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Plasticity of language pathways in patients with low-grade glioma A diffusion tensor imaging study 被引量:3
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作者 Gang Zheng Xiaolei Chen +7 位作者 Bainan Xu Jiashu Zhang Xueming Lv jinjiang li Fangye li Shen Hu Ting Zhang Ye li 《Neural Regeneration Research》 SCIE CAS CSCD 2013年第7期647-654,共8页
Knowledge of the plasticity of language pathways neurosurgeons to achieve maximum resection wh n patients with low-grade glioma is important for e preserving neurological function. The current study sought to investig... Knowledge of the plasticity of language pathways neurosurgeons to achieve maximum resection wh n patients with low-grade glioma is important for e preserving neurological function. The current study sought to investigate changes in the ventral language pathways in patients with low-grade glioma located in regions likely to affect the dorsal language pathways. The results revealed no significant difference in fractional anisotropy values in the arcuate fasciculus between groups or between hemispheres. However, fractional anisotropy and lateralization index values in the left inferior longitudinal fasciculus and lateralization index values in the left inferior fronto-occpital fasciculus were higher in patients than in healthy subjects. These results indicate plasticity of language pathways in patients with low-grade glioma. The ventral language pathways may perform more functions in patients than in healthy subjects. As such, it is important to protect the ventral language pathways intraoperatively. 展开更多
关键词 neural regeneration neuroimaging low-grade glioma PLASTICITY language pathways dlllUSlOntensor imaging fractional anisotropy lateralization index ventral language pathway dorsallanguage pathway glioma grants-supported paper photographs-containing paper neuroregeneration
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Effects of gentamicin on choline acetyltransferase expression in paraolivary nucleus neurons of guinea pigs
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作者 Mingguang Zhao Xiaochen Wang +4 位作者 Yong liang Peng Xie Xuejun Guo jinjiang li WeiWang 《Neural Regeneration Research》 SCIE CAS CSCD 2008年第11期1229-1232,共4页
BACKGROUND: It is generally accepted that gentamicin can damage the cochlear nerve and acoustic nerve. In recent years, scholars have focused on neuronal changes and neurochemical information in the brainstem primary... BACKGROUND: It is generally accepted that gentamicin can damage the cochlear nerve and acoustic nerve. In recent years, scholars have focused on neuronal changes and neurochemical information in the brainstem primary auditory center. OBJECTIVE: To explore morphological changes of choline acetyltransferase (ChAT)-positive neurons in the paraolivary nucleus (PON) of guinea pigs, and the effect on hearing following gentamicin injection. DESIGN, TIME AND SETTING: Randomized grouping and morphological observational study was performed at Animal Experimental Center of General Hospital of Shenyang Military Area Command of Chinese PLA from January to August 2007. MATERIALS: A total of 48 healthy guinea pigs were randomly divided into model (n = 40) and control (n = 8) groups. The model group was divided into five subgroups at five time points of 1 and 3 days, 1, 2, and 3 weeks. METHODS: Guinea pigs in the model group were intraperitoneally injected with gentamicin, and those in the control group were intraperitoneally injected with the same volume of saline. MAIN OUTCOME MEASURES: Auditory brainstem-evoked potential was used to record auditory threshold; distribution and morphological changes of ChAT-positive neurons in the PON were observed with immunohistochemistry; section area and gray value of ChAT-positive neurons were measured with Quantimet 570 image-analyzing system. RESULTS: ChAT-positive neurons were diffusedly distributed in the PON. The majority was composed of large, round cells, with positive neurites that could be clearly observed. Following gentamicin injection, the positive neurons displayed an irregular outline, and their neurites began to shorten and disappear. The gray value increased with prolonged gentamicin administration (P 〈 0.05). In addition, the somatic cross-sectional area was enlarged in the model group at 1 and 3 days after injection (P 〈 0.05), whereas cell number significantly decreased at ;three weeks after injection (P 〈 0.05). Starting at 3-4 days, behavioral features and auditory degrees became gradually aggravated with prolonged gentamicin administration (P 〈 0.05). CONCLUSION: Gentamicin damaged ChAT-positive neurons in the PON, and long-term gentamicin treatment aggravated hearing impairment. 展开更多
