【作者】 顾晓东；

【导师】 刘健；

【作者基本信息】 大连理工大学 ， 机械制造及其自动化， 2003， 博士

【摘要】 本文主要研究了在计算机视觉大背景下基于偏微分方程的图像几何处理方法，利用偏微分方程构造非线性滤波器，研究各种类型的非线性扩散方程在图像处理中的应用并将其推广到曲面上。 基于偏微分方程的图像几何处理方法----图像视为一分片光滑曲面，利用偏微分方程变形给定的曲线(图像的等值线)、曲面(图像的灰度曲面)，演化的曲线、曲面成为方程解的几何表征，从而将偏微分方程的解与图像联系起来，通过求解偏微分方程实现图像的非线性滤波。本文由非线性扩散方程与规整化的内在关联将各种迭代滤波器统一为基于最大后验估计(MAP)的变分规整化，从而将寻找扩散方程的传导系数(扩散系数)的问题转化为寻找变分积分函数(先验能)的问题，选择不同的变分积分函数得到不同的偏微分方程，从而构造出不同的非线性滤波器。最后本文将此方法推广到曲面上以解决曲面上图像的非线性滤波问题。 摄像机自标定是计算机视觉的重要内容，在本文的开头研究了摄像机自标定技术，基于Kruppa方程或Huang_Faugeras约束给出了任意运动变焦摄像机的分步线性自标定方法。本文在统一了各种迭代滤波器的基础上，将图像规整化复原的思想引入小波阀值技术实现图像低比特率压缩中，探讨了自适应总变分规整化和熵变分规整化方法在图像有损压缩中的应用，使重构的图像在去除图像噪声的同时保留了图像的特征细节，消除了振铃效应(Gibbs现象)。本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。更多还原

【Abstract】 Based on the fusion of nonlinear diffusion and multiscale analysis, the methods of Partial Differential Equations (PDE) have developed in parallel with Bayesian image restoration techniques. In this paper, the methods of PDE based geometric technique are discussed under the background of the computer vision.The basic idea of PDE based geometric technique in image processing is to deform a given curve (isophote), surface, or image with the PDE, and obtain the desired nonlinear filter result as the solution of this PDE. A variational approach to MAP (Maximum A Posteriori) Estimation unify various nonlinear filters, and the question of the choice of diffusion coefficients has been transformed as the question in search of the variational integral function (prior energy), the different variational integral function is equivalent to different PDE, and derive different nonlinear filters. Finally this processing method has been extended to the image that define maps onto a given generic surface.On the head of this dissertation, based on the Kruppa equation or Huang-Faugeras constraints, a step-by-step linear self-calibration algorithms of arbitrary-motion digital camera with variable focal length have been proposed. Secondly, regarding prior energy as probability distribution, the entropic variation approach and/or the entropic-total variation approaches have been discussed. Further, the adaptive total variation regularization or/and the entropic variation approach have been employed in image’ s wavelet transforms space, to select and modify the remained standard wavelet coefficients so that the reconstructed images have fewer oscillations near edges (Gibbs phenomenon). Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface(manifold) as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.更多还原