonal grid is generated by a half-pixel shifting, its results show that the generated hexagonal images are superior in detection of curvature edges to the square images. (c) The grid and pixel are hexagonal and there is no gap [30]. ...
Our vision system has a combination of different sensor arrangements from hexagonal to elliptical ones. Inspired from this variation in type of arrangements we propose a general framework by which it becomes feasible to create virtual deformable sensor arrangements. In the framework for a certain sensor arrangement a configuration of three optional variables are used which includes the structure of arrangement, the pixel form and the gap factor. We show that the histogram of gradient orientations of a certain sensor arrangement has a specific distribution (called ANCHOR) which is obtained by using at least two generated images of the configuration. The results showed that ANCHORs change their patterns by the change of arrangement structure. In this relation pixel size changes have 10-fold more impact on ANCHORs than gap factor changes. A set of 23 images; randomly chosen from a database of 1805 images, are used in the evaluation where each image generates twenty-five different images based on the sensor configuration. The robustness of ANCHORs properties is verified by computing ANCHORs for totally 575 images with different sensor configurations. We believe by using the framework and ANCHOR it becomes feasible to plan a sensor arrangement in the relation to a specific application and its requirements where the sensor arrangement can be planed even as combination of different ANCHORs.
... However practical issues and history of camera development have made us to use fixed arrangements and forms of pixel sensors. Our previous works [1,2] showed that despite the limitations of hardware, it is possible to implement a software method to change the size of pixel sensors. In this paper, we present a software-based method to change the arrangement and form of pixel sensors. ...
The arrangement and form of the image sensor have a fundamental effect on any further image processing operation and image visualization. In this paper, we present a software-based method to change the arrangement and form of pixel sensors that generate hexagonal pixel forms on a hexagonal grid. We evaluate four different image sensor forms and structures, including the proposed method. A set of 23 pairs of images; randomly chosen, from a database of 280 pairs of images are used in the evaluation. Each pair of images have the same semantic meaning and general appearance, the major difference between them being the sharp transitions in their contours. The curviness variation is estimated by effect of the first and second order gradient operations, Hessian matrix and critical points detection on the generated images; having different grid structures, different pixel forms and virtual increased of fill factor as three major properties of sensor characteristics. The results show that the grid structure and pixel form are the first and second most important properties. Several dissimilarity parameters are presented for curviness quantification in which using extremum point showed to achieve distinctive results. The results also show that the hexagonal image is the best image type for distinguishing the contours in the images.
... In the regular hexagonal lattice, the vertical and horizontal pitch ratio is ≈ 3 : 2 0.8660, and in the "brick wall" approach, the ratio is 1:1, while in the "hyperpel" approach, the ratio is 7:8 = 0.8750. Therefore, the "hyperpel" approach can be treated as a good approximation and it is the most common displaying approach used in current hexagonal image research [2,3,[16][17][18]. ...
Hexagonal image processing is theoretically superior to that based on the common square lattice, and due to the lack of practical imaging devices, this paper intends to implement a simulated display. The paper investigates the sampling lattices used in the hexagonal image processing, and finds that variable lattices occur in hexagonal discrete Fourier transform (HDFT), while the most commonly used “hyperpel” approach, due to its fixed cell pattern, cannot handle such displaying tasks. Then, the paper proposes to represent each pixel with the exact Voronoi cell (VC) according to the sampling lattice. In the paper, a simple algorithm is presented to compute the VC vertices, and each simulated pixel is constructed with the VC filled with its intensity value, and then the simulated display is implemented by the tessellation of each simulated pixel on the correct lattice position. Finally, experimental results show that the proposed simulated display can display data without geometric distortion.
The quality assessment of a high dynamic image is a challenging task. The few available no reference image quality methods for high dynamic range images are generally in evaluation stage. The most available image quality assessment methods are designed to assess low dynamic range images. In the paper, we show the assessment of high dynamic range images which are generated by utilizing a virtually flexible fill factor on the sensor images. We present a new method in the assessment process and evaluate the amount of improvement of the generated high dynamic images in comparison to original ones. The results show that the generated images not only have more number of tonal levels in comparison to original ones but also the dynamic range of images have significantly increased due to the measurable improvement values.
