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Deblurring images of dynamic scenes is a challenging task because blurring occurs due to a combination of many factors. In recent years, the use of multi-scale pyramid methods to recover high-resolution sharp images has been extensively studied. We have made improvements to the lack of detail recovery in the cascade structure through a network using progressive integration of data streams. Our new multi-scale structure and edge feature perception design deals with changes in blurring at different spatial scales and enhances the sensitivity of the network to blurred edges. The coarse-to-fine architecture restores the image structure, first performing global adjustments, and then performing local refinement. In this way, not only is global correlation considered, but also residual information is used to significantly improve image restoration and enhance texture details. Experimental results show quantitative and qualitative improvements over existing methods.

An important goal of color image gray-scale is to keep the edge details of the original color image as much as possible. In many cases, the degree of feature discrimination is maintained, but in some cases, edge details are still lost or blurred. Therefore, this paper first uses an improved non-linear global mapping grayscale method to grayscale the color image, and then proposes a grayscale image detail enhancement algorithm based on rolling guided filtering. The method in this paper is to enhance the edge details of the grayscale image by rolling guided filter processing on the basis of the grayscale image. In addition, the rolling-guided filter is a local linear model with better edge retention characteristics, which can overcome the defect that other filters are prone to gradient flips on the edges where the gray level of the image changes sharply, causing the image to appear “false edges”. The experimental results show that when the traditional method loses or blurs the detailed features, the method in this paper can maintain better detailed features.

Let N be a sufficiently large real number. In this paper, it is proved that, for $$1

Let N be a sufficiently large real number. In this paper, we prove that, for $$10$$ , the Diophantine inequality $$\begin{aligned} \big |p_1^c+p_2^c+p_3^c-N\big

Remote sensing images with high spatial resolution and high spectral resolution have important applications in human society. In general, due to the limitations faced by the optical sensors’, we are limited to obtain only low spatial resolution multispectral images (MS) and high spatial resolution panchromatic images (PAN). To address this limitation, this study proposes a pyramid-attention based multi-scale feature fusion network (PAMF-Net) that combines the pyramid attention mechanism and feature aggregation. Initially, the MS and PAN images are input to the network, and the PAN images pass through the input pyramid branch to generate a multi-level receiving domain. Then, the result is combined with the features of the MS image as the input of the encoder, and these composite features are input to the pyramid attention mechanism module to capture multi-scale corresponding features. Next, the result of the input pyramid branch is input to the feature aggregation module to seamlessly merge with the features of the pyramid attention mechanism. Finally, in the encoding stage, multiple levels of features are multiplexed as encoding secondary lines by skipping connections to obtain high-quality HRMS images. After quantitative and qualitative experiments, the results show that our method is superior to other advanced methods.

Multi-focus image fusion is always a difficult problem in digital image processing. To achieve efficient integration, we propose a new end-to-end network. This network uses the residual atrous spatial pyramid pooling module to extract multi-level features from the space of different scales and share parameters to ensure the consistency and correspondence of features. We also introduced a disparities attention module for the network which allows for information retention. These two parts can make our method overcome the difficulties of target edge artifacts, small range blur, poor detail capture, and so on. In addition, in order to improve the semantic ambiguity easily caused by unsupervised learning, we also proposed a new multi-focus image fusion dataset with groundtruth for supervised learning. We performed sufficient experiments, and the results show that the network can quickly capture the corresponding features of multi-focus images, and improve the fusion performance with less computation and lower storage cost. Compared with the existing nine fusion methods, our network is superior to other methods in subjective visual evaluation and objective evaluation, reaching a higher level.

Let $$\mathcal {P}_r$$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, we establish a theorem of Bombieri–Vinogradov type for the Piatetski–Shapiro primes $$p=[n^{1/\gamma }]$$ with $$\frac{85}{86}

According to the atmospheric physical model, we can use accurate transmittance and atmospheric light information to convert a hazy image into a clean one. The scene-depth information is very important for image dehazing due to the transmittance directly corresponds to the scene depth. In this paper, we propose a multi-scale depth information fusion network based on the U-Net architecture. The model uses hazy images as inputs and extracts the depth information from these images; then, it encodes and decodes this information. In this process, hazy image features of different scales are skip-connected to the corresponding positions. Finally, the model outputs a clean image. The proposed method does not rely on atmospheric physical models, and it directly outputs clean images in an end-to-end manner. Through numerous experiments, we prove that the multi-scale deep information fusion network can effectively remove haze from images; it outperforms other methods in the synthetic dataset experiments and also performs well in the real-scene test set.