关键词 choline acetyltransferase GENTAMICIN guinea pigs paraolivary nucleus
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Consistent image processing based on co-saliency
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作者 Xiangnan Ren jinjiang li +1 位作者 Zhen Hua Xinbo Jiang 《CAAI Transactions on Intelligence Technology》 EI 2021年第3期324-337,共14页
In a group of images,the recurrent foreground objects are considered as the key objects in the group of images.In co-saliency detection,these are described as common saliency objects.The aim is to be able to naturally... In a group of images,the recurrent foreground objects are considered as the key objects in the group of images.In co-saliency detection,these are described as common saliency objects.The aim is to be able to naturally guide the user's gaze to these common salient objects.By guiding the user's gaze,users can easily find these common saliency objects without interference from other information.Therefore,a method is proposed for reducing user visual attention based on co-saliency detection.Through the co-saliency detection algorithm and matting algorithm for image preprocessing,the exact position of non-common saliency objects(called Region of Interest here,i.e.ROI)in the image group can be obtained.In the attention retargeting algorithm,the internal features of the image to adjust the saliency of the ROI areas are considered.In the HSI colour space,the three components H,S,and I are adjusted separately.First,the hue distribution is constructed by the Dirac kernel function,and then the most similar hue distribution to the sur-rounding environment is selected as the best hue distribution of ROI areas.The S and I components can be set as the contrast difference between ROI areas and surrounding background areas according to the user's demands.Experimental results show that this method effectively reduces the ROI areas'attraction to the user's visual attention.Moreover,comparing this method with other methods,the saliency adjustment effect achieved is much better,and the processed image is more natural. 展开更多
关键词 IMAGE ALGORITHM DISTRIBUTION
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Resistance Evaluation of Indica Rice Varieties with Bacterial Blight Resistance Genes Xa21 and Xa23 under Different Genetic Backgrounds
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作者 Jianghui YU jinjiang li +1 位作者 lihua DENG Lushui WENG 《Plant Diseases and Pests》 CAS 2022年第1期1-8,12,共9页
[Objectives]The paper was to evaluate the resistance of indica rice varieties with bacterial blight resistance genes Xa21 and Xa23 under different genetic backgrounds.[Methods]The rice materials with bacterial blight ... [Objectives]The paper was to evaluate the resistance of indica rice varieties with bacterial blight resistance genes Xa21 and Xa23 under different genetic backgrounds.[Methods]The rice materials with bacterial blight resistance genes Xa21 or Xa23 were used as the donors,and those without the genes were used as the receptors.By back crossing,composite crossing and other methods,combined with molecular marker-assisted selection(MAS),the materials with Xa21 or Xa23 gene,and their sister lines with/without Xa21 or Xa23 gene were inoculated with 7 widely used physiological races of Xanthomonas oryzae,and the resistance of the materials to bacterial blight was analyzed.[Results]The proportions of cumulative resistance(HR,R,MR)of rice materials with resistance gene Xa21 were HNA1-4/PXO86(84.62%)>YN24(82.14%)>GD1358(73.08%)>PXO99(67.86%)>GDA2(63.33%)>FuJ(6.67%),indicating that the materials with Xa21 gene had no resistance to bacterial blight induced by strain FuJ,but for other strains,there were still 36.67%-15.38%of the materials susceptible to the disease.The cumulative resistance(HR,R,MR)of the materials with Xa23 gene was over 76%,but there were still 23.02%-15.52%of the materials that had no resistance to the 7 strains.The analysis of variation coefficient of lesion length showed that the resistance of materials with Xa21 or Xa23 genes varied among strains,or the resistance to the same strain varied among materials.Correlation analysis demonstrated that there was significant or extremely significant positive correlation between strain GDA2 or HNA1-4 and other 6 corresponding strains in the materials with Xa21 gene,and there was extremely significant positive correlation between strain YN24,GD1358 or PXO86 and other 6 corresponding strains in the materials with Xa23 gene.Selection of these strains for resistance identification could improve the efficiency of breeding.Analysis of sister lines showed that bacterial blight resistance of Xa21 or Xa23 genes was related to the donor of the materials.Correlation analysis showed that the resistance of the materials with Xa21 gene had extremely significant positive correlation with parents(R=0.5725**),and the resistance of the materials with Xa23 gene had significant positive correlation with parents(R=0.2212*).[Conclusions]The study provides the reference for molecular resistance breeding of bacterial blight. 展开更多
