多视图图像三维重建若干关键技术研究
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摘要
多视图图像三维重建技术就是从图像或图像序列中获取场景及场景中对象的三维模型，是计算机图形学和计算机视觉领域解决三维建模的手段之一，它对提高三维真实感建模及实时大规模复杂场景三维建模有非常重要的现实意义。目前其研究成果已应用于医学成像、数字化城市、机器人自主导航及数字娱乐等领域。但多视图图像三维重建技术仍未成熟，在实际应用中还存在诸多问题。本文围绕多视图图像三维重建的关键技术进行研究和探讨，为多视图图像三维重建提供一些有效的解决方案，主要研究内容包括图像特征的提取与匹配，多视图几何约束关系的计算，鲁棒性参数模型的估计，场景结构和摄像机运动的恢复，稠密表面的估计。本文的主要创新点如下：
（1）提出一种新的差分形态分解（Differential Morphological Decomposition，DMD）特征检测和描述算法。该算法通过研究尺度空间理论的多尺度特征检测算法的不足，利用差分形态分解构造金字塔尺度空间，去除噪声和边缘信息的干扰，并在不同的尺度图像上运用Harris算子，检测出尺度图像上的特征点。然后将特征点进行分组，确保每组特征点只描述图像的一个局部结构。在每一组中，本文根据空域内变化最强的角点值，同时加上尺度域的高斯拉普拉斯函数(Laplacian ofGaussian，LoG)值来选择唯一的特征点来代表图像的局部结构。最后运用PCA-SIFT方法对特征进行描述。实验表明该算法在尺度变换、模糊变换和亮度变换的情况下，对局部不变特征点的检测和描述都取得了较好的效果。
（2）提出基于序贯概率检测(Sequential Probability Ratio Test, SPRT)及局部优化技术的随机抽样一致性（Random Sample Consensus, RANSAC）算法。针对模型参数估计的速度和精度问题，本文对RANSAC算法进行了优化和改进。在RANSAC算法模型参数检验阶段，利用SPRT来对模型进行预检验，先在数据集上随机的抽取少量的数据点，并在这些数据点上执行对模型的统计检验；只有当初始的预检验通过，才在所有的数据点上执行对模型的最终检验，否则不再对此模型进行检验。该方法优化了模型检验过程，节约了大量数据对模型的检验，提高了RANSAC算法的速度。同时，当完成所有数据对模型的检验后，计算出与模型相一致的数据点。在得到所有可能的数据点集后，本文采用局部优化技术，在得到的数据点集上局部执行RANSAC算法，由于此时的数据点集绝大多数与模型相一致，因而精度得到提高。实验表明，本文提出的基于SPRT和局部优化技术的RANSAC算法运行速度和精度得到明显的提高。
（3）提出基于块预处理和嵌入点迭代（Embedded Point Iterations，EPIs）的共轭梯度光束法平差（Bundle Adjustment）算法。针对大规模场景三维重建时，光束法平差仍然是计算的主要瓶颈问题。本文采用共轭梯度算法实现光束法平差内部迭代，其主要计算过程只包含了一个简单的矩阵、向量及雅可比行列式相乘，使得计算开销减少。同时，通过利用光束法平差的最小二乘法特性，本文采用了一种易于计算，基于块预处理的QR因式分解预处理方法，减小每次迭代的计算量。改进后的算法只有标准共轭梯度算法约一半的计算量。为了更进一步提高运算速度，还使用EPIs办法，在每一个摄像机标定阶段运行EPIs，使得每个摄像机标定步骤开销进一步减少。实验表明该算法在大规模场景重建时，可节约大量计算时间及取得较好的优化效果。
（4）提出一种深度图生成稠密三维点云的方法，并针对稀疏三维点云，利用几何约束和自适应提出改进的基于物方面元多视图立体视觉（Patch-BasedMultiview Stereo，PMVS）准稠密算法。首先，为了得到精确的表面，假定已知摄像机的位置和方向，本文在体空间上运用非线性全局最优化来获得图像的深度图，得到深度图后，将深度图中的每个像素反投影到一个三维空间中，产生一个稠密三维点云。根据这些点云，采用泊松重建方法，重建出场景的表面网格，然后将图像纹理投影到表面网格上完成场景的表面重建。其次，针对未标定的多视图图像三维重建，从摄像机运动恢复结构（Structure From Motion，SFM）只能重建出稀疏的三维点云，不能准确、真实重建出场景或场景中对象，不具有可视化效果。本文在PMVS算法的Patch扩散过程中，加入几何空间约束及自适应扩展算法，用较少的图像序列即可生成鲁棒、精确的几何估计，得到高稠密的三维点云，然后进行表面重建，得到真实感的场景或场景对象的三维模型。实验表明该算法能够重建出尽可能光滑的精确表面，提高了三维模型的真实感。
Multi-view3D reconstruction is one of approaches for3D modeling in computergraphics and computer vision, which aims to abstract the scene and scenery objectsfrom an image or a series of images. It is actually critical for improving the sense ofphotorealistic3D modeling and building the3D model for real-time scenery. Currently,relevant research achievements are used in the worlds of digital medicine image, digitalcity, autonomous robot, and digital entertainment. However, the technology ofmulti-view3D reconstruction still has certain problems that should be solved inreal-world applications. This dissertation explored the problems related with themulti-view3D reconstruction, and proposed several effective solutions to the relevantproblems. This dissertation focuses on extracting the feature vectors problems and thematching problems of images, counting the limited geometrical relationship, estimatingthe parameters and the dense surface robustly, as well as rebuilding the scene throughstructure from motion. This dissertation makes the following contributions:
(1) An approach called as new DMD (Differential Morphological Decomposition)is proposed to detect and describe local invariant features of the image effectively, whenextracting robust feature points in a series of images with complicated scenes, as well asimages have some complicated features, such as multiple dimensions, fuzzytransformation and both of them. Being aware of these drawbacks of the existingmulti-scale feature-detecting algorithms in the scale space theory, this dissertation firstproposed a pyramid scale space, which is adopted by DMD. And then applied a Harrisoperator on scale images in the pyramid scale space, so that feature points can bedivided into deferent groups, and every group of points just needs to describe a localstructure of the image. Finally, a PCA-SIFT descriptor is leveraged for featuring andmatching a feature point, which is selected by a LoG value in a scale domain. Theexperiments with real-world and artificial data sets have confirmed that the proposedapproach achieved better results in detecting and describing local invariant featurepoints in the cases when scale fuzzy transformation and luminance transformationoccurred.