Rice accumulates higher levels of cadmium (Cd) in grain than other cereals, and hybrid rice varieties cover around half of the total rice area in China. Therefore, understanding the phenotypic and genetic characteristics of Cd accumulation in rice hybrids is vital for food safety. An incomplete diallel cross design was used to analyse the heritability and combining ability of Cd accumulation in rice hybrids growing in soil contaminated with Cd. The quantitative real-time PCR was used to detect the gene expressions that related to Cd uptake and transport. The Cd contents in brown rice, nodes and roots were detected by ICPOES, and the Cd contents in xylem sap were detected by ICPMS. Additive effects dominated the Cd accumulation in brown rice, upper nodes, and the Cd translocation efficiency from roots to nodes of hybrids. The Cd accumulation in brown rice was positively correlated with Cd accumulation in upper nodes and translocation efficiency from roots to nodes. Regarding the general combining ability, the restorer lines R2292 and R2265, and the male sterile lines KeBX58S, Ke20A, Ke76-1BS and Ke244-1BS were found to be potential elite parental lines for developing hybrid rice with low Cd accumulation. Hybrid rice with low Cd accumulation in brown rice can be derived from parental lines with low general combining ability for Cd content in brown rice.

Let $$\mathcal {P}_r$$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan (Bull Lond Math Soc 17(1):17–20, 1985) for ternary ‘admissible exponent’. Moreover, we use the refined ‘admissible exponent’ to prove that, for $$3\leqslant k\leqslant 14$$ and for every sufficiently large even integer n, the following equation $$\begin{aligned} n=x^2+p_1^2+p_2^3+p_3^3+p_4^3+p_5^k \end{aligned}$$ is solvable with x being an almost-prime $$\mathcal {P}_{r(k)}$$ and the other variables primes, where r(k) is defined in Theorem 1.1. This result constitutes a deepening of previous results.

Images captured by cameras in low-light conditions have low quality and appear dark due to insufficient light exposure, which critically affects the view. Most of the traditional enhancement methods are based on the entire image for exposure enhancement, so overexposed areas in the image have the risk of secondary enhancement. In order to fully consider the exposure in low-light images, we propose a low-light image enhancement based on multi-illumination estimation, which can robustly produce high-quality results for various underexposures. The core of the proposed method is to derive multiple exposure correction images using light estimation. Then, we used a Laplacian multi-scale fusion method to combine the weight map and the images with different degrees of exposure. We used gamma correction and inversion on the original image to produce images with different exposure levels (such as underexposure, overexposure, and partial area overexposure and underexposure). The gamma-corrected image is used for lighting adjustment of underexposed areas in low-light images, while the inversion image is used for adjustment of the overexposed regions. We performed experiments on various images using multiple methods and evaluated and compared the experimental results, qualitatively and quantitatively. Experimental results show that the proposed method in this study can effectively eliminate the effects of low light and improve image quality.

Rain not only reduces visibility, but also prevents many computer vision algorithms from functioning properly. Removing rain from a single image is an important issue in the field of computer vision. Rain usually produces a phenomenon similar to fog, which is more pronounced when the rain is dense. We constructed a rain model, including rain streaks and fog generated by rainfall. Based on this model, we constructed a multi-task learning network to learn the rain streaks and fog in the image as well as the final clean background. To take advantage of contextual information, we use an expanded convolution network to handle different levels of rain and fog. We learn the residual images of fog and rain based on the deep residual network to avoid the influence of inaccurate parameter estimation on the results. Experiments show that the method in this paper can effectively remove rain and fog in the image.