关键词 RICE Bacterial blight Resistance analysis Resistance gene
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MLSE-assisted decision feedback equalizer for error-propagation suppression in high-speed IM-DD transmission systems
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作者 周家豪 张静 +7 位作者 赵雪 王芮 李劲江 胡少华 张倩武 杨奇 许渤 邱昆 《Chinese Optics Letters》 SCIE EI CAS CSCD 2024年第5期36-40,共5页
We propose a trellis-compressed maximum likelihood sequence estimation(TC-MLSE)-assisted sliding-block decision feedback equalizer(DFE)to suppress the error propagation resulting from the DFE in high-speed systems.We ... We propose a trellis-compressed maximum likelihood sequence estimation(TC-MLSE)-assisted sliding-block decision feedback equalizer(DFE)to suppress the error propagation resulting from the DFE in high-speed systems.We use an out-ofrange detector to detect the end of burst errors from the DFE and activate the optional TC-MLSE to correct burst errors.We conduct experiments to transmit a 201-Gbit/s PAM-8 signal.The results show that the proposed method achieves a bit error rate of 3.65×10^(-3),which is close to that of MLSE.The optional MLSE is only activated when needed and processes 11.4%of the total symbols.Moreover,the proposed method compresses the maximum length of burst errors from 19 to 5. 展开更多
关键词 intensity modulation direct detection sliding-block decision feedback equalizer error propagation maximum likelihood sequence estimation out-of-range detector
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Intraoperative diffusion tensor imaging predicts the recovery of motor dysfunction after insular lesions 被引量:2
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作者 jinjiang li Xiaolei Chen +6 位作者 Jiashu Zhang Gang Zheng Xueming Lv Fangye li Shen Hu Ting Zhang Bainan Xu 《Neural Regeneration Research》 SCIE CAS CSCD 2013年第15期1400-1409,共10页
Insular lesions remain surgically challenging because of the need to balance aggressive resection and functional protection. Motor function deficits due to corticospinal tract injury are a common complication of surge... Insular lesions remain surgically challenging because of the need to balance aggressive resection and functional protection. Motor function deficits due to corticospinal tract injury are a common complication of surgery for lesions adjacent to the internal capsule and it is therefore essential to evaluate the corticospinal tract adjacent to the lesion. We used diffusion tensor imaging to evaluate the corticospinal tract in 89 patients with insular lobe lesions who underwent surgery in Chinese PLA General Hospital from February 2009 to May 2011. Postoperative motor function evaluation revealed that 57 patients had no changes in motor function, and 32 patients suffered motor dysfunction or aggravated motor dysfunction. Of the affected patients, 20 recovered motor function during the 6-12-month follow-up, and an additional 12 patients did not recover over more than 12 months of follow-up. Following reconstruction of the corticospinal tract, fractional anisotropy comparison demonstrated that preoperative, intraoperative and follow-up normalized fractional anisotropy in the stable group was higher than in the transient deficits group or the long-term deficits group. Compared with the transient deficits group, intraoperative normalized fractional anisotropy significantly decreased in the long-term deficits group. We conclude that intraoperative fractional anisotropy values of the corticospinal tracts can be used as a prognostic indicator of motor function outcome. 展开更多
关键词 neural regeneration NEUROIMAGING magnetic resonance imaging diffusion tensor imaging fractional anisotropy insular lobe corticospinal tracts motor function grants-supported paper NEUROREGENERATION
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Magnetic resonance diffusion tensor imaging-based evaluation of optic-radiation shape and position in meningioma 被引量:1
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作者 Xueming Lv Xiaolei Chen +5 位作者 Bainan Xu Jiashu Zhang Gang Zheng jinjiang li Fangye li Guochen Sun 《Neural Regeneration Research》 SCIE CAS CSCD 2012年第9期686-691,共6页
