Efficient Gradient‐Domain Compositing Using an Approximate Curl‐free Wavelet Projection

Ren, Xu Dong; Lyu, Luan; He, Xiang; Zhang, Yanci; Wu, Enhua

doi:10.1111/cgf.13286

Cited by 3 publications

(4 citation statements)

References 49 publications

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“…In computer graphics, Ren et al [RLH*17] introduced an approximate curl‐free wavelet projection inspired by the work of Deriaz and Perrier [DP06]. This approach achieved state‐of‐the‐art results in gradient‐domain compositing compared to multigrid methods on both CPUs and GPUs.…”

Section: Related Workmentioning

confidence: 99%

“…Drawing inspiration from the curl‐free wavelet projection methods introduced by Ren et al [RLH*17; RLH*18] for applications in gradient‐domain compositing and 3D surface reconstruction, we propose a robust and efficient divergence‐free wavelet projection method for vector potential recovery. Our method has a time complexity of O ( n ) and can improve the accuracy when the input velocity exhibits a certain degree of divergence.…”

Section: Introductionmentioning

confidence: 99%

“…We now present Lemarié‐Rieusset's proposition [Lem92], which connects two MRAs through differentiation and serves as the foundation for our method. For more details, please refer to [DP09; RLH*17; RLH*18].…”

Section: Introductionmentioning

confidence: 99%

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Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids

Lyu,

Ren,

Cao

et al. 2024

Computer Graphics Forum

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We introduce an efficient technique for recovering the vector potential in wavelet space to simulate pointwise incompressible fluids. This technique ensures that fluid velocities remain divergence‐free at any point within the fluid domain and preserves local volume during the simulation. Divergence‐free wavelets are utilized to calculate the wavelet coefficients of the vector potential, resulting in a smooth vector potential with enhanced accuracy, even when the input velocities exhibit some degree of divergence. This enhanced accuracy eliminates the need for additional computational time to achieve a specific accuracy threshold, as fewer iterations are required for the pressure Poisson solver. Additionally, in 3D, since the wavelet transform is taken in‐place, only the memory for storing the vector potential is required. These two features make the method remarkably efficient for recovering vector potential for fluid simulation. Furthermore, the method can handle various boundary conditions during the wavelet transform, making it adaptable for simulating fluids with Neumann and Dirichlet boundary conditions. Our approach is highly parallelizable and features a time complexity of O(n), allowing for seamless deployment on GPUs and yielding remarkable computational efficiency. Experiments demonstrate that, taking into account the time consumed by the pressure Poisson solver, the method achieves an approximate 2x speedup on GPUs compared to state‐of‐the‐art vector potential recovery techniques while maintaining a precision level of 10−6 when single float precision is employed. The source code of ‘Wavelet Potentials’ can be found in https://github.com/yours321dog/WaveletPotentials.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids

Lyu,

Ren,

Cao

et al. 2024

Computer Graphics Forum

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“…In this paper, the concept of elementary calculus is improved, and its flexible description is adopted to extend the corresponding field theory concept in functional analysis. Compared with the elementary calculus, the Bahhoepr criterion is described intuitively and concisely, which makes it almost self-evident [5]. In the case of non-fixed boundary conditions, the above concepts are generalized and the decomposition formulas are deduced, that is, not only the criteria of Euler operator and derivative operator are deduced, but also the criteria of additional natural boundary conditions are obtained.…”

Section: Introductionmentioning

confidence: 99%

Demonstration of Gradient and Curl Concept in Functional Analysis

Chen¹

2018

2018 2nd International Conference on Systems, Computing, and Applications (SYSTCA 2018)

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This paper first establishes the concept of "one-point variation" and points out the improper formulation in this respect, and takes the view that the functional is infinitely many variables. In this way, the concept of gradient is more naturally introduced in functional analysis than in the usual literature. Thus, the criterion of Bahhoepr's Euler operator (i.e. gradient operator) is intuitively and concisely expounded, which makes it almost self-evident. It is difficult for students majoring in electronics to study the course "Electromagnetic Field and Microwave Technology". This is because the theory of this course is strong, the concept is abstract, and the applied mathematics knowledge is more. Especially, it is necessary to understand and master the concept of gradient and curl involved in field theory and two important integral formulas, namely Gauss formula and Stokes formula. However, there are few steps in the common textbooks and this part of the content, so this paper makes a more detailed introduction in order to reduce the difficulties in learning. After discussing the concept of gradient in depth, this method is extended to include natural boundary conditions. The concept of curl is also discussed, and the general form of operator decomposition theorem is given. Contrasting with elementary calculus, the concept of Two-type line integral in functional analysis is formed, which eliminates the contingency of existing parameters in solving inverse variational problems. Finally, some assumptions about the field theory of functional analysis are given, and the criterion of general derivation operator is derived.

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Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations

Ren

Lyu

He³

et al. 2018

Computer Graphics Forum

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We introduce a new biorthogonal wavelet approach to creating a water‐tight surface defined by an implicit function, from a finite set of oriented points. Our approach aims at addressing problems with previous wavelet methods which are not resilient to missing or nonuniformly sampled data. To address the problems, our approach has two key elements. First, by applying a three‐dimensional partial integration, we derive a new integral formula to compute the wavelet coefficients without requiring the implicit function to be an indicator function. It can be shown that the previously used formula is a special case of our formula when the integrated function is an indicator function. Second, a simple yet general method is proposed to construct smooth wavelets with small support. With our method, a family of wavelets can be constructed with the same support size as previously used wavelets while having one more degree of continuity. Experiments show that our approach can robustly produce results comparable to those produced by the Fourier and Poisson methods, regardless of the input data being noisy, missing or nonuniform. Moreover, our approach does not need to compute global integrals or solve large linear systems.

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Efficient Gradient‐Domain Compositing Using an Approximate Curl‐free Wavelet Projection

Cited by 3 publications

References 49 publications

Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids

Wavelet Potentials: An Efficient Potential Recovery Technique for Pointwise Incompressible Fluids

Demonstration of Gradient and Curl Concept in Functional Analysis

Biorthogonal Wavelet Surface Reconstruction Using Partial Integrations

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