有限条件下单帧光谱影像三维重构研究
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摘要
作为一项重要基础数据,数字地面模型广泛应用于测绘、农林业、工程设计等国民经济各个领域。摄影测量是目前获取数字地面模型的最主要方法,它基于特征匹配原理,通过寻找立体像对上的同名像点以获取视差信息。然而,在一些表面光滑或缺乏纹理的区域,如沙漠、水域、山区等,摄影测量方法无法快速有效地提取特征点、特征边缘及纹理特征,其精度受到较大影响。另外,受多云、多雾、光照不足等天气条件限制,一些地区可能无法获取同一时间的高分辨率立体像对,此时摄影测量方法的应用受到极大地限制。
较之于立体像对,单幅高分辨率遥感图像更易获取。若能基于单幅图像较精确的提取地表三维,辅以有限个数的地面控制点,插值生成高分辨率的数字地面模型,则能克服立体像对在上述条件下的限制。明暗恢复形状(Shape from Shading,简称SFS)理论作为计算机视觉领域的一个重要课题,旨在从单张影像上获取物体表面的形状信息,是重建三维表面的重要工具,在单幅遥感影像三维重建方面极具潜力。本文在有限的地面控制点条件下,将SFS理论引入地学研究,利用该理论对单幅影像进行三维重建,获取关于地表坡度坡向等辅助信息,用以对控制点格网进行插值,最终得到更高分辨率的地面三维格网,实现在稀疏控制点条件下的地形表面三维重建。本文所发展的方法顾及了地形格网内部地表真实变化趋势,能对无法获取立体像对的地区进行三维重建,克服了立体像对的技术限制,对于快速获取大范围地区的高分辨率数字地面模型具有重要意义。
针对SFS理论中的反射率同一性假设问题、立体匹配方法失效区域的三维重建问题、以及立体匹配中由缺乏纹理特征和透视收缩导致的误匹配问题,本文主要研究工作及创新点如下：
(1)解决朗伯体表面假设下SFS理论中反射率同一性假设限制：详述了朗伯体表面下的SFS理论,并对该问题的两类主要解算方法：最小化方法和传播方法进行了详细的研究。针对朗伯体SFS问题中物体反射率同一性假设的限制,提出了结合本征图像理论建立多尺度下的朗伯体表面II-SFS重建方法,通过图像分解减小由物体表面反射率变化导致的SFS重建误差。实验表明该方法可有效解决朗伯体SFS理论中反射率同一性假设的限制,大大提高SFS算法三维重建精度。
(2)建立非朗伯体反射表面快速三维重建方法：详细研究了基于Oren-Nayar模型和Phong模型的三维重建算法,将相关反射图方程写为Hamilton-Jacobi方程(简称H-J方程)的形式,利用Lax-Friedrichs函数对该方程进行离散化,采用高阶快速扫描法(High Order Fast Sweeping method,简称HO-FSM方法)求解得到地表法向量的估计值。
(3)利用SFS理论针对立体匹配方法失效的区域三维重建：提出了基于Oren-Nayar反射模型的有限条件下各向异性表面三维重建的NSDMI(?)里论框架,本文首先根据不同地表覆盖类型对影像进行分类,估算每种地物类别的反射率值,再将相关反射图方程写为H-J方程的形式,采用HO-FSM方法求解得到地表法向量的估计值,最后利用最小二乘法对控制点格网进行内插。实验表明该方法可解决立体匹配失效区域无法重建三维的问题,在有限个地面控制点条件下可得到较高精度的地面三维模型。
(4)讨论未知光照条件下影像光源参数估计问题：本文总结了在光源方向和反射率值未知时的经典盲估算算法,以及基于样本学习的光源、反射率、形状联合估计算法。最后采用合成影像和真实遥感影像作为实验图像,对三种经典盲估算方法进行实验分析,表明Zheng方法对于合成影像的光源估算精度最高。
(5)提出立体像对与SFS相结合的SFS-SDI-SR重建模型：在分析了立体像对与SFS的优缺点的基础上,探讨了如何将两者有效结合的研究思路,并给出了基于立体像对和明暗恢复形状相结合的三维重建的理论框架。首先对左右片提取特征点并进行特征匹配：采用FSM-SFS方法对特征点区域进行三维恢复,将恢复得到的表面形状作为新的相似似性测度;其次对不同像素点进行三维重建：特征匹配方法仅匹配可靠的点,非特征点采用SFS方法恢复高度；最后将不同区域的重建结果相结合得到整个观测区域的三维模型。对月球三线阵影像进行实验,结果表明本文方法相较于单一立体匹配和SFS方法可获得更高分辨率的表面三维信息,克服基于图像亮度信息的匹配方法中存在的不足,在光滑的和纹理特征不丰富的区域也能得到较好的重建结果。总而言之,本文首先解决了当前SFS理论中本身存在的反射率同一性假设带来的问题；再针对立体匹配方法失效的区域,利用有限个数地而控制点和单张遥感影像SFS三维重建结果建立数字地面模型；最后为解决立体匹配中由缺乏纹理特征和透视收缩导致的误匹配问题,建立立体像对与SFS相结合的三维重建框架,建立高度相似性测度,得到更高分辨率的数字地面模型。本文的研究显著减小了SFS理论对真实影像三维重建的误差,极大提高基于特征点的立体匹配精度,解决了立体匹配失效区域三维重建困难的问题,并推动了SFS理论在地学研究中的应用。
Digital Terrain Model (DTM in short), as an important data, is widely used in mapping, agriculture, forestry, industrial and other applicable filed. Photogrammetry is the main method to generate the DTM, which is based on the principle of feature extraction and feature matching. It is aim to find the pairs of matched points and get the parallax information. However, in some areas seriously lack of texture, such as deserts, waters, mountains and so on, it is unable to quickly and efficiently extract the feature points and edges, under this condition, the matching accuracy will be declined. Meanwhile, some areas often fail to obtain stereo image pairs of high spatial resolution due to the bad weather such as cloud and fog, so terrain reconstruction can't be done by stereo method.
