scholarly journals Urban Planning Image Feature Enhancement and Simulation Based on Partial Differential Equation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Duo Li
Keyword(s):  
Partial Differential Equations ◽  
Path Planning ◽  
Differential Equations ◽  
Change Detection ◽  
Dimensional Space ◽  
Speckle Noise ◽  
Planning Problem ◽  
Partial Differential ◽  
Difference Image ◽  
The Difference

Based on the introduction of the basic ideas and related technologies of partial differential equations, as well as the method of path planning, the application of partial differential equations in solving urban path planning is studied. The path planning model of partial differential equations and the setting of obstacle boundary conditions are introduced, and adaptive. Theoretical research and experimental results show that it is feasible and effective to solve urban path planning by partial differential equations, which provides a new way for urban path planning research ideas and methods. This paper proposes an image detection algorithm based on diffusion equation. According to the logarithmic transformation, the multiplicative speckle noise in the image can be converted into additive noise. We first perform logarithmic transformation on the image and then use the denoising model of the diffusion equation to filter out the noise in the image and then use the logarithm to recognize the image. The difference image is obtained by the domain difference method, and finally, the difference image is classified by the clustering algorithm, and the change area is extracted. Experiments show that the algorithm can effectively reduce the effect of multiplicative speckle noise on the change detection results, improve the accuracy of change detection, and shorten the change detection time. This article takes the path planning problem of a two-dimensional space city as an example to discuss the application of partial differential equations. According to the principle of energy conservation, this paper uses the two-dimensional space radiant heat conduction equation as an example to model and illustrate the solution of the path planning problem.

scholarly journals SAR Image Change Detection Based on Multi-scale Feature Extraction

2021 ◽  
Vol 10 (4) ◽  
pp. 077-081
Author(s):  
Xiaoqian Yuan ◽  
Chao Chen ◽  
Shan Tian ◽  
Jiandan Zhong
Keyword(s):  
Feature Extraction ◽  
Change Detection ◽  
Speckle Noise ◽  
Kernel Matrix ◽  
Sar Image ◽  
Scale Feature ◽  
Difference Image ◽  
Multi Scale ◽  
Image Change Detection ◽  
The Difference

In order to improve the contrast of the difference image and reduce the interference of the speckle noise in the synthetic aperture radar (SAR) image, this paper proposes a SAR image change detection algorithm based on multi-scale feature extraction. In this paper, a kernel matrix with weights is used to extract features of two original images, and then the logarithmic ratio method is used to obtain the difference images of two images, and the change area of the images are extracted. Then, the different sizes of kernel matrix are used to extract the abstract features of different scales of the difference image. This operation can make the difference image have a higher contrast. Finally, the cumulative weighted average is obtained to obtain the final difference image, which can further suppress the speckle noise in the image.

scholarly journals Change Detection from SAR Images Based on Convolutional Neural Networks Guided by Saliency Enhancement

2021 ◽  
Vol 13 (18) ◽  
pp. 3697
Author(s):  
Liangliang Li ◽  
Hongbing Ma ◽  
Zhenhong Jia
Keyword(s):  
Neural Networks ◽  
Change Detection ◽  
Saliency Detection ◽  
Speckle Noise ◽  
Saliency Map ◽  
Wavelet Neural Networks ◽  
Sar Images ◽  
Difference Image ◽  
The Difference ◽  
Log Ratio

Change detection is an important task in identifying land cover change in different periods. In synthetic aperture radar (SAR) images, the inherent speckle noise leads to false changed points, and this affects the performance of change detection. To improve the accuracy of change detection, a novel automatic SAR image change detection algorithm based on saliency detection and convolutional-wavelet neural networks is proposed. The log-ratio operator is adopted to generate the difference image, and the speckle reducing anisotropic diffusion is used to enhance the original multitemporal SAR images and the difference image. To reduce the influence of speckle noise, the salient area that probably belongs to the changed object is obtained from the difference image. The saliency analysis step can remove small noise regions by thresholding the saliency map, and interest regions can be preserved. Then an enhanced difference image is generated by combing the binarized saliency map and two input images. A hierarchical fuzzy c-means model is applied to the enhanced difference image to classify pixels into the changed, unchanged, and intermediate regions. The convolutional-wavelet neural networks are used to generate the final change map. Experimental results on five SAR data sets indicated the proposed approach provided good performance in change detection compared to state-of-the-art relative techniques, and the values of the metrics computed by the proposed method caused significant improvement.

scholarly journals Variational symmetries and pluri-Lagrangian structures for integrable hierarchies of PDEs

2020 ◽  
Author(s):  
Matteo Petrera ◽  
Mats Vermeeren
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integrable Hierarchies ◽  
Dimensional Space ◽  
Original System ◽  
Lagrange Equations ◽  
Partial Differential ◽  
Dimensional Space Time ◽  
Variational Symmetries ◽  
Nonlinear Math

Abstract We investigate the relation between pluri-Lagrangian hierarchies of 2-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings in Petrera and Suris (Nonlinear Math. Phys. 24(suppl. 1):121–145, 2017) for ordinary differential equations. We consider hierarchies of 2-dimensional Lagrangian PDEs (many of which have a natural $$(1\,{+}\,1)$$ ( 1 + 1 ) -dimensional space-time interpretation) and show that if the flow of each PDE is a variational symmetry of all others, then there exists a pluri-Lagrangian 2-form for the hierarchy. The corresponding multi-time Euler–Lagrange equations coincide with the original system supplied with commuting evolutionary flows induced by the variational symmetries.

scholarly journals Exact Solutions for Some Fractional Partial Differential Equations by the Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Bin Zheng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Wave Equations ◽  
Dimensional Space ◽  
Space Time ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Liouville Derivative ◽  
Dimensional Space Time

We apply the method to seek exact solutions for several fractional partial differential equations including the space-time fractional (2 + 1)-dimensional dispersive long wave equations, the (2 + 1)-dimensional space-time fractional Nizhnik-Novikov-Veselov system, and the time fractional fifth-order Sawada-Kotera equation. The fractional derivative is defined in the sense of modified Riemann-liouville derivative. Based on a certain variable transformation, these fractional partial differential equations are transformed into ordinary differential equations of integer order. With the aid of mathematical software, a variety of exact solutions for them are obtained.

scholarly journals New Approach for Solving Three Dimensional Space Partial Differential Equation

2019 ◽  
Vol 16 (3(Suppl.)) ◽  
pp. 0786 ◽  
Author(s):  
Enadi Et al.
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Partial Differential ◽  
Transform Method ◽  
New Approach ◽  
Practical Implications ◽  
Three Dimensional Space

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.        Finally, all algorithms in this paper are implemented in MATLAB version 7.12.

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