In this paper, we present a way to create an accurate trimap. Since the matting problem is a serious under-constrained problem, the user is required to provide additional constraint information to estimate the alpha value of the mixed pixels. The smaller the area of the unknown region of the user-provided trimap, the more accurate the alpha value of the estimated mixed pixels. But manually creating the trimap is a complicated and time-consuming task, and it is even impractical to manually create trimaps for some tasks. We use the ant colony algorithm to determine the boundary information of the foreground objects, and fuse different pheromone images at the superpixel level to create an accurate trimap. The trimap generated by our method also has higher precision when the edge of the foreground object has a lot of fine hair. Experiments show that the high-quality trimap can be generated by the method of this paper, which can effectively improve the performance of the matting algorithm and achieve accurate alpha mask estimation.

Under low illumination, the colour constancy of human vision can be used for correctly determining the colour of objects according to the fixed reflection coefficient of external light and objects. However, video image acquisition equipment does not implement the colour constancy characteristic of the human visual system. Under low illumination, only a small amount of light is reflected from the surface of the imaged object; as a result, the captured image is underexposed. After statistical analysis of low-light images, these inverted underexposed images appear foggy. Inversion is a uniform and reversible operation that is performed on the entire image. Hereby, a method is proposed for resolving low-light images using conventional physical models. First, a low-light image is inverted for obtaining a foggy image. Subsequently, a pyramid-type dense residual block network and a dark channel prior K-means classification method are applied to the foggy image, to calculate the transmission and atmospheric light. Finally, the parameters obtained from this solution are incorporated into the low-light imaging model to obtain a clear image. We subjectively and qualitatively analysed the experimental results, and used information entropy and average gradient for objective quantitative analysis. We demonstrate that the algorithm improves the overall brightness and contrast of the imaged scenes, and the obtained enhanced images are clear and natural.

Let N be a sufficiently large integer. In this paper, it is proved that, with at most $$O(N^{7/18+\varepsilon })$$ exceptions, all even positive integers up to N can be represented in the form $$p_1^2+p_2^2+p_3^3+p_4^3+p_5^4+p_6^4$$ , where $$p_1,p_2,p_3,p_4,p_5,p_6$$ are prime numbers, which constitutes an improvement over some previous work.

Improper functioning, or lack, of human cone cells leads to vision defects, making it impossible for affected persons to distinguish certain colors. Colorblind persons have color perception, but their ability to capture color information differs from that of normal people: colorblind and normal people perceive the same image differently. It is necessary to devise solutions to help persons with color blindness understand images and distinguish different colors. Most research on this subject is aimed at adjusting insensitive colors, enabling colorblind persons to better capture color information, but ignores the attention paid by colorblind persons to the salient areas of images. The areas of the image seen as salient by normal people generally differ from those seen by the colorblind. To provide the same saliency for colorblind persons and normal people, we propose a saliency-based image correction algorithm for color blindness. Adjusted colors in the adjusted image are harmonious and realistic, and the method is practical. Our experimental results show that this method effectively improves images, enabling the colorblind to see the same salient areas as normal people.

Let N be a sufficiently large integer. In this paper, it is proved that, with at most $$O(N^{4/27+\varepsilon })$$ exceptions, all even positive integers up to N can be represented in the form $$p_1^2+p_2^2+p_3^3+p_4^3+p_5^6+p_6^6$$ , where $$p_1,p_2,p_3,p_4,p_5,p_6$$ are prime numbers. This gives a large improvement of a recent result $$O(N^{127/288+\varepsilon })$$ due to Liu (Proc. Indian Acad. Sci. (Math. Sci.) 130(1) (2020) Article ID. 8).

Let d(n) denote the Dirichlet divisor function. Define $$\begin{aligned} \mathcal {S}_k(x,y):= \sum _{\begin{array}{c} x-y

This paper proposes a novel method for detecting a photographer's shooting trajectory based on select images. Firstly, in a Lab color space, directional information and perceived color information were combined, and similar images were found by a color difference histogram. Local invariant descriptors were then constructed by the contrast context histogram method to match feature point areas and their context, and to judge whether these areas corresponded. Through this, the corresponding relationship for feature points between image sequences was obtained. Furthermore, the essential matrix for a pair of images was obtained through the singular value decomposition method to determine photographer trajectories.

