基于像素间孤波的图像处理模型分析

通过对数字图像像素栅格之间非线性影响的研究,建立了像素间非线性影响的一维和二维时间演化方程模型,通过对方程模型的分析可知图像在空间上是离散的,图像像素之间的作用关系是非线性连续的,且方程具有解析性的孤波解.模型重点研究像素孤波的两个孤波之间的相互作用,给出了像素孤波的二孤波解,利用像素孤波的相互作用来研究模型的性能,发现像素孤波相互作用后仍能保持自身性质不变,因此可用像素孤波代替像素本身.同时发现像素孤波在相互作用时其幅值是两者的非线性叠加,可以作为影响的结果;并且像素孤波相互作用时其相位会发生特定的改变,可以将其映射为像素之间相互影响的方向信息.通过实验表明,模型可以用在图像滤波中,平滑度并不最优但是图像细节得到更多保留. 

Analysis of image processing model based on pixels of solitary waves

Through the study on nonlinear effect of digital image pixel grid, the one-dimensional and two-dimensional time evolution equations model of nonlinear effect between pixels were established, the analysis of the equation model shows that the image was discrete in space, but on the structure of mutual information was a continuous differential difference equations, and the equation had analytic solitary wave solutions. The model was used to study the interaction of image pixels between two solitary waves, pixel solitary wave of two solitary wave solutions were given, and used the interaction of solitary waves of the pixel to study the performance of model, it was found that pixel solitary wave can still maintain their properties unchanged after the interaction, so pixel itself can be replaced by pixel solitary wave. To study the interaction situation of pixel solitary wave, it was found that pixel solitary wave amplitude was nonlinear superposition of the two, so it could be used as the result of the influence. The phase change of pixel solitary wave can map for direction and provide direction information of the image. The experiment result shows that the model can be used in image filtering, although the smoothness is not optimal, image details retain more.