后验概率算法用于位移场的确定

Determination of Displacement Fields by Means of Maximum a Posteriori Estimator

提出了一种基于贝叶斯最大后验估计算法确定固体表面位移场的方法。在图像处理过程中,把位移看作随机变量,首先建立贝叶斯模型,对变形前数字图像中的一个像素点,选定变形前后两幅数字图像中对应的圆形子区,将两子区所对应的所有可能位移逐一代入贝叶斯后验概率公式进行计算,使后验概率最大的位移值就是所求该点的位移。在得到整像素位移之后,引入亚像素重建技术,确定图像的精确位移场。本文通过计算机数字模拟实验和实物标准位移实验,验证了该方法的可行性,并得到了0.02pixel的位移测量精度。

Experimental methods in solid mechanics rely heavily on surface displacement measurements. Many optical methods have been developed for that purpose. Digital speckle correlation method (DSCM), based on the correlation-matching search algorithm, is developed to measure the surface deformation. In this work, we propose a formulation derived from the information of probability between subsets in initial image and deformed images. The formulation maximizes the information between subset in the un-deformed image and the deformed image. After obtaining the correspondence of subset in un-deformed image, we can get the relative displacement of pixels in reference image and deformed image. This paper presents the theory of the method, the computer numerical simulation and the experimental verification.This paper presents a method applied to measure displacement fields using Bayesian MAP (maximum a posteriori) estimate. Based on analysis of digital image sequences, we formulate a Bayesian framework for estimating the displacement. In the support region of image before deformation, it is possible for the displacement of each pixel to evaluate the formulation of the MAP estimator for all the pixels in the region and select the optimal displacement that maximizes the formulation. After obtaining the integer pixel displacement, we can get accurate displacement field using sub-pixel technique. In the experiments, the method is validated and the resulting solution can show accuracy to 0.02 pixel.