偏微分(PDE)非线性图像滤波方法具有优良特性,但由于其计算量大而无法满足实时控制需求.细胞神经网(CNN)可以描述图像PDE模型,利用模拟CNN芯片并行求解,有助于提高其实时性.本文用CNN实现了PDE偏差非线性图像滤波器,提出了一种局部运算的噪声估计方法以选择适当的平滑系数.计算结果表明,这种噪声估计方法可以对不同噪声水平作出较精确的估计.仿真实验结果表明,CNN-PDE非线性滤波器取得了满意的滤波效果,用CNN实现PDE非线性滤波器的方法是有效可行的

1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension

为了抑止采用分水岭方法分割红外图像时的过分割现象,首先利用细胞神经网络高效求解偏微分方程的能力,实现了可调偏差异质扩散滤波器并用其对图像作预处理.为了消除噪声残留,引入了平滑系数与限制强度系数对梯度图作阈值化处理.实际红外图像的分水岭分割结果显示,所提出的预处理方法能够有效抑止过分割现象

1 First Order ave Equation SLIDE 1 The simplest first order partial differential equation in two variables(a, t)is the linear wave equation. Recall that all first order PDE's are of hyperbolic type INITIAL BOUNDARY VALUE PROBLEM (IBVP) 0,x∈(0,1)

Finete Difference Methods 五点离散 A,(x, u(x+h, y)-2u(x, y)+u(x-h,y) h (x, y+h)-2u(x, y)+u(x,y-h)