Partial differential equation based methods in medical image processing

2007 ◽  
Author(s):  
Kwok-wing, Anthony Sum
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Medical Image ◽  
Medical Image Processing ◽  
Partial Differential

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.

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 Recognition of High Difference Features in Urban Planning Images Based on Morphological Filtering

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Peipei Liu
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Urban Planning ◽  
Image Enhancement ◽  
Feature Recognition ◽  
Human Life ◽  
Image Feature ◽  
Human Beings ◽  
Partial Differential

As an effective information carrier, image is the main source for human beings to obtain and exchange information. Therefore, the application field of image processing involves all aspects of human life and work. Image enhancement is an important part of image processing and plays an important role in the whole process of image processing. This paper mainly studies the image enhancement method based on partial differential equation. By analysing the combination of partial differential equation theory and enhancement, aiming at the shortcomings of low recognition accuracy, high error rate, and long time consuming in the current method of urban planning image feature recognition, a feature enhancement and simulation of urban planning image based on partial differential equation method is proposed; the preprocessing of urban planning image is realized by collecting the urban planning image. On the basis of preprocessing the urban planning image, the urban planning image is divided into several equal area subareas; the pixel gray value of each subarea and the average value of pixel distribution density of node landscape image are calculated; and whether the pixel points are at the edge of urban planning image is judged by setting the comprehensive mean threshold. According to the judgment results, the high difference features of urban planning images are intelligently recognized. Simulation results show that the proposed method can realize efficient and accurate recognition of high difference features in urban planning images.

Digital Image Processing Method Based Partial Differential Equation for Rock’s Microstructure

2011 ◽  
Vol 90-93 ◽  
pp. 2597-2600
Author(s):  
Jun Yue ◽  
Pan Huang ◽  
Jin Feng Cao ◽  
Bao Cheng Feng
Keyword(s):  
Differential Equation ◽  
Image Processing ◽  
Partial Differential Equation ◽  
Digital Image Processing ◽  
Digital Image ◽  
Processing Method ◽  
Partial Differential ◽  
Image Processing Method ◽  
Self Adaptation ◽  
Main Components

A digital image processing method based on partial differential equation(PDE) for rock’s heterogeneity is introduced. The actual microstructures of the rock sample was obtained by multiphase level set method. The main components of granite, quartz, feldspar and biotite, can be easily identified. The numerical results show that the method has advantage of self-adaptation and is benefit for grid generation in the following mechanical properties analyzing with Abaqus.

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