由手提相机获得的序列图像进行三维重建
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摘要
本论文研究了如何由非定标图像序列恢复三维实体模型，对其中的若干关键技术进行了深入研究，特别是立体像对的稠密匹配。本文的重点是在理论和实践两方面研究了在有遮挡的情况下，如何由长图像序列进行三维欧氏重建并最终获得物体完整结构的问题。由本文所给的算法可以恢复具有很好真实感的完整三维实体模型。主要研究成果如下：
1．提出了一种新的用于种子点可靠匹配的两层算法，该算法在图像边缘提取的基础上，首先比较目标点匹配的边缘相似性，这种特征匹配具有简单可靠的优点。在此基础上，在一个相对较小的搜索范围内比较其灰度相似性，从而得到目标点的精确匹配。该算法可以有效地避免由于重复图案所引起的匹配误差。
2．提出了一种基于图像划分的传播式稠密匹配算法，该算法不仅适用于未经校正的图像对，而且适用于存在大视差的图像对，以及图像中纹理稀疏的区域。通过用种子点的Voronoi图对图像划分，并以特征跟踪的结果作为匹配传播的起点，有效地消除了匹配误差的积累。传播算法在极大提高匹配效率的同时，也增加了算法的准确性。
3．提出了一种新的三维重建算法，该算法可以恢复目标物体完整的三维结构。首先将整个图像序列划分为几个子序列，使每个子序列中的重建点均不被遮挡；然后利用迭代分解算法求出物体局部的射影重建；接着通过自定标将射影重建升级至欧氏重建。这时由每个子序列得到的不同部分的重建结果是相对于不同的坐标系而言的。我们将它们通过一组相似变换转移至同一坐标系下，就得到了物体整体的三维结构。最后通过最小化重投影误差对投影矩阵和空间点坐标进行全局优化。该重建算法的突出优点在于它可以从一个长图像序列中恢复物体的完整结构，从而克服由遮挡(occlusion)引起的数据点的丢失问题。
4．提出了一种适用于存在丢失数据(missing data)的全局优化算法。为了弥补重建算法将一个长图像序列划分为几个子序列所带来的不足，我们对结构整合后的数据进行带有加权矩阵的全局优化，最小化重投影误差以提高数据(包括投影矩阵和重建点三维坐标)的整体精度。该算法通过引入加权矩阵，将可见点和被遮挡点同等处理，提高了数据的一致性。
5．采用带边缘约束的三角剖分算法，对模拟数据和存在遮挡的真实图像序列进行三维重建，这里的长图像序列是围绕目标物体一周拍摄得到的。每一个重建点在大约连续的10幅图像中均可见，而在其余的图像中被遮挡。我们的重建算法很好地恢复出了物体完整的几何结构。最后，通过构造相应的虚拟与真实混
由手提相机获得的序列图像进行二维重建
合的场景，进一步说明了该算法具有很好的准确性与实用性。这样重建出的三
维场景与纯虚拟场景相比，具有更好的真实感。
今后工作中需要进一步研究的问题有:继续研究存在遮挡问题的三维重建算
法，进一步提高算法的准确性与实用性，减少其中一些需要手工干预的步骤:继
续研究相机定标算法，增加外部约束条件以提高其准确性。另外，相机的内外参
数会因为投影矩阵的微小差异而发生较大变化，其求解稳定性也有待于进一步研
究。
Our research is focused on the problems of the recovery of a realistic textured model from image sequences and some critical issues related to this subject, such as dense matching to stereo images. The thesis investigates both the theoretical and practical feasibility in recovering the complete structure of an object from a long image sequence captured around it with occlusions. In this case, some points may be visible in a number of frames and then disappear in the following several frames. The main contributions of the thesis are as follows:
1. We propose a new two level matching algorithm for seed points in propagation. Firstly, our algorithm compares edge similarity around the target pixel based on edge extraction. This level of feature matching is both simple and reliable. Then intensity similarity is compared within a small search window, which is constrained by the results of the first level matching. In this way, the corresponding point is located accurately. This algorithm efficiently avoids mismatches caused by the repetitive patterns.
2. A novel and efficient dense matching method is proposed, which is based on the propagation by the Voronoi decomposition of the images. The significