New Development of Statistical Optimization and Model Selection for Motion Image Analysis

1. 图像三维分析的统计理论我们提出了一种数学上一致的图像噪声统计特性建模理论，用于分析图像三维重建的精度，从图像灰度估计协方差矩阵，渐近评价这种分析的精度，并推导出“几何AIC”和“几何MDL”等模型选择标准。我们还提出了一种“规范理论”来分析重构形状的规格化如何影响其可靠性评估。基于图像的三维重建统计优化构建了两幅图像重建三维形状和光流重建三维形状的最优系统。然后，我们使用真实的图像对它们的性能进行了评估和比较。图像之间的自动对应检测我们开发了一种自动匹配两幅图像中独立检测到的特征点的技术。这是一种多阶段技术，迭代地升级包含各种全局约束的试探性匹配。我们将该技术应用于多幅图像的图像拼接以及场景和物体的三维重建。视频序列中运动物体的分离我们开发了一种检测视频序列中运动物体的技术，其中物体和背景都是独立运动的。我们设计了一种自动去除外围轨迹的统计检验方法和一种自动选择最适合运动分离的数学条件的方案。通过实际的视频图像验证了该方法的有效性。

1. Statistical theory for 3-D analysis of imagesWe presented a mathematically consistent theory for modeling statistical properties of image noise for analyzing the accuracy of 3-D reconstruction from images, estimating the covariance matrix from the image gray levels, asymptotically evaluating the accuracy of such analysis, and deriving model selection criteria such as "geometric AIC" and "geometric MDL". We also proposed a "gauge theory" for analyzing how the normalization of the reconstructed shape affects its reliability evaluation.2. Statistical optimization of 3-D reconstruction from imagesWe built an optimal system for reconstructing 3-D shape from two images and reconstructing 3-D shape from optical flow. We then evaluated and compared their performance, using real images.3. Automatic correspondence detection between imagesWe developed a technique for automatically matching feature points independently detected in two images. This is a ulti-stage technique, iteratively upgrading tentative matches incorporating various global constraints. We applied our technique to image mosaicing of multiple images and 3-D reconstruction of scenes and objects.4. Separation of moving objects in a video sequenceWe developed a technique for detecting moving objects in a video sequence in which objects and, backgrounds are both moving independently. We devised a statistical testing method for automatically removing outlying trajectories and a scheme for automatically selecting most appropriate mathematical conditions fo the motion separation. Using real video images, we confirmed that out method was very effective.