Since single remote sensing image is more accessible compared with stereo pairs, if we can acquire the terrain details from single image and consider it as the auxiliary data in surface reconstruction; it is possible to generate an accurate dense surface model by using sparse ground control points with the help of the single imagery. Shape from Shading technology (we can call it SFS in short), is aim to obtain surface shape information from a single image, which is based on the inverse process of the physical imaging. It is an important tool for3D surface reconstruction and very potential in terrain surface reconstruction of a single remote sensing image. In this paper, SFS is introduced in geoscientific research. Interpolating the surface model according to the information about the surface details recovered from SFS, can not only generate the DTM for the areas where the stereo image pairs can't be obtained, but also take the real trend of the internal surface of the grid into account. It is of great significance for quickly creating surface model for wide areas. The main works of this paper are as follows:
(1) Solving the limitation of the reflectance in SFS theory under Lambertain surface assumption:described the Lambertian SFS theory and the two main types of solution method:minimization and propagating method. To solve the limitation in SFS theory that reflection should be a constant in the image, a reconstruction method combined the Intrinsic Image theory and SFS theory was proposed. The reconstruction error caused by surface reflectance variation was reduced by image decomposition. Experiments performed on synthetic images show that the intrinsic image decomposition can effectively separate the image reflectance component from the original image and improve the accuracy of the SFS algorithm.
(2) Establishing the non-Lambertian surface fast reconstruction method:gave a detailed study of the Oren-Nayar model and the Phong model based3D reconstruction algorithm, rewrote the reflection map equation in the form of the Hamilton-Jacobi equation (referred to as H-J equation), then used the Lax-Friedrichs Hamiltonian in the equation discretization, finally utilized the high-ordered fast sweeping method (referred to as HO-FSM method) for estimating the surface normal vectors.
(3) Reconstructing the area where stereo matching method fails to work:Based on the Oren-Nayar reflectance model, a theoretical framework of anisotropic surface reconstruction under the limited condition was proposed. First of all, supervised classification was performed, and the reflectance for each land cover type was estimated; then the reflection map equation was written as the H-J equation, and HO-FSM method was used for solving it; Finally, the least squares was utilized to interpolate the grid of control points.
(4) Discussing the important parameters estimation problems in the SFS theory. This paper reviewed the approach how to estimate the illumination direction using image reflection equation. Then three classic methods were compared and analyzed in both synthetic and real image experiments.
(5) Giving a combination framework for stereo and SFS algorithm on the basis of the advantages and disadvantages for each one:Firstly the FSM-SFS algorithm was implemented for the feature region reconstruction, and the results were used to form a new depth similarity measurement; then only the stable and reliable points were regarded as the matching points, and other points were reconstructed by SFS algorithm; Finally the results for all the surface points were combined to generate the3D model. The reconstruction experiment was implemented based on the three-line array moon images and the results show that the proposed method could give more accurate result than stereo and SFS each of themselves.