(2) Afast and accurate RANSAC (Random Sample Consensus) is proposed, whichis based on SPRT (Sequential Probability Ratio Test) and local optimization technique.At first, in order to improve velocity of RANSAC, this dissertation employed SPRT andcertain preview evaluation methods to optimize the procedure of model verification. Tothis end, the proposed mechanism randomly selected a few of sample data from sourcedata sets and then made statistical verification for these data, this process is also calledas preview evaluation. Therefore, the final verification will be conducted on the wholedata set when the preview evaluation has passed; otherwise, no tests will be done. Thesecond motivation is to improve the accuracy of RANSAC. After the previewevaluation, inliers (the data that is fit the hypothesis in the supposed model) can beexplored; then, the explored potential inliers sets can be used in a local optimizationRANSAC with the selected optimal model. The experimental results have disclosed thatthe proposed approach can gain lots of benefits from the theory of RANSAC with thenewly proposed approaches.
(3) Anew algorithm is designed for conjugate gradient bundle adjustment which isbased on the block preconditioned and EPIs (Embedded Point Iterations). Whilereconstructing a large scale of scene, the method of bundle adjustment is a well-knownbottleneck during computation. In this newly conjugate gradient method, the maincomputational tasks include a simple matrix and vector multiplication with the jacobian.Furthermore, this newly presented algorithm has an alternative method, which iteratesinteriorly with a conjugate gradient algorithm. In this dissertation, for enhancingefficiency of the proposed bundle adjustment algorithm by using conjugate gradient, thealgorithm first decreased the cost of per iteration to almost a half by completelyutilizing a property of the least square method, because the improved method employsan easy preprocess system of QR factorization based on block preprocess. Besides, inorder to accelerate processing speed, by using the EPIs method, this algorithmembedded iteration points into every camera correction phase, so that the cost of everycamera correction step can be reduced. The experimental results show that whilerebuilding a large-scale scene, this newly proposed algorithm outperforms otherapproaches.
(4) This dissertation presented a new method that computes a dense3D point cloudfrom depth maps. In order to realize surface reconstruction from sparse3D points, this dissertation presented an improved PMVS (Patch-based Multi-view Stereo) quasi-densealgorithm based on geometrical constraint and self-adaption. At first, this algorithmassumes that the information about location and orientation of the camera is available,and then it computes depth maps by solving a global energy minimization problem in animage space, so that each pixel in a depth map can be projected back into a common3Dspace to yield an extremely dense point cloud, which contains of millions of points.Eventually, this point cloud can reconstruct a surface mesh by using Poissonreconstruction. Secondly, aiming at the issue of3D reconstruction from a series ofuncorrected images, the mechanism of SFM (Structure From Motion) can onlyreconstruct sparse3D points. It is well known that although these points are enough fortracing the camera's position, it is not enough for reconstructing the scene or objectswith fairy accuracy and authenticity. This newly presented algorithm adds geometricalspace constraints and adaptive expanding algorithm into the procedure of patchexpanding in PMVS algorithm. Therefore, it can generate robust and accurate geometryestimation, and obtain a highly dense3D point cloud with fewer images. As a result,this algorithm obtains realistic3D models of the scene and objects by using surfacereconstruction approach. The experiments have shown that this improved algorithm isable to rebuild accurate surfaces as far as possible and improve authenticity of the3Dmodel.
