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ObjectiveTo construct the 3D point cloud model of green plants a large number of clear images are needed. Due to the limitation of the depth of field of the lens, part of the image would be out of focus when the green plant image with a large depth of field is collected, resulting in problems such as edge blurring and texture detail loss, which greatly affects the accuracy of the 3D point cloud model. However, the existing processing algorithms are difficult to take into account both processing quality and processing speed, and the actual effect is not ideal. The purpose of this research is to improve the quality of the fused image while taking into account the processing speed.MethodsA plant image fusion method based on non-subsampled shearlet transform (NSST) based parameter-adaptive dual channel pulse-coupled neural network (PADC-PCNN) and stationary wavelet transform (SWT) was proposed. Firstly, the RGB image of the plant was separated into three color channels, and the G channel with many features such as texture details was decomposed by NSST in four decomposition layers and 16 directions, which was divided into one group of low frequency subbands and 64 groups of high frequency subbands. The low frequency subband used the gradient energy fusion rule, and the high frequency subband used the PADC-PCNN fusion rule. In addition, the weighting of the eight-neighborhood modified Laplacian operator was used as the link strength of the high-frequency fusion part, which enhanced the fusion effect of the detailed features. At the same time, for the R and B channels with more contour information and background information, a SWT with fast speed and translation invariance was used to suppress the pseudo-Gibbs effect. Through the high-precision and high-stability multi-focal length plant image acquisition system, 480 images of 8 experimental groups were collected. The 8 groups of data were divided into an indoor light group, natural light group, strong light group, distant view group, close view group, overlooking group, red group, and yellow group. Meanwhile, to study the application range of the algorithm, the focus length of the collected clear plant image was used as the reference (18 mm), and the image acquisition was adjusted four times before and after the step of 1.5 mm, forming the multi-focus experimental group. Subjective evaluation and objective evaluation were carried out for each experimental group to verify the performance of the algorithm. Subjective evaluation was analyzed through human eye observation, detail comparison, and other forms, mainly based on the human visual effect. The image fusion effect of the algorithm was evaluated using four commonly used objective indicators, including average gradient (AG), spatial frequency (SF), entropy (EN), and standard deviation (SD).Results and DiscussionsThe proposed PADC-PCNN-SWT algorithm and other five algorithms of common fast guided filtering algorithm (FGF), random walk algorithm (RW), non-subsampled shearlet transform based PCNN (NSST-PCNN) algorithm, SWT algorithm and non-subsampled shearlet transform based parameter-adaptive dual-channel pulse-coupled neural network (NSST-PADC) and were compared. In the objective evaluation data except for the red group and the yellow group, each index of the PADC-PCNN-SWT algorithm was second only to the NSST-PADC algorithm, but the processing speed was 200.0% higher than that of the NSST-PADC algorithm on average. At the same time, compared with the FDF, RW, NSST-PCNN, and SWT algorithms, the PADC-PCN -SWT algorithm improved the clarity index by 5.6%, 8.1%, 6.1%, and 17.6%, respectively, and improved the spatial frequency index by 2.9%, 4.8%, 7.1%, and 15.9%, respectively. However, the difference between the two indicators of information entropy and standard deviation was less than 1%, and the influence was ignored. In the yellow group and the red group, the fusion quality of the non-green part of the algorithm based on PADC-PCNN-SWT was seriously degraded. Compared with other algorithms, the sharpness index of the algorithm based on PADC-PCNN-SWT decreased by an average of 1.1%, and the spatial frequency decreased by an average of 5.1%. However, the indicators of the green part of the fused image were basically consistent with the previous several groups of experiments, and the fusion effect was good. Therefore, the algorithm based on PADC-PCNN-SWT only had a good fusion effect on green plants. Finally, by comparing the quality of four groups of fused images with different focal length ranges, the results showed that the algorithm based on PADC-PCNN-SWT had a better contour and color restoration effect for out-of-focus images in the range of 15-21 mm, and the focusing range based on PADC-PCNN-SWT was about 6 mm.ConclusionsThe multi-focal length image fusion algorithm based on PADC-PCNN-SWT achieved better detail fusion performance and higher image fusion efficiency while ensuring fusion quality, providing high-quality data, and saving a lot of time for building 3D point cloud model of green plants.

It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters m (m∈N) and λ (λ>0). The constant factors expressed by the Euler number and π as well as by the Bernoulli number and π, respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.

It is shown that a weighted Hilbert inequality for double series can be established by introducing a proper weight function. Thus, a quite sharp result of the classical Hilbert inequality for double series is obtained. And a similar result for the Hilbert integral inequality is also proved. Some applications are considered.

It is shown that some new extensions of Hilbert's integral inequality with parameter λ(λ>1/2) can be established by introducing a proper weight function. In particular, when λ=1, a refinement of Hilbert's integral inequality is obtained. As applications, some new extensions of Widder's inequality and Hardy-Littlewood's inequality are given.

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u(x) and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality in Hp function are given.

Abstract: The aim of this study was to elucidate the pharmacokinetics of olerciamide A in rats after oral and intravenous administration of Portulaca oleracea L. extract by a simple and rapid ultra high‐performance liquid chromatography method with bergapten as internal standard. The pharmacokinetic results indicated that olerciamide A was rapidly distributed with a time to peak concentration of 30 min after oral administration and presented a low oral absolute bioavailability of 4.57%. The metabolism of olerciamide A in rats was also investigated using ultra‐high‐performance liquid chromatography electrospray coupled with quadrupole–time of flight mass spectrometry to elucidate the reason for the low absolute bioavailability of olerciamide A and seven metabolites of oleraciamide A were found in rat plasma and urine. [ABSTRACT FROM AUTHOR]

Two novel alkaloids named oleraciamide A (1) and oleraciamide B (2) were isolated fromPortulaca oleraceaL., and spectroscopic methods including 1D and 2D nuclear magnetic resonance and high-resolution electrospray ionisation quadrupole-time of flight mass spectrometer spectrometry techniques are employed to determine their structures. Oleraciamide A (1) was evaluated no cytotoxicity at concentrations up to 80 μM over 72 h against human adipose-derived stem cells (hADSCs) by CCK-8 method. [ABSTRACT FROM PUBLISHER]

In this paper we study the inequalities of the determinants of the positive definite matrices and the invertible matrices by applying the integral method and matrix theory such that extensions of Fan Ky's inequality are established. And then an improvement of Fan Ky's inequality is given by using the positive definiteness of Gram matrix. [ABSTRACT FROM AUTHOR]

In this paper it is shown that an extension of the Hilbert integral inequality can be built by introducing a parameter λ (λ > -1). Constant factor expressed by Γ- function is proved to be the best possible. As applications, some equivalent forms are given. [ABSTRACT FROM AUTHOR]

In this paper it is shown that the Hilbert inequality for double series can be improved by introducing a weight function of the form (Multiple line equation(s) cannot be represented in ASCII text), where n ϵ N. A similar result for the Hilbert integral inequality is also given. As applications, some sharp results of Hardy-Littlewood's theorem and Widder's theorem are obtained. [ABSTRACT FROM AUTHOR]

The article discusses a study which examines the effectiveness of the weighted Hilbert inequality in establishing new inequalities. The study found that weighted Hilbert inequality is effective in establishing new inequalities with the help of the weight function method and the technique of analysis. The study revealed that the constant factor of the Hilbert theorem for double series is the best possible value of the new inequalities. The study also assessed that real function of the weighted Hilbert inequality has satisfied the conditions of establishing new inequalities.