In summary, this paper first solved the inherent problems in the current SFS theory, proposed solutions to improve the accuracy of SFS algorithm; then, in the area where stereo matching method fails to work, an DTM generation algorithm using single remote sensing imagery and certain ground control points was proposed; finally, when the stereo pairs are available, the SFS theory and stereo method was combined to improve the accuracy of stereo matching, so the DTM with higher resolution could be generated.
较之于立体像对,单幅高分辨率遥感图像更易获取。若能基于单幅图像较精确的提取地表三维,辅以有限个数的地面控制点,插值生成高分辨率的数字地面模型,则能克服立体像对在上述条件下的限制。明暗恢复形状(Shape from Shading,简称SFS)理论作为计算机视觉领域的一个重要课题,旨在从单张影像上获取物体表面的形状信息,是重建三维表面的重要工具,在单幅遥感影像三维重建方面极具潜力。本文在有限的地面控制点条件下,将SFS理论引入地学研究,利用该理论对单幅影像进行三维重建,获取关于地表坡度坡向等辅助信息,用以对控制点格网进行插值,最终得到更高分辨率的地面三维格网,实现在稀疏控制点条件下的地形表面三维重建。本文所发展的方法顾及了地形格网内部地表真实变化趋势,能对无法获取立体像对的地区进行三维重建,克服了立体像对的技术限制,对于快速获取大范围地区的高分辨率数字地面模型具有重要意义。
针对SFS理论中的反射率同一性假设问题、立体匹配方法失效区域的三维重建问题、以及立体匹配中由缺乏纹理特征和透视收缩导致的误匹配问题,本文主要研究工作及创新点如下：
(1)解决朗伯体表面假设下SFS理论中反射率同一性假设限制：详述了朗伯体表面下的SFS理论,并对该问题的两类主要解算方法：最小化方法和传播方法进行了详细的研究。针对朗伯体SFS问题中物体反射率同一性假设的限制,提出了结合本征图像理论建立多尺度下的朗伯体表面II-SFS重建方法,通过图像分解减小由物体表面反射率变化导致的SFS重建误差。实验表明该方法可有效解决朗伯体SFS理论中反射率同一性假设的限制,大大提高SFS算法三维重建精度。
(2)建立非朗伯体反射表面快速三维重建方法：详细研究了基于Oren-Nayar模型和Phong模型的三维重建算法,将相关反射图方程写为Hamilton-Jacobi方程(简称H-J方程)的形式,利用Lax-Friedrichs函数对该方程进行离散化,采用高阶快速扫描法(High Order Fast Sweeping method,简称HO-FSM方法)求解得到地表法向量的估计值。
(3)利用SFS理论针对立体匹配方法失效的区域三维重建：提出了基于Oren-Nayar反射模型的有限条件下各向异性表面三维重建的NSDMI(?)里论框架,本文首先根据不同地表覆盖类型对影像进行分类,估算每种地物类别的反射率值,再将相关反射图方程写为H-J方程的形式,采用HO-FSM方法求解得到地表法向量的估计值,最后利用最小二乘法对控制点格网进行内插。实验表明该方法可解决立体匹配失效区域无法重建三维的问题,在有限个地面控制点条件下可得到较高精度的地面三维模型。
(4)讨论未知光照条件下影像光源参数估计问题：本文总结了在光源方向和反射率值未知时的经典盲估算算法,以及基于样本学习的光源、反射率、形状联合估计算法。最后采用合成影像和真实遥感影像作为实验图像,对三种经典盲估算方法进行实验分析,表明Zheng方法对于合成影像的光源估算精度最高。
(5)提出立体像对与SFS相结合的SFS-SDI-SR重建模型：在分析了立体像对与SFS的优缺点的基础上,探讨了如何将两者有效结合的研究思路,并给出了基于立体像对和明暗恢复形状相结合的三维重建的理论框架。首先对左右片提取特征点并进行特征匹配：采用FSM-SFS方法对特征点区域进行三维恢复,将恢复得到的表面形状作为新的相似似性测度;其次对不同像素点进行三维重建：特征匹配方法仅匹配可靠的点,非特征点采用SFS方法恢复高度；最后将不同区域的重建结果相结合得到整个观测区域的三维模型。对月球三线阵影像进行实验,结果表明本文方法相较于单一立体匹配和SFS方法可获得更高分辨率的表面三维信息,克服基于图像亮度信息的匹配方法中存在的不足,在光滑的和纹理特征不丰富的区域也能得到较好的重建结果。总而言之,本文首先解决了当前SFS理论中本身存在的反射率同一性假设带来的问题；再针对立体匹配方法失效的区域,利用有限个数地而控制点和单张遥感影像SFS三维重建结果建立数字地面模型；最后为解决立体匹配中由缺乏纹理特征和透视收缩导致的误匹配问题,建立立体像对与SFS相结合的三维重建框架,建立高度相似性测度,得到更高分辨率的数字地面模型。本文的研究显著减小了SFS理论对真实影像三维重建的误差,极大提高基于特征点的立体匹配精度,解决了立体匹配失效区域三维重建困难的问题,并推动了SFS理论在地学研究中的应用。
Digital Terrain Model (DTM in short), as an important data, is widely used in mapping, agriculture, forestry, industrial and other applicable filed. Photogrammetry is the main method to generate the DTM, which is based on the principle of feature extraction and feature matching. It is aim to find the pairs of matched points and get the parallax information. However, in some areas seriously lack of texture, such as deserts, waters, mountains and so on, it is unable to quickly and efficiently extract the feature points and edges, under this condition, the matching accuracy will be declined. Meanwhile, some areas often fail to obtain stereo image pairs of high spatial resolution due to the bad weather such as cloud and fog, so terrain reconstruction can't be done by stereo method.