（1）提出一种新的差分形态分解（Differential Morphological Decomposition，DMD）特征检测和描述算法。该算法通过研究尺度空间理论的多尺度特征检测算法的不足，利用差分形态分解构造金字塔尺度空间，去除噪声和边缘信息的干扰，并在不同的尺度图像上运用Harris算子，检测出尺度图像上的特征点。然后将特征点进行分组，确保每组特征点只描述图像的一个局部结构。在每一组中，本文根据空域内变化最强的角点值，同时加上尺度域的高斯拉普拉斯函数(Laplacian ofGaussian，LoG)值来选择唯一的特征点来代表图像的局部结构。最后运用PCA-SIFT方法对特征进行描述。实验表明该算法在尺度变换、模糊变换和亮度变换的情况下，对局部不变特征点的检测和描述都取得了较好的效果。
（2）提出基于序贯概率检测(Sequential Probability Ratio Test, SPRT)及局部优化技术的随机抽样一致性（Random Sample Consensus, RANSAC）算法。针对模型参数估计的速度和精度问题，本文对RANSAC算法进行了优化和改进。在RANSAC算法模型参数检验阶段，利用SPRT来对模型进行预检验，先在数据集上随机的抽取少量的数据点，并在这些数据点上执行对模型的统计检验；只有当初始的预检验通过，才在所有的数据点上执行对模型的最终检验，否则不再对此模型进行检验。该方法优化了模型检验过程，节约了大量数据对模型的检验，提高了RANSAC算法的速度。同时，当完成所有数据对模型的检验后，计算出与模型相一致的数据点。在得到所有可能的数据点集后，本文采用局部优化技术，在得到的数据点集上局部执行RANSAC算法，由于此时的数据点集绝大多数与模型相一致，因而精度得到提高。实验表明，本文提出的基于SPRT和局部优化技术的RANSAC算法运行速度和精度得到明显的提高。
（3）提出基于块预处理和嵌入点迭代（Embedded Point Iterations，EPIs）的共轭梯度光束法平差（Bundle Adjustment）算法。针对大规模场景三维重建时，光束法平差仍然是计算的主要瓶颈问题。本文采用共轭梯度算法实现光束法平差内部迭代，其主要计算过程只包含了一个简单的矩阵、向量及雅可比行列式相乘，使得计算开销减少。同时，通过利用光束法平差的最小二乘法特性，本文采用了一种易于计算，基于块预处理的QR因式分解预处理方法，减小每次迭代的计算量。改进后的算法只有标准共轭梯度算法约一半的计算量。为了更进一步提高运算速度，还使用EPIs办法，在每一个摄像机标定阶段运行EPIs，使得每个摄像机标定步骤开销进一步减少。实验表明该算法在大规模场景重建时，可节约大量计算时间及取得较好的优化效果。
（4）提出一种深度图生成稠密三维点云的方法，并针对稀疏三维点云，利用几何约束和自适应提出改进的基于物方面元多视图立体视觉（Patch-BasedMultiview Stereo，PMVS）准稠密算法。首先，为了得到精确的表面，假定已知摄像机的位置和方向，本文在体空间上运用非线性全局最优化来获得图像的深度图，得到深度图后，将深度图中的每个像素反投影到一个三维空间中，产生一个稠密三维点云。根据这些点云，采用泊松重建方法，重建出场景的表面网格，然后将图像纹理投影到表面网格上完成场景的表面重建。其次，针对未标定的多视图图像三维重建，从摄像机运动恢复结构（Structure From Motion，SFM）只能重建出稀疏的三维点云，不能准确、真实重建出场景或场景中对象，不具有可视化效果。本文在PMVS算法的Patch扩散过程中，加入几何空间约束及自适应扩展算法，用较少的图像序列即可生成鲁棒、精确的几何估计，得到高稠密的三维点云，然后进行表面重建，得到真实感的场景或场景对象的三维模型。实验表明该算法能够重建出尽可能光滑的精确表面，提高了三维模型的真实感。
Multi-view3D reconstruction is one of approaches for3D modeling in computergraphics and computer vision, which aims to abstract the scene and scenery objectsfrom an image or a series of images. It is actually critical for improving the sense ofphotorealistic3D modeling and building the3D model for real-time scenery. Currently,relevant research achievements are used in the worlds of digital medicine image, digitalcity, autonomous robot, and digital entertainment. However, the technology ofmulti-view3D reconstruction still has certain problems that should be solved inreal-world applications. This dissertation explored the problems related with themulti-view3D reconstruction, and proposed several effective solutions to the relevantproblems. This dissertation focuses on extracting the feature vectors problems and thematching problems of images, counting the limited geometrical relationship, estimatingthe parameters and the dense surface robustly, as well as rebuilding the scene throughstructure from motion. This dissertation makes the following contributions:
(1) An approach called as new DMD (Differential Morphological Decomposition)is proposed to detect and describe local invariant features of the image effectively, whenextracting robust feature points in a series of images with complicated scenes, as well asimages have some complicated features, such as multiple dimensions, fuzzytransformation and both of them. Being aware of these drawbacks of the existingmulti-scale feature-detecting algorithms in the scale space theory, this dissertation firstproposed a pyramid scale space, which is adopted by DMD. And then applied a Harrisoperator on scale images in the pyramid scale space, so that feature points can bedivided into deferent groups, and every group of points just needs to describe a localstructure of the image. Finally, a PCA-SIFT descriptor is leveraged for featuring andmatching a feature point, which is selected by a LoG value in a scale domain. Theexperiments with real-world and artificial data sets have confirmed that the proposedapproach achieved better results in detecting and describing local invariant featurepoints in the cases when scale fuzzy transformation and luminance transformationoccurred.