Employing magnetic resonance diffusion tensor imaging, three-dimensional white-matter imaging and conventional magnetic resonance imaging can demonstrate the tumor parenchyma, peritumoral edema and compression on surr... Employing magnetic resonance diffusion tensor imaging, three-dimensional white-matter imaging and conventional magnetic resonance imaging can demonstrate the tumor parenchyma, peritumoral edema and compression on surrounding brain tissue. A color-coded tensor map and three-dimensional tracer diagram were applied to clearly display the optic-radiation location, course and damage. Results showed that the altered anisotropy values of meningioma patients corresponded with optic-radiation shape, size and position on both sides. Experimental findings indicate that the magnetic resonance diffusion tensor imaging technique is a means of tracing and clearly visualizing the optic radiation. 展开更多
关键词 magnetic resonance diffusion tensor imaging diffusion tensor tractography MENINGIOMA optic radiation
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Guided filter-based multi-scale super-resolution reconstruction 被引量:1
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作者 Xiaomei Feng jinjiang li Zhen Hua 《CAAI Transactions on Intelligence Technology》 2020年第2期128-140,共13页
The learning-based super-resolution reconstruction method inputs a low-resolution image into a network,and learns a non-linear mapping relationship between low-resolution and high-resolution through the network.In thi... The learning-based super-resolution reconstruction method inputs a low-resolution image into a network,and learns a non-linear mapping relationship between low-resolution and high-resolution through the network.In this study,the multi-scale super-resolution reconstruction network is used to fuse the effective features of different scale images,and the non-linear mapping between low resolution and high resolution is studied from coarse to fine to realise the end-to-end super-resolution reconstruction task.The loss of some features of the low-resolution image will negatively affect the quality of the reconstructed image.To solve the problem of incomplete image features in low-resolution,this study adopts the multi-scale super-resolution reconstruction method based on guided image filtering.The high-resolution image reconstructed by the multi-scale super-resolution network and the real high-resolution image are merged by the guide image filter to generate a new image,and the newly generated image is used for secondary training of the multi-scale super-resolution reconstruction network.The newly generated image effectively compensates for the details and texture information lost in the low-resolution image,thereby improving the effect of the super-resolution reconstructed image.Compared with the existing super-resolution reconstruction scheme,the accuracy and speed of super-resolution reconstruction are improved. 展开更多
关键词 RESOLUTION IMAGE NETWORK
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Evaluating the robustness of image matting algorithm
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作者 Genji Yuan jinjiang li Hui Fan 《CAAI Transactions on Intelligence Technology》 EI 2020年第4期247-259,共13页
In this study,the authors propose a method to calculate the consistency of alpha masking to assess the robustness of the matting algorithm.This study evaluates consistent alpha masks based on the Gaussian-Hermite mome... In this study,the authors propose a method to calculate the consistency of alpha masking to assess the robustness of the matting algorithm.This study evaluates consistent alpha masks based on the Gaussian-Hermite moment in combination with gradient amplitude and gradient direction.The gradient direction describes the appearance and shape of local objects in the image,and the gradient amplitude accurately reflects the contrast and texture changes of small details in the image.They selected Gaussian blur,pretzel noise,and combined noise to destroy the image,and then evaluated the consistency of the original alpha mask and noise alpha mask.To determine the robustness of the matting algorithm,they assessed the degree of consistency of the alpha mask using three different evaluation levels.The experimental results show that noise has a greater impact on the performance of the matting algorithm,which shows a decreasing trend as the noise level in the image deepens.In noisy images,the traditional matting algorithm exhibits better robustness compared to the recently proposed trap matting algorithm.Different matting algorithms present different adaptations to different noises. 展开更多
关键词 IMAGE algorithm. ALGORITHM
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A Study on the Innovation of U-Education of Party Members from the Perspective of Big Data
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作者 jinjiang li 《Journal of Educational Theory and Management》 2017年第1期65-69,共5页
