>> 王伟玺，2007，基于广义立体像对的三维重建方法研究
摘 要
随着高分辨率卫星遥感成像技术的发展，现代遥感技术已进入一个动态、快速、准确、及时提供多波段、多时相、海量对地观测数据的阶段，在国防建设、经济建设和社会发展等关系国计民生等领域有着越来越广泛的应用。
随着遥感卫星数量的增多，以及卫星立体成像能力的不断提高，越来越多的卫星影像资源为全球范围内目标的三维重建提供了可能。但由于各种特殊因素的制约（如政治因素、经济因素、技术因素、安全因素等），导致了可用的遥感影像资源十分有限，采用传统方法实现急需的各种三维重建还面临极大的挑战。基于上述原因，有时针对某些特定区域，往往难以得到同一颗卫星传感器或者同一相机所拍摄的立体影像（要么根本没有，要么价格昂贵），却可得到不同卫星传感器或者不同相机所拍摄的该区域影像。因此，从数据的可得性和成本考虑，利用不同传感器或相机所拍摄的非立体影像，按照摄影测量与遥感原理和相应的数学理论，同样能够构建起广义上的立体影像对（即左右影像的成像几何模型可以完全不同），达到提取三维立体信息的目的，从而实现对该地区地形和目标地物的三维重建。因此，如何利用多源遥感数据以及相关信息实现准确可靠的地形与地面目标三维重建，这一问题越来越凸显出其迫切性和重要性。
论文以基于多源遥感数据的三维重建为研究目标，对基于RFM（有理函数模型）的新型空间前方交会数学模型、广义立体像对的构建及计算方法等模型和算法进行了系统的研究，并进行了初步实验，主要研究内容如下：
⑴ 对目前国内外利用遥感影像进行三维重建的研究现状进行了综合评述，并着重介绍了RFM 模型在遥感影像三维重建方面的应用现状，分析了三维重建的发展趋势。
⑵ 提出广义立体像对的概念，并对此概念从内涵、适用对象、现实意义和数学意义等方面进行了详细的阐述。并对广义立体像对的构建方法进行了说明。
⑶ 提出了多源遥感影像数据规范化处理的技术框架，并对规范化处理所包含的内容和方法进行了探讨和说明。
⑷ 扩展了基于RFM 的空间前方交会数学模型。针对多源影像的复杂性，提出了RFM+CEM（共线方程模型）、RFM+AM（仿射变换模型）和RFM+DLT（直接线性变换模型）三种基于RFM 的空间前方交会数学模型。
⑸ 在模型算法研究的基础上，论文利用现有多源遥感数据对广义立体像对的构建和地面目标三维重建的精度进行了实验分析，着重分析和讨论了观测值权阵的引入及其对模型计算精度的影响。依据模型系数矩阵的状态，对RFM+RFM 模型，提出了对观测值权阵的等步长探测法和多项式回归法，以求出观测值权阵的最优解，提高计算精度；对RFM+AM 模型和RFM+DLT模型，提出矩阵QR 分解或者岭估计的方法，保证模型解算的稳定性。最后证明了构建广义立体像对的可行性。
关键词：
三维重建、广义立体像对、多源遥感数据、RFM、规范化处理、观测值权阵、等步长探测、多项式回归、矩阵QR 分解、岭估计
Abstract
Along with the development of high resolution satellite imaging technology,the modern remote sensing (RS) technology, providing multi-band, multi-time and abundant earth observation data in time, enters a dynamic, fast, and precise
era. And there are more and more applications in fields of national defence,
economy construction and social development and so on.
The increase of quantity and the stereo imaging ability improvement of satellites, affords the possibility to reconstruct global targets. But due to the
restriction of various factors (such as polity factor, economy factor, technique
factor and security factor), the practicable RS imagery resources are quite finite.
It faces huge challenge for us to obtain various imperative 3D reconstructions
with traditional methods. Based on above reasons, sometimes in certain
specifical regions, it is difficult to get stereopairs acquired by the same satellites
or cameras (maybe imagery do not exist at all, maybe price is expensive), but
easy to get imagery acquired by different satellites or cameras. Considering the
availability and the cost of RS data, we can utilize these different non-stereo
imagery, obey the principles of photogrammetry and RS and homologous
mathematics theories, construct generalized stereopairs samely, reach the
purpose to obtain 3D information, and then realize the 3D reconstruction for the
terrain and target objects in these regions. So it is a problem that how to utilize
these multi-source RS data and correlative information to realize the exact and
reliable 3D reconstruction of terrain and objects. And this problem reveals its
instancy and importance more and more, and needs to resolve the key theories
and techniques relating to this problem.
This dissertation focuses on the 3D reconstruction based on multi-source
RS data, and makes systemic investigation in space intersection mathematics
models based on Rational Function Model (RFM), construction of generalized
stereopairs and relative arithmetics, and analysis of some primary experiments.The main study contents are as the following:
⑴ This dissertation reviews the up-to-date 3D reconstruction technologies
utilizing RS imagery, and recommends the applications of RFM. Then prospects
the developing trendency of 3D reconstruction.
⑵ Proposes a concept of “generalized stereopair”, and expatiates this
concept detailedly in connotation, fitting objects, siganificance of realism and
mathematics. Then illuminates the construction methods of generalized
stereopairs.
⑶Aimming at the multi-source RS imagery, establishes a standardizational
processing framework, then studies and explains the contents and methods
included in standardizational processing.
⑷ Expands the space intersection mathematics model based on RFM, and
considering the complexity of multi-source RS imagery, brings out three new
models: the RFM+CEM (Collinearity Equation Model), RFM+AM (Affine
Model), and RFM+DLT (Direct Linear Transformation) .
⑸ Based on the study of models and arithmetics, this dissertation utilizes
multi-source RS data in existance to construct generalized stereopairs and
analyses the precision of 3D reconstruction in experiments. Then stressly
analyses and discusses the intruduction of observation-value weight matrix, and
its effection on computing precision of these models. According to the state of
coefficient matrix of medels, for RFM+RFM model, brings out the equal-step
detection and polynomial regression for observation-value weight matrix in
order to compute the optimum values, and improve the computing precision; for
RFM+AM and RFM+DLT models, utilizes matrix QR decomposition and ridge
regression methods to guarantees the computing stability of these models.
Finally proves the feasibility of construction of generalized stereopairs.
Key words: 3D reconstruction, generalized stereopair, multi-source RS data, RFM,
standardizational processing, observation-value weight matrix, equal-step
detection, polynomial regression, matrix QR decomposition , ridge regression.