(2) Afast and accurate RANSAC (Random Sample Consensus) is proposed, whichis based on SPRT (Sequential Probability Ratio Test) and local optimization technique.At first, in order to improve velocity of RANSAC, this dissertation employed SPRT andcertain preview evaluation methods to optimize the procedure of model verification. Tothis end, the proposed mechanism randomly selected a few of sample data from sourcedata sets and then made statistical verification for these data, this process is also calledas preview evaluation. Therefore, the final verification will be conducted on the wholedata set when the preview evaluation has passed; otherwise, no tests will be done. Thesecond motivation is to improve the accuracy of RANSAC. After the previewevaluation, inliers (the data that is fit the hypothesis in the supposed model) can beexplored; then, the explored potential inliers sets can be used in a local optimizationRANSAC with the selected optimal model. The experimental results have disclosed thatthe proposed approach can gain lots of benefits from the theory of RANSAC with thenewly proposed approaches.
(3) Anew algorithm is designed for conjugate gradient bundle adjustment which isbased on the block preconditioned and EPIs (Embedded Point Iterations). Whilereconstructing a large scale of scene, the method of bundle adjustment is a well-knownbottleneck during computation. In this newly conjugate gradient method, the maincomputational tasks include a simple matrix and vector multiplication with the jacobian.Furthermore, this newly presented algorithm has an alternative method, which iteratesinteriorly with a conjugate gradient algorithm. In this dissertation, for enhancingefficiency of the proposed bundle adjustment algorithm by using conjugate gradient, thealgorithm first decreased the cost of per iteration to almost a half by completelyutilizing a property of the least square method, because the improved method employsan easy preprocess system of QR factorization based on block preprocess. Besides, inorder to accelerate processing speed, by using the EPIs method, this algorithmembedded iteration points into every camera correction phase, so that the cost of everycamera correction step can be reduced. The experimental results show that whilerebuilding a large-scale scene, this newly proposed algorithm outperforms otherapproaches.
(4) This dissertation presented a new method that computes a dense3D point cloudfrom depth maps. In order to realize surface reconstruction from sparse3D points, this dissertation presented an improved PMVS (Patch-based Multi-view Stereo) quasi-densealgorithm based on geometrical constraint and self-adaption. At first, this algorithmassumes that the information about location and orientation of the camera is available,and then it computes depth maps by solving a global energy minimization problem in animage space, so that each pixel in a depth map can be projected back into a common3Dspace to yield an extremely dense point cloud, which contains of millions of points.Eventually, this point cloud can reconstruct a surface mesh by using Poissonreconstruction. Secondly, aiming at the issue of3D reconstruction from a series ofuncorrected images, the mechanism of SFM (Structure From Motion) can onlyreconstruct sparse3D points. It is well known that although these points are enough fortracing the camera's position, it is not enough for reconstructing the scene or objectswith fairy accuracy and authenticity. This newly presented algorithm adds geometricalspace constraints and adaptive expanding algorithm into the procedure of patchexpanding in PMVS algorithm. Therefore, it can generate robust and accurate geometryestimation, and obtain a highly dense3D point cloud with fewer images. As a result,this algorithm obtains realistic3D models of the scene and objects by using surfacereconstruction approach. The experiments have shown that this improved algorithm isable to rebuild accurate surfaces as far as possible and improve authenticity of the3Dmodel.
引文
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