直线三维重建优化准则及算法研究

As the manmade environment has drawn more and more attention, the 3D reconstruction of straight line in them became a hot topic in computer vision. Because of the measurement error from the line extraction and lacking the description of its statistic property in the optimality criteria of known algorithms, the 3D line reconstruction is far from being satisfactory. Therefore, in our research projection, the statistic model of measurement error of edge point by line extraction will be researched to construct the estimation function of single line coordinates. To improve the estimation accuracy of line coordinates further, parallel lines will be detected and their coordinates will be reformulated to construct the estimation function of multiple image line coordinates. Based on these, the optimality criteria of multiple line coordinates, which will be solved globally with the linear matrix inequality and the convex optimization, will be constructed by researching the algebraic representations of triple-view and multiple-view line projective geometric relation . Moreover, the reformulation of the algebraic representation will be researched to construct the optimality criterion of single image line coordinates, and an efficient method will be proposed to solve the criterion. Via this research projection, not only the statistically meaningful optimality criteria of the 3D line reconstruction will be constructed, which indicates that this projection is of value to academia, but also some more extract and more efficient algorithms will be supplied for manmade environment reconstruction, which means that this projection is of value to application.

随着人们对人造场景的日益关注，其中大量存在的直线特征的三维重建成为计算机视觉研究的热点。由于直线提取中存在测量误差，而已知算法的优化准则无法准确描述测量误差的统计特性，使得直线三维重建结果不理想。为此，本项目通过研究图像直线提取方法，建立边缘点位置误差统计模型，构造包含单条直线坐标的估计函数。为了进一步提高估计精度，通过平行直线检测并重新建立其坐标表示，构造包含多条直线坐标的估计函数。在此基础上，通过研究三视及多视直线投影几何关系的代数表示，建立包含多条直线坐标的优化准则，根据线性矩阵不等式以及凸优化方法提出全局最优的求解方法；通过研究代数表示的变化形式，建立包含单条直线的优化准则，提出在一定精度下效率更高的求解方法。本项目的研究不仅建立了具有统计意义的直线三维重建优化准则，具有学术价值，还给人造场景结构提供更加实时精确的算法，具有重要的应用前景。

随着人造场景日益得到人们的关注，对人造场景进行三维重建成为了计算机视觉领域的研究热点。由于人造场景中存在大量直线特征，获得空间直线的精确坐标成为人造场景精确重建的关键。本项目的研究围绕空间直线三维重建展开，通过建立更加合理的空间直线坐标优化准则并进行求解，提高空间直线重建精度。主要内容包括：通过研究图像直线提取方法，提出两种直线提取时产生的误差；根据直线提取过程，通过数学推导，提出两种提取误差对应的概率统计模型；基于这两种统计模型，建立四种具有统计意义的空间直线优化准则；在三视情况下和多视情况下，提出基于边缘点位置误差统计分布优化准则的最优空间直线重建算法；在三视情况下提出基于边缘点位置误差的直线重建实效算法，在多视情况下提出基于边缘法向误差的直线重建实效算法以及四种统计误差优化准则的直线重建实效算法；结合图像直线提取方法的研究，提出一种针对合成孔径雷达图像的多尺度边缘检测方法，并基于此提出新的合成孔径雷达图像显著性区域检测算法。本项目的研究不仅提出了新的直线三维重建理论方法，还给出了直线重建的具体算法，为直线重建的应用打下基础。