Potential cognition of the social development system centered on economic construction has been changed. To a certain extent, it has formed the new concept of "world outlook and views on life and values" for... Potential cognition of the social development system centered on economic construction has been changed. To a certain extent, it has formed the new concept of "world outlook and views on life and values" for the younger generation. It is imperative that innovation on the form of education of party members in the new era be enforced. In today's big data, problems in the education of party members can be concluded from the analysis of data collection and mining. To explore the U-Education methods and modes for special party members of a certain age group and create an "internet Party Construction platform +" can effectively deal with the shortcomings of the existing education, and through more convenient and quicker APP operation, widely used mobile phones can effectively conduct education and study, and data statistics function of the platform can be used for evaluation and analysis to seek a more perfect education mode. 展开更多
关键词 PARTY MEMBER EDUCATION INNOVATION
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Filter-cluster attention based recursive network for low-light enhancement
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作者 Zhixiong HUANG jinjiang li +1 位作者 Zhen HUA linwei FAN 《Frontiers of Information Technology & Electronic Engineering》 SCIE EI CSCD 2023年第7期1028-1044,共17页
The poor quality of images recorded in low-light environments affects their further applications.To improve the visibility of low-light images,we propose a recurrent network based on filter-cluster attention(FCA),the ... The poor quality of images recorded in low-light environments affects their further applications.To improve the visibility of low-light images,we propose a recurrent network based on filter-cluster attention(FCA),the main body of which consists of three units:difference concern,gate recurrent,and iterative residual.The network performs multi-stage recursive learning on low-light images,and then extracts deeper feature information.To compute more accurate dependence,we design a novel FCA that focuses on the saliency of feature channels.FCA and self-attention are used to highlight the low-light regions and important channels of the feature.We also design a dense connection pyramid(DenCP)to extract the color features of the low-light inversion image,to compensate for the loss of the image's color information.Experimental results on six public datasets show that our method has outstanding performance in subjective and quantitative comparisons. 展开更多
关键词 Low-light enhancement Filter-cluster attention Dense connection pyramid Recursive network
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On the Waring-Goldbach problem for one cube and nine biquadrates
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作者 jinjiang li Min ZHANG 《Frontiers of Mathematics in China》 CSCD 2024年第4期229-246,共18页
Let N be a sufficiently large integer.In this paper,it is proved that with at most O(N17/18+ε)exceptions,all positive integers satisfying some necessary congruence conditions up to N can be represented in the form p_... Let N be a sufficiently large integer.In this paper,it is proved that with at most O(N17/18+ε)exceptions,all positive integers satisfying some necessary congruence conditions up to N can be represented in the form p_(1)^(3)+p_(2)^(4)+p_(3)^(4)+p_(5)^(4)+p_(6)^(4)+p_(7)^(4)+p_(8)^(4)+p_(9)^(4)+p_(10)^(4),where p1,p2,…,P_(10)are prime numbers. 展开更多
关键词 Waring-Goldbach problem Hardy-Littlewood method exceptional set
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Saliency-based image correction for colorblind patients 被引量:1
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作者 jinjiang li Xiaomei Feng Hui Fan 《Computational Visual Media》 CSCD 2020年第2期169-189,共21页
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 captu... 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. 展开更多
关键词 color vision colorblindness SALIENCY color correction
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GMTS: GNN-based multi-scale transformer siamese network for remote sensing building change detection
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作者 Xinyang Song Zhen Hua jinjiang li 《International Journal of Digital Earth》 SCIE EI 2023年第1期1685-1706,共22页