We prove that there are infinite cube-free numbers of the form [n c ] for any fixed real number c ∈ (1, 11/6).

Biologic products encounter various types of interfacial stress during development, manufacturing, and clinical administration. When proteins come in contact with vapor-liquid, solid-liquid, and liquid-liquid surfaces, these interfaces can significantly impact the protein drug product quality attributes, including formation of visible particles, subvisible particles, or soluble aggregates, or changes in target protein concentration due to adsorption of the molecule to various interfaces. Protein aggregation at interfaces is often accompanied by changes in conformation, as proteins modify their higher order structure in response to interfacial stresses such as hydrophobicity, charge, and mechanical stress. Formation of aggregates may elicit immunogenicity concerns; therefore, it is important to minimize opportunities for aggregation by performing a systematic evaluation of interfacial stress throughout the product development cycle and to develop appropriate mitigation strategies. The purpose of this white paper is to provide an understanding of protein interfacial stability, explore methods to understand interfacial behavior of proteins, then describe current industry approaches to address interfacial stability concerns. Specifically, we will discuss interfacial stresses to which proteins are exposed from drug substance manufacture through clinical administration, as well as the analytical techniques used to evaluate the resulting impact on the stability of the protein. A high-level mechanistic understanding of the relationship between interfacial stress and aggregation will be introduced, as well as some novel techniques for measuring and better understanding the interfacial behavior of proteins. Finally, some best practices in the evaluation and minimization of interfacial stress will be recommended.

Spray-dried dispersions (SDDs) have become an important formulation technology for the pharmaceutical product development of poorly water-soluble (PWS) compounds. Although this technology is now widely used in the industry, especially in the early-phase development, the lack of mechanistic understanding still causes difficulty in selecting excipients and predicting stability of SDD-based drug products. In this review, the authors aim to discuss several principles of polymer science pertaining to the development of SDDs, in terms of selecting polymers and solvents, optimizing drug loading, as well as assessing physical stability on storage and supersaturation maintenance after dissolution, from both thermodynamic and kinetic considerations. In order to choose compatible solvents with both polymers and active pharmaceutical ingredients (APIs), a symmetric Flory-Huggins interaction (Δχ ∼0) approach was introduced. Regarding spray drying of polymer-API solutions, low critical solution temperature (LCST) was discussed for setting the inlet temperature for drying. In addition, after being exposed to moisture, SDDs are practically converted to ternary systems with asymmetric Flory-Huggins interactions, which are thermodynamically not favored. In this case, the kinetics of phase separation plays a significant role during the storage and dissolution of SDD-based drug products. The impact of polymers on the supersaturation maintenance of APIs in dissolution media was also discussed. Moreover, the nature of SDDs, with reference to solid solution and the notion of solid solubility, was examined in the context of pharmaceutical application. Finally, the importance of robust analytical techniques to characterize the SDD-based drug products was emphasized, considering their complexity.

Although using spray-dried dispersions (SDDs) to improve the bioavailability of poorly water-soluble compounds has become a common practice in supporting the early phases of clinical studies, their performance evaluation, whether in solid dosage forms or alone, still presents significant challenges. A microcentrifuge dissolution method has been reported to quickly assess the dissolution performance of SDDs. While the microcentrifuge dissolution method has been used in the SDD community, there is still a need to understand the mechanisms about the molecular species present in supernatant after centrifugation, the molecular nature of active pharmaceutical ingredients (APIs), as well as the impact of experimental conditions. In this paper, we aim to assess the effect of API and polymer properties on the dissolution behavior of SDDs along with centrifuging parameters, and for this, two poorly water-soluble compounds (indomethacin and ketoconazole) and two commonly used polymers in the pharmaceutical industry (PVP and HPMC-AS) were chosen to prepare SDDs. A typical microcentrifuge dissolution procedure as reported in the publication (Curatolo et al., Pharm Res 26:1419-1431, 2009) was followed. In addition, after separation of the supernatant from precipitation, some of the samples were filtered through filters of various sizes to investigate the particulate nature (particle size) of the supernatant. Furthermore, the centrifuge speed was varied to study sedimentation of API, SDD, or polymer particles. The results indicated that for the SDDs of four drug-polymer pairs, microcentrifuge dissolution exhibited varied behaviors, depending on the polymer and the drug used. The SDDs of indomethacin with either PVP or HPMC-AS showed a reproducible dissolution with minimum variability even after filtration and subjecting to varied centrifugation speed, suggesting that the supernatant behaved solution-like. However, ketoconazole-PVP and ketoconazole-HPMC-AS SDDs displayed a significant variation in concentration as the speed of centrifugation and the pore sizes of filters were altered, indicating that their supernatant was heterogeneous with the presence of particulates. In conclusion, microcentrifuge dissolution method was more suitable for indomethacin-PVP and indomethacin-HPMC-AS systems compared with ketoconazole-PVP and ketoconazole-HPMC-AS. Therefore, the use of microcentrifuge dissolution method depends on both compounds and polymers selected, which should be examined case by case.

