The representation of visual depth perception based on the plenoptic function in the retina and its neural computation in visual cortex V1.

BACKGROUND: How it is possible to "faithfully" represent a three-dimensional stereoscopic scene using Cartesian coordinates on a plane, and how three-dimensional perceptions differ between an actual scene and an image of the same scene are questions that have not yet been explored in depth. They seem like commonplace phenomena, but in fact, they are important and difficult issues for visual information processing, neural computation, physics, psychology, cognitive psychology, and neuroscience. RESULTS: The results of this study show that the use of plenoptic (or all-optical) functions and their dual plane parameterizations can not only explain the nature of information processing from the retina to the primary visual cortex and, in particular, the characteristics of the visual pathway's optical system and its affine transformation, but they can also clarify the reason why the vanishing point and line exist in a visual image. In addition, they can better explain the reasons why a three-dimensional Cartesian coordinate system can be introduced into the two-dimensional plane to express a real three-dimensional scene. CONCLUSIONS: 1. We introduce two different mathematical expressions of the plenoptic functions, Pw and Pv that can describe the objective world. We also analyze the differences between these two functions when describing visual depth perception, that is, the difference between how these two functions obtain the depth information of an external scene.2. The main results include a basic method for introducing a three-dimensional Cartesian coordinate system into a two-dimensional plane to express the depth of a scene, its constraints, and algorithmic implementation. In particular, we include a method to separate the plenoptic function and proceed with the corresponding transformation in the retina and visual cortex.3. We propose that size constancy, the vanishing point, and vanishing line form the basis of visual perception of the outside world, and that the introduction of a three-dimensional Cartesian coordinate system into a two dimensional plane reveals a corresponding mapping between a retinal image and the vanishing point and line.

Effect of foliage applied chitosan-based silicon nanoparticles on arsenic uptake and translocation in rice (Oryza sativa L.).

In this study, chitosan-based silicon nanoparticles (Chsi-NPs) are prepared that primarily consists of C (57.9%), O (31.3%), N (5.6%), and Si (3.5%) and are 10-180 nm in size. We then explore the effect on the foliage applied on rice planted on soil contaminated with 104 mg·kg-1 arsenic (As); low (3 mg·L-1)and high (15 mg·L-1) doses of the foliar Chsi-NPs are administered during the rice grain filling stage. The results showed that the higher dose foliar Chsi-NPs treatment reduced the As concentration in the grain by 61.2% but increased As concentration in the leaves by 47.1% compared to the control treatment. The foliar spraying of the Chsi-NPs inhibited As transport to the grain by facilitating the attachment of As to the cell wall, with higher doses of the foliar Chsi-NPs treatment increased by 8.7%. The foliar spraying of Chsi-NPs increased the malondialdehyde levels by 18.4%, the catalase activity by 49.0%, and the glutathione activity by 99.0%. These results indicated that the foliar Chsi-NPs application was effective for alleviating As toxicity and accumulation in rice. This study provides a novel method for effectively alleviating As accumulation in rice.

Neural computation of visual imaging based on Kronecker product in the primary visual cortex.

BACKGROUND: What kind of neural computation is actually performed by the primary visual cortex and how is this represented mathematically at the system level? It is an important problem in the visual information processing, but has not been well answered. In this paper, according to our understanding of retinal organization and parallel multi-channel topographical mapping between retina and primary visual cortex V1, we divide an image into orthogonal and orderly array of image primitives (or patches), in which each patch will evoke activities of simple cells in V1. From viewpoint of information processing, this activated process, essentially, involves optimal detection and optimal matching of receptive fields of simple cells with features contained in image patches. For the reconstruction of the visual image in the visual cortex V1 based on the principle of minimum mean squares error, it is natural to use the inner product expression in neural computation, which then is transformed into matrix form. RESULTS: The inner product is carried out by using Kronecker product between patches and function architecture (or functional column) in localized and oriented neural computing. Compared with Fourier Transform, the mathematical description of Kronecker product is simple and intuitive, so is the algorithm more suitable for neural computation of visual cortex V1. Results of computer simulation based on two-dimensional Gabor pyramid wavelets show that the theoretical analysis and the proposed model are reasonable. CONCLUSIONS: Our results are: 1. The neural computation of the retinal image in cortex V1 can be expressed to Kronecker product operation and its matrix form, this algorithm is implemented by the inner operation between retinal image primitives and primary visual cortex's column. It has simple, efficient and robust features, which is, therefore, such a neural algorithm, which can be completed by biological vision. 2. It is more suitable that the function of cortical column in cortex V1 is considered as the basic unit of visual image processing (such unit can implement basic multiplication of visual primitives, such as contour, line, and edge), rather than a set of tiled array filter. Fourier Transformation is replaced with Kronecker product, which greatly reduces the computational complexity. The neurobiological basis of this idea is that a visual image can be represented as a linear combination of orderly orthogonal primitive image containing some local feature. In the visual pathway, the image patches are topographically mapped onto cortex V1 through parallel multi-channels and then are processed independently by functional columns. Clearly, the above new perspective has some reference significance to exploring the neural mechanisms on the human visual information processing.