With the remarkable success of change detection(CD)in remote sensing images in the context of deep learning,many convolutional neural network(CNN)based methods have been proposed.In the current research,to obtain a be... With the remarkable success of change detection(CD)in remote sensing images in the context of deep learning,many convolutional neural network(CNN)based methods have been proposed.In the current research,to obtain a better context modeling method for remote sensing images and to capture more spatiotemporal characteristics,several attention-based methods and transformer(TR)-based methods have been proposed.Recent research has also continued to innovate on TR-based methods,and many new methods have been proposed.Most of them require a huge number of calculation to achieve good results.Therefore,using the TR-based mehtod while maintaining the overhead low is a problem to be solved.Here,we propose a GNN-based multi-scale transformer siamese network for remote sensing image change detection(GMTS)that maintains a low network overhead while effectively modeling context in the spatiotemporal domain.We also design a novel hybrid backbone to extract features.Compared with the current CNN backbone,our backbone network has a lower overhead and achieves better results.Further,we use high/low frequency(HiLo)attention to extract more detailed local features and the multi-scale pooling pyramid transformer(MPPT)module to focus on more global features respectively.Finally,we leverage the context modeling capabilities of TR in the spatiotemporal domain to optimize the extracted features.We have a relatively low number of parameters compared to that required by current TR-based methods and achieve a good effect improvement,which provides a good balance between efficiency and performance. 展开更多
关键词 Remote sensing(RS) change detection(CD) depthwise over-parameterized convolutional(DO-Conv) attention mechanism TRANSFORMER graph convolution
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Computing knots by quadratic and cubic polynomial curves 被引量:3
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作者 Fan Zhang jinjiang li +1 位作者 Peiqiang liu Hui Fan 《Computational Visual Media》 EI CSCD 2020年第4期417-430,共14页
A new method is presented to determine parameter values(knot)for data points for curve and surface generation.With four adjacent data points,a quadratic polynomial curve can be determined uniquely if the four points f... A new method is presented to determine parameter values(knot)for data points for curve and surface generation.With four adjacent data points,a quadratic polynomial curve can be determined uniquely if the four points form a convex polygon.When the four data points do not form a convex polygon,a cubic polynomial curve with one degree of freedom is used to interpolate the four points,so that the interpolant has better shape,approximating the polygon formed by the four data points.The degree of freedom is determined by minimizing the cubic coefficient of the cubic polynomial curve.The advantages of the new method are,firstly,the knots computed have quadratic polynomial precision,i.e.,if the data points are sampled from a quadratic polynomial curve,and the knots are used to construct a quadratic polynomial,it reproduces the original quadratic curve.Secondly,the new method is affine invariant,which is significant,as most parameterization methods do not have this property.Thirdly,it computes knots using a local method.Experiments show that curves constructed using knots computed by the new method have better interpolation precision than for existing methods. 展开更多
关键词 KNOT interpolation polynomial curve affine invariant
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New progress in geometric computing for image and video processing 被引量:1
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作者 jinjiang li Hanyi GE 《Frontiers of Computer Science》 SCIE EI CSCD 2012年第6期769-775,共7页
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, e... 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. 展开更多
关键词 IMAGE VIDEO geometric computing geometric patterns embedded geometry structure
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Progressive edge-sensing dynamic scene deblurring
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作者 Tianlin Zhang jinjiang li Hui Fan 《Computational Visual Media》 SCIE EI CSCD 2022年第3期495-508,共14页
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... 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. 展开更多
关键词 image deblurring dynamic scenes multiscale edge features
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Distribution of cube-free numbers with form [n^c]
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作者 Min ZHANG jinjiang li 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第6期1515-1525,共11页
We prove that there are infinite cube-free numbers of the form [n^c] for any fixed real number c E (1, 11/6).
关键词 Cube-free number exponential sum asymptotic formula
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