An Efficient Image Segmentation Using Partial Differential Equation for Image Processing Applications

2021 ◽  
Vol 11 (10) ◽  
pp. 2538-2545
Author(s):  
P. Geetha ◽  
S. Nagarani
Keyword(s):  
Differential Equation ◽  
Mathematical Method ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Image Segmentation ◽  
Image Restoration ◽  
Geometric Analysis ◽  
Stochastic Modelling ◽  
Partial Differential ◽  
Structural Work

Different processing of the images, such as the image captured, saved and retrieved from another use of the specific image, must be restructured in various ways in the process. More methods such as image restoration, picture segmentation, improvement of the picture etc can be used when processing images. Reconstructed in 3D picture 2D pictures are need to be proper. Including geometric wavelets and geometric analysis the structural work focused upon a variational and a selectable differential equation to test PDE’s which is a convergence of stochastic modelling and analysis of harmonics. This paper focuses primarily on the critical reviews of the image segmentation collection with the PDE application as a mathematical method and introduces the key tool of mathematics and techniques along with the literature-based analysis.

scholarly journals Noise Data Removal and Image Restoration Based on Partial Differential Equation in Sports Image Recognition Technology

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shi Junmei
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Image Restoration ◽  
Image Recognition ◽  
Image Data ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Image Information ◽  
Noise Data

With the rapid development of image processing technology, the application range of image recognition technology is becoming more and more extensive. Processing, analyzing, and repairing graphics and images through computer and big data technology are the main methods to obtain image data and repair image data in complex environment. Facing the low quality of image information in the process of sports, this paper proposes to remove the noise data and repair the image based on the partial differential equation system in image recognition technology. Firstly, image recognition technology is used to track and obtain the image information in the process of sports, and the fourth-order partial differential equation is used to optimize and process the image. Finally, aiming at the problem of low image quality and blur in the transmission process, denoising is carried out, and image restoration is studied by using the adaptive diffusion function in partial differential equation. The results show that the research content of this paper greatly improves the problems of blurred image and poor quality in the process of sports and realizes the function of automatically tracking the target of sports image. In the image restoration link, it can achieve the standard repair effect and reduce the repair time. The research content of this paper is effective and applicable to image processing and restoration.

scholarly journals Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent Approach-Based Multiscale Denoising Model for Texture Image

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Yi-Fei Pu ◽  
Ji-Liu Zhou ◽  
Patrick Siarry ◽  
Ni Zhang ◽  
Yi-Guang Liu
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Fractional Order ◽  
Differential Calculus ◽  
Order Partial Differential Equation ◽  
Texture Image ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Integer Order

The traditional integer-order partial differential equation-based image denoising approaches often blur the edge and complex texture detail; thus, their denoising effects for texture image are not very good. To solve the problem, a fractional partial differential equation-based denoising model for texture image is proposed, which applies a novel mathematical method—fractional calculus to image processing from the view of system evolution. We know from previous studies that fractional-order calculus has some unique properties comparing to integer-order differential calculus that it can nonlinearly enhance complex texture detail during the digital image processing. The goal of the proposed model is to overcome the problems mentioned above by using the properties of fractional differential calculus. It extended traditional integer-order equation to a fractional order and proposed the fractional Green’s formula and the fractional Euler-Lagrange formula for two-dimensional image processing, and then a fractional partial differential equation based denoising model was proposed. The experimental results prove that the abilities of the proposed denoising model to preserve the high-frequency edge and complex texture information are obviously superior to those of traditional integral based algorithms, especially for texture detail rich images.

scholarly journals A Partial Differential Equation-Based Image Restoration Method in Environmental Art Design

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Chen Li
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Image Restoration ◽  
Rapid Development ◽  
Real Life ◽  
Generative Adversarial Networks ◽  
Environmental Art ◽  
Partial Differential ◽  
Art Design ◽  
Restoration Model

With the rapid development of networks and the emergence of various devices, images have become the main form of information transmission in real life. Image restoration, as an important branch of image processing, can be applied to real-life situations such as pixel loss in image transmission or network prone to packet loss. However, existing image restoration algorithms have disadvantages such as fuzzy restoration effect and slow speed; to solve such problems, this paper adopts a dual discriminator model based on generative adversarial networks, which effectively improves the restoration accuracy by adding local discriminators to track the information of local missing regions of images. However, the model is not optimistic in generating reasonable semantic information, and for this reason, a partial differential equation-based image restoration model is proposed. A classifier and a feature extraction network are added to the dual discriminator model to provide category, style, and content loss constraints to the generative network, respectively. To address the training instability problem of discriminator design, spectral normalization is introduced to the discriminator design. Extensive experiments are conducted on a data dataset of partial differential equations, and the results show that the partial differential equation-based image restoration model provides significant improvements in image restoration over previous methods and that image restoration techniques are exceptionally important in the application of environmental art design.

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