scholarly journals Research on Virtual Color Restoration of Complex Building System Based on Discrete Wavelet Transform

2022 ◽  
Vol 2022 ◽  
pp. 1-11
Author(s):  
Chunqiao Song ◽  
Xutong Wu
Keyword(s):  
Image Restoration ◽  
Texture Synthesis ◽  
Lagrange Equation ◽  
Energy Functional ◽  
Mean Value ◽  
Source Image ◽  
Discrete Wavelet ◽  
Visual Effects ◽  
Low Efficiency ◽  
Automatic Matching

At present, image restoration has become a research hotspot in computer vision. The purpose of digital image restoration is to restore the lost information of the image or remove redundant objects without destroying the integrity and visual effects of the image. The operation of user interactive color migration is troublesome, resulting in low efficiency. And, when there are many kinds of colors, it is prone to errors. In response to these problems, this paper proposes automatic selection of sample color migration. Considering that the respective gray-scale histograms of the visual source image and the target image are approximately normal distributions, this paper takes the peak point as the mean value of the normal distribution to construct the objective function. We find all the required partitions according to the user’s needs and use the center points in these partitions as the initial clustering centers of the fuzzy C-means (FCM) algorithm to complete the automatic clustering of the two images. This paper selects representative pixels as sample blocks to realize automatic matching of sample blocks in the two images and complete the color migration of the entire image. We introduced the curvature into the energy functional of the p-harmonic model. According to whether there is noise in the image, a new wavelet domain image restoration model is proposed. According to the established model, the Euler–Lagrange equation is derived by the variational method, the corresponding diffusion equation is established, and the model is analyzed and numerically solved in detail to obtain the restored image. The results show that the combination of image sample texture synthesis and segmentation matching method used in this paper can effectively solve the problem of color unevenness. This not only saves the time for mural restoration but also improves the quality of murals, thereby achieving more realistic visual effects and connectivity.

scholarly journals Regularity of Weak Solution of Variational Problems Modeling the Cosserat Micropolar Elasticity

2020 ◽  
Author(s):  
Yimei Li ◽  
Changyou Wang
Keyword(s):  
Weak Solution ◽  
Harmonic Maps ◽  
Lagrange Equation ◽  
Variational Problems ◽  
Energy Functional ◽  
Geometrically Nonlinear ◽  
Micropolar Elasticity ◽  
One Dimensional ◽  
The Poisson Equation ◽  
System Coupling

Abstract In this paper, we consider weak solutions of the Euler–Lagrange equation to a variational energy functional modeling the geometrically nonlinear Cosserat micropolar elasticity of continua in dimension three, which is a system coupling between the Poisson equation and the equation of $p$-harmonic maps ($2\le p\le 3$). We show that if a weak solution is stationary, then its singular set is discrete for $2<p<3$ and has zero one-dimensional Hausdorff measure for $p=2$. If, in addition, it is a stable-stationary weak solution, then it is regular everywhere when $p\in [2, \frac{32}{15}]$.

Multi-Frame Super-Resolution Reconstruction Algorithm Based on Diffusion Tensor Regularization Term

2014 ◽  
Vol 543-547 ◽  
pp. 2828-2832 ◽  
Author(s):  
Xiao Dong Zhao ◽  
Zuo Feng Zhou ◽  
Jian Zhong Cao ◽  
Long Ren ◽  
Guang Sen Liu ◽  
...  
Keyword(s):  
Diffusion Tensor ◽  
Lagrange Equation ◽  
Super Resolution ◽  
Reconstruction Algorithm ◽  
Energy Functional ◽  
L1 Norm ◽  
Regularization Term ◽  
Sr Reconstruction ◽  
Image Edges ◽  
Anisotropic Diffusion Equation

This paper presents a multi-frame super-resolution (SR) reconstruction algorithm based on diffusion tensor regularization term. Firstly, L1-norm structure is used as data fidelity term, anisotropic diffusion equation with directional smooth characteristics is introduced as a prior knowledge to optimize reconstruction result. Secondly, combined with shock filter, SR reconstruction energy functional is established. Finally, Euler-Lagrange equation based on nonlinear diffusion model is exported. Simulation results validate that the proposed algorithm enhances image edges and suppresses noise effectively, which proves better robustness.

