作　　者： ; (许憬）; (曾庆煜）;

机构地区： 科技部

出　　处： 《电视技术》 2013年第11期57-60,65,共5页

摘　　要： 采用数值模拟的方法研究一维连续和离散各向异性扩散方程的行为差异。研究结果表明:当没有逆向扩散时,连续和离散方程的演化方式类似;当有逆向扩散时,连续方程不收敛,但其相对应的离散方程会在图像灰度函数的拐点处形成阶梯边缘。揭示了离散逆向扩散的一个重要特性:其扩散结果由图像灰度函数拐点的初始分布预先确定,而虚假阶梯边缘的形成是由于计算噪声引起了假拐点。提出了用约束图像灰度函数凸凹性的方法来避免由计算噪声引起的虚假阶梯边缘。该方法仅对计算噪声引起的虚假阶梯边缘有效,不能避免由观测/量化噪声或图像纹理拐点形成的虚假阶梯边缘。 Motivated by the need to implement anisotropic diffusion equations numerically, numerical simulation is used to illustrate the behavioral discrepancy of one-dimensional continuous and discrete anisotropie diffusion equations. It shows that, when no backward diffusion is involved, both the continuous and discrete equations evolve in a similar manner. When there is backward diffusion, however, a continuous equations diverges with time but its discrete counterpart converges to step edges at inflection points of the image. It reveals an important property of discrete backward diffusion： its destination is predetermined by the initial distribution of inflection points of the image intensity function and false step edges are formed because computational noise creates false points of inflection. Convexity-constrained diffusion is proposed to prevent the formation of false step edges caused by false inflection points that are incurred by computational noise. But this approach cannot prevent the formation of false step edges corresponding to inflection points due to observation/quantization noise or image textures.

关 键 词： 扩散方程 图像增强 离散化 拐点 偏微分方程

领　　域： [电子电信] [电子电信]