Since single remote sensing image is more accessible compared with stereo pairs, if we can acquire the terrain details from single image and consider it as the auxiliary data in surface reconstruction; it is possible to generate an accurate dense surface model by using sparse ground control points with the help of the single imagery. Shape from Shading technology (we can call it SFS in short), is aim to obtain surface shape information from a single image, which is based on the inverse process of the physical imaging. It is an important tool for3D surface reconstruction and very potential in terrain surface reconstruction of a single remote sensing image. In this paper, SFS is introduced in geoscientific research. Interpolating the surface model according to the information about the surface details recovered from SFS, can not only generate the DTM for the areas where the stereo image pairs can't be obtained, but also take the real trend of the internal surface of the grid into account. It is of great significance for quickly creating surface model for wide areas. The main works of this paper are as follows:
(1) Solving the limitation of the reflectance in SFS theory under Lambertain surface assumption:described the Lambertian SFS theory and the two main types of solution method:minimization and propagating method. To solve the limitation in SFS theory that reflection should be a constant in the image, a reconstruction method combined the Intrinsic Image theory and SFS theory was proposed. The reconstruction error caused by surface reflectance variation was reduced by image decomposition. Experiments performed on synthetic images show that the intrinsic image decomposition can effectively separate the image reflectance component from the original image and improve the accuracy of the SFS algorithm.
(2) Establishing the non-Lambertian surface fast reconstruction method:gave a detailed study of the Oren-Nayar model and the Phong model based3D reconstruction algorithm, rewrote the reflection map equation in the form of the Hamilton-Jacobi equation (referred to as H-J equation), then used the Lax-Friedrichs Hamiltonian in the equation discretization, finally utilized the high-ordered fast sweeping method (referred to as HO-FSM method) for estimating the surface normal vectors.
(3) Reconstructing the area where stereo matching method fails to work:Based on the Oren-Nayar reflectance model, a theoretical framework of anisotropic surface reconstruction under the limited condition was proposed. First of all, supervised classification was performed, and the reflectance for each land cover type was estimated; then the reflection map equation was written as the H-J equation, and HO-FSM method was used for solving it; Finally, the least squares was utilized to interpolate the grid of control points.
(4) Discussing the important parameters estimation problems in the SFS theory. This paper reviewed the approach how to estimate the illumination direction using image reflection equation. Then three classic methods were compared and analyzed in both synthetic and real image experiments.
(5) Giving a combination framework for stereo and SFS algorithm on the basis of the advantages and disadvantages for each one:Firstly the FSM-SFS algorithm was implemented for the feature region reconstruction, and the results were used to form a new depth similarity measurement; then only the stable and reliable points were regarded as the matching points, and other points were reconstructed by SFS algorithm; Finally the results for all the surface points were combined to generate the3D model. The reconstruction experiment was implemented based on the three-line array moon images and the results show that the proposed method could give more accurate result than stereo and SFS each of themselves.
In summary, this paper first solved the inherent problems in the current SFS theory, proposed solutions to improve the accuracy of SFS algorithm; then, in the area where stereo matching method fails to work, an DTM generation algorithm using single remote sensing imagery and certain ground control points was proposed; finally, when the stereo pairs are available, the SFS theory and stereo method was combined to improve the accuracy of stereo matching, so the DTM with higher resolution could be generated.
引文
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