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Optimal constrained multi-degree reduction of Bézier curves with explicit expressions based on divide and conquer

Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 577-582页

作者： Lian ZHOU Guo-jin WANG Institute of Computer Graphics and Image Processing State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

We decompose the problem of the optimal multi-degree reduction of Bézier curves with corners constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of 'divide and conquer' has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm.

关键词： Bezier curves Multi-degree reduction Divide and conquer

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A new method in highway route design:joining circular arcs by a single C-Bézier curve with shape parameter

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2009年第4期10卷 562-569页

作者： Hua-hui CAI Guo-jin WANG Institute of Computer Graphics and Image Processing State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages：（1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement.

关键词： Transition curve C-Bezier curve Monotone curvature Shape parameter

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Symmetric alteration of four knots of B-spline and NURBS surfaces

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2006年第6期7卷 1084-1087页

作者： LI Ya-juan WANG Guo-zhao Institute of Computer Graphics and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 China

Modifying the knots of a B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface, the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.

关键词： B-spline surface NURBS surface Knot modification Path

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Efficient Fault Detection in Nonlinear Industrial Process: A Reduced Kernel PCA-Based Spectral Clustering Approach

Efficient Fault Detection in Nonlinear Industrial Process: A...

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Artificial Intelligence, Applications, Innovation and Ethics (AI2E), International Conference for

作者： Khadija Attouri Majdi Mansouri Mansour Hajji Kais Bouzrara Laboratory of Advanced Materials and Nanotechnologies Higher Institute of Applied Sciences and Technology of Kasserine Kairouan University Tunisia Department of Electrical and Computer Engineering College of Engineering Sultan Qaboos University Muscat Oman Research Laboratory of Automation Signal Processing and Image National Engineering School of Monastir Tunisia

ISBN: (数字)9798331513733

ISBN: (纸本)9798331513740

The challenges posed by nonlinearities in industrial systems necessitate innovative techniques that outperform the limitations of traditional methods such as principal component analysis (PCA). While Kernel Principal Component Analysis (KPCA) offers a robust solution to handle nonlinear data, its computational requirements are a significant issue, especially for large-sized datasets. In this work, we propose a novel technique, namely, reduced kernel principal component analysis-based spectral clustering (RKPCA SpC ), to monitor and detect faults in the benchmark Tennessee Eastman process. The suggested approach addresses the complexity associated with KPCA by reducing data size during the model training phase. This reduction involves retaining only the principal components, preserving informative features, and selecting pertinent samples without compromising the original data's content. The efficacy of the proposed method is evaluated through key performance metrics, including false alarm rate (FAR), missed detection rate (MDR), detection time delay (DTD), and computation time (CT). Additionally, gained execution time (GET), gained storage space (GSP), and loss function (LF) are considered, providing a comprehensive assessment of the developed paradigms' effectiveness. The results demonstrate the promising capabilities of our proposed scheme.

关键词： Training Measurement Technological innovation Fault detection Delay effects Computational modeling Complexity theory Kernel Monitoring Principal component analysis

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RELIEF MAPPING USING NONPHOTOGRAPHIC SPACEBORNE imageRY

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ISPRS JOURNAL OF PHOTOGRAMMETRY AND REMOTE SENSING 1989年第1期44卷 21-36页

作者： RAGGAM, J BUCHROITHNER, MF MANSBERGER, R Institute for Image Processing and Computer Graphics Joanneum Research Graz Austria Institute for Applied Geodesy and Photogrammetry University of Technology Graz Austria

Three-dimensional restitution of images with unconventional imaging geometry can be performed in an operational mode using existing commercial analytical plotters without any extra investments in hardware. The paper presents two programme systems developed for the Kern DSR analytical stereo-plotter for mapping with spaceborne stereo-imagery, one for images acquired by the SPOT HRV sensor, the other one for stereo-mensuration of SAR images. Due to the movement of the satellite platforms the software requires appropriate algorithms for the consideration of time-varying orientation parameters like sensor position, sensor attitude or others. The performance of the programme systems is demonstrated with practical results derived from Space Shuttle SIR-B imagery as well as from SPOT images showing realistically achievable accuracies of a few pixels in planimetry.

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Conversion matrix between two bases of the algebraic hyperbolic space

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Journal of Zhejiang University: Science 2006年第SUPPL. 2期7卷 181-186页

作者： Fan, Feng-Tao Wang, Guo-Zhao Institute of Computer Graphics and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 China

This paper presents the matrix representation for the hyperbolic polynomial B-spline basis and the algebraic hyperbolic Bézier basis in a recursive way, which are both generated over the space Ωn=span{sinht, cosht, tn-3, , t, 1} in which n is an arbitrary integer larger than or equal to 3. The conversion matrix from the hyperbolic polynomial B-spline basis of arbitrary order to the algebraic hyperbolic Bézier basis of the same order is also given by a recursive approach. As examples, the specific expressions of the matrix representation for the hyperbolic polynomial B-spline basis of order 4 and the algebraic hyperbolic Bézier basis of order 4 are given, and we also construct the conversion matrix between the two bases of order 4 by the method proposed in the paper. The results in this paper are useful for the evaluation and conversion of the curves and surfaces constructed by the two bases.