This study aimed in understanding the degradation behaviors of an IgG 1 subtype therapeutic monoclonal antibody A (mAb-A) associated with pH and buffer species. The information obtained in this study can augment conventional, stability-based screening paradigms by providing the direction necessary for efficient experimental design. Differential scanning calorimetry (DSC) was used for studying conformational stability. Dynamic light scattering (DLS) was utilized to generate B 22*, a modified second virial coefficient for the character of protein-protein interaction. Size-exclusion chromatography (SEC) and hydrophobic interaction chromatography (HIC) were employed to separate degradation products. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) was used for determining the molecular size and liquid chromatography mass spectrometry (LC-MS) were used for identifying the sequence of the separated fragments. The results showed that both pH and buffer species played the roles in controlling the degradation behaviors of mAb-A, but the pH was more significant. In particular, pH 4.5 induced additional thermal transition peaks occurring at a low temperature compared with pH 6.5. A continual temperature-stress study illustrated that the additional thermal transition peaks related to the least stable structure and a greater fragmentation. Although mAb-A showed the comparable conformational structures and an identical amount of aggregates at time zero between the different types of buffer species at pH 6.5, the aggregation formation rate showed a buffer species-dependent discrepancy over a temperature-stress period. It was found that the levels of aggregations associated with the magnitudes of protein-protein interaction forces.

In this paper, we propose a new robust feature extraction algorithm for 3D models based on principal curvature direction. Generally, the feature regions tend to be more noisy, so it demands a robust technique to handle features effectively. Because the integral invariants are robust against noise, the principal curvature information is estimated based on principal component analysis. After fuzzy filtering of the principal curvature direction, it becomes a good description of the geometric discontinuity. Compared with the curvature values, the impact of noise on the principal curvature direction is small. Therefore, feature extraction based on principal curvature direction is more robust and accurate. The experimental results show that the proposed algorithm can efficiently extract feature and distinguish noise.

Purpose. The objective of this study was to examine the effect of a citric acid-citrate buffer system on the chemical instability of lyophilized amorphous samples of quinapril hydrochloride (QHCl).

Hospital Patient Scheduling is an inherently distributed problem because of the way real hospitals are organized. As medical procedures have become more complex, and their associated tests and treatments have become interrelated, the current ad hoc patient scheduling solutions have been observed to break down. We propose a multi-agent solution using the Generalized Partial Global Planning (GPGP) approach that preserves the existing human organization and authority structures, while providing better system-level performance (increased hospital unit throughput and decreased patient stay time). To do this, we extend GPGP with a new coordination mechanism to handle mutually exclusive resource relationships. Like the other GPGP mechanisms, the new mechanism can be applied to any problem with the appropriate resource relationship. We evaluate this new mechanism in the context of the hospital patient scheduling problem, and examine the effect of increasing interrelations between tasks performed by different hospital units.

In recent years, geometry-based image and video processing methods have aroused significant interest. This paper considers progress from four aspects: geometric characteristics and shape, geometric transformations, embedded geometric structure, and differential geometry methods. Current research trends are also pointed out.