scholarly journals Nonlocal Variational Model for Saliency Detection

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Meng Li ◽  
Yi Zhan ◽  
Lidan Zhang
Keyword(s):  
Visual Attention ◽  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Temporal Evolution ◽  
Lagrange Equation ◽  
Saliency Detection ◽  
Energy Functional ◽  
Experimental Results ◽  
Variational Model ◽  
Still Images

We present a nonlocal variational model for saliency detection from still images, from which various features for visual attention can be detected by minimizing the energy functional. The associated Euler-Lagrange equation is a nonlocalp-Laplacian type diffusion equation with two reaction terms, and it is a nonlinear diffusion. The main advantage of our method is that it provides flexible and intuitive control over the detecting procedure by the temporal evolution of the Euler-Lagrange equation. Experimental results on various images show that our model can better make background details diminish eventually while luxuriant subtle details in foreground are preserved very well.

scholarly journals GENERALIZED TWISTS AS ELASTIC ENERGY EXTREMALS ON ANNULI, QUATERNIONS AND LIFTING TWIST LOOPS TO THE SPINOR GROUPS

2013 ◽  
Vol 11 (02) ◽  
pp. 1350008 ◽  
Author(s):  
M. S. SHAHROKHI-DEHKORDI ◽  
A. TAHERI
Keyword(s):  
Elastic Energy ◽  
Lagrange Equation ◽  
Energy Functional ◽  
Double Cover ◽  
Explicit Representation ◽  
Exponential Map ◽  
Dirichlet Energy ◽  
Smooth Solutions ◽  
Low Dimensions ◽  
Admissible Maps

Let X = {x ∈ ℝn : a < |x| < b} be a generalized annulus and consider the Dirichlet energy functional [Formula: see text] over the space of admissible maps [Formula: see text] where φ is the identity map. In this paper we consider a class of maps referred to as generalized twists and examine them in connection with the Euler–Lagrange equation associated with 𝔽[⋅, X] on [Formula: see text]. The approach is novel and is based on lifting twist loops from SO(n) to its double cover Spin(n) and reformulating the equations accordingly. We restrict our attention to low dimensions and prove that for n = 4 the system admits infinitely many smooth solutions in the form of twists while for n = 3 this number sharply reduces to one. We discuss some qualitative features of these solutions in view of their remarkable explicit representation through the exponential map of Spin(n).

AN EFFICIENT MULTI-RESOLUTION TEXTURE SYNTHESIZING METHOD BASED ON WAVELET TRANSFORM

2009 ◽  
Vol 18 (08) ◽  
pp. 1505-1516
Author(s):  
XIN ZHENG ◽  
XIAODONG WANG ◽  
HAIFENG CUI ◽  
TONG RUAN
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Real Time ◽  
Efficient Algorithm ◽  
Texture Synthesis ◽  
Discrete Wavelet ◽  
High Quality ◽  
The Real

The real-time rendering of high-quality, non-uniform scenes based on viewpoint has always been one of the most difficult problems in the CG area. In this paper, we propose one efficient algorithm to solve this problem with the help of merging texture synthesis and discrete wavelet transform (DWT) techniques. Using a single normal-sized image input, we can efficiently obtain texture sizes with different resolutions and update these in real-time rendering with the help of DWT. The results of our experiments prove that our algorithm can smoothly and efficiently render the non-uniform scenes based on viewpoint.

FINSLER LAPLACIANS AND MINIMAL-ENERGY MAPS

2000 ◽  
Vol 11 (01) ◽  
pp. 1-13 ◽  
Author(s):  
PAUL CENTORE
Keyword(s):  
Riemannian Metric ◽  
Energy Functional ◽  
Mean Value ◽  
Finsler Metric ◽  
Harmonic Mappings ◽  
Laplacian Operator ◽  
Minimal Energy ◽  
Finsler Manifolds ◽  
The Mean ◽  
Energy Maps

For any Finsler manifold, there is a geometrically natural Laplacian operator, called the mean-value Laplacian, which generalizes the Riemannian Laplacian. We show that, like the Riemannian Laplacian (for functions), we can see the vanishing of the mean-value Laplacian at some function f as the minimizing of an energy functional e(f) by f. This energy functional e depends on a Riemannian metric canonically associated to the Finsler metric and on a canonically associated volume form. We relate this construction to a more general construction of Jost, and define a notion of harmonic mappings between Finsler manifolds.

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