关键词： computer graphics

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Optimal multi-degree reduction of Bézier curves with G1-continuity

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Journal of Zhejiang University: Science 2006年第SUPPL. 2期7卷 174-180页

作者： Lu, Li-Zheng Wang, Guo-Zhao Institute of Computer Graphics and Image Processing Department of Mathematics Zhejiang University Hangzhou 310027 China

This paper presents a novel approach to consider optimal multi-degree reduction of Bézier curve with G1-continuity. By minimizing the distances between corresponding control points of the two curves through degree raising, optimal approximation is achieved. In contrast to traditional methods, which typically consider the components of the curve separately, we use geometric information on the curve to generate the degree reduction. So positions and tangents are preserved at the two endpoints. For satisfying the solvability condition, we propose another improved algorithm based on regularization terms. Finally, numerical examples demonstrate the effectiveness of our algorithms.

关键词： computer graphics

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Short-Term Photovoltaic Power Forecasting-Based Kernel Ridge Regression

Short-Term Photovoltaic Power Forecasting-Based Kernel Ridge...

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Artificial Intelligence, Applications, Innovation and Ethics (AI2E), International Conference for

作者： Manel Marweni Majdi Mansouri Mansour Hajji Mohamed Faouzi Mimouni Research Laboratory of Automation Signal Processing and Image National Engineering School of Monastir Tunisia Department of Electrical and Computer Engineering College of Engineering Sultan Qaboos University Muscat Oman Laboratory of Advanced Materials and Nanotechnologies Higher Institute of Applied Sciences and Technology of Kasserine Kairouan University Kasserine Tunisia

ISBN: (数字)9798331513733

ISBN: (纸本)9798331513740

The modern energy landscape is undergoing a seismic change from traditional, finite energy sources and toward cleaner, renewable alternatives. The restrictions faced by traditional sources, which are not only finite but increasingly shrink in the face of burgeoning global energy demands driven by population increase and industrial expansion, are driving this change. Although promising, renewable energy poses complications, particularly the reliance on climatic conditions. An important aspect of addressing these difficulties is effective energy management within distribution systems, which includes forecasting and optimization phases. This research focuses on forecasting using an advanced machine learning (ML) approach. Accurately forecasting renewable energy generation over time is critical for improving energy management. This technique is evaluated using a variety of performance indicators, including Mean Error (ME), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the Coefficient of Determination (R 2 ). Empirical studies support the method's usefulness, demonstrating noteworthy performance with low error rates.

关键词： Photovoltaic systems Renewable energy sources Technological innovation Accuracy Machine learning Predictive models Forecasting Kernel Energy management Optimization

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Free-Form Deformation with Rational DMS-Spline Volumes

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Journal of computer Science & Technology 2008年第5期23卷 862-873页

作者：徐岗汪国昭陈小雕 Institute of Computer Graphics and Image Processing Zhejiang University Department of Mathematics Zhejiang University College of Computer Science Hangzhou Dianzi University INRIA Nancy France

In this paper, we propose a novel free-form deformation （FFD） technique, RDMS-FFD （Rational DMS-FFD）, based on rational DMS-spline volumes. RDMS-FFD inherits some good properties of rational DMS-spline volumes and combines more deformation techniques than previous FFD methods in a consistent framework, such as local deformation, control lattice of arbitrary topology, smooth deformation, multiresolution deformation and direct manipulation of deformation. We first introduce the rational DMS-spline volume by directly generalizing the previous results related to DMS-splines. How to generate a tetrahedral domain that approximates the shape of the object to be deformed is also introduced in this paper. Unlike the traditional FFD techniques, we manipulate the vertices of the tetrahedral domain to achieve deformation results. Our system demonstrates that RDMS-FFD is powerful and intuitive in geometric modeling.

关键词： free-form deformation rational DMS-spline volume control lattice of arbitrary topology multiresolution deformation direct manipulation

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Dynamics of Masked image Modeling in Hyperspectral image Classification

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IEEE Transactions on Geoscience and Remote Sensing 2025年 63卷

作者： Ma, Chen Li, Huayi Jiang, Junjun Aybar, Cesar Yao, Jiaqi Camps-Valls, Gustau Harbin Institute of Technology Research Center of Satellite Technology State Key Laboratory of Micro-Spacecraft Rapid Design and Intelligent Cluster School of Astronautics Harbin150001 China Harbin Institute of Technology School of Computer Science and Technology Harbin150001 China University of València Image Signal Processing Laboratory València46980 Spain Tianjin Normal University Tianjin300387 China

Masked image modeling (MIM), a common self-supervised learning (SSL) technique, has been extensively studied for remote sensing (RS) image processing. Nevertheless, its effectiveness for hyperspectral imagery (HSI) remains underexplored due to the distinct data structures and high dimensionality. This article aims to provide a detailed understanding of MIM from different perspectives of representation learning and statistical analysis for HSI classification tasks. Our study reveals that the MIM paradigm injects inductive bias in the attention mechanism of the transformer model, which is advantageous for capturing the local discrepancies between the spectra. We also show that MIM can increase the diversity of the attention heads in every layer, which is beneficial for the model in extracting more discriminative features from different spectral bands. The similarity of representations from various layers further proves this. Furthermore, our investigation highlights how MIM introduces a dynamic perspective to spectral representations, enabling the model to learn more robust and discriminative features. The final numerical experiments indicate that a moderate mask ratio can enhance the performance of downstream tasks. This suggests that designing a more targeted masking strategy might be necessary to achieve higher and more stable gains in downstream task performance. Without bells and whistles, the vanilla MIM improves the overall classification accuracy by an average of 2.69% over its supervised learning (SL) counterpart. We hope that our findings can advance the understanding of MIM in HSI and inspire the design of a more stable SSL paradigm for HSI processing. © 1980-2012 IEEE.

关键词： Self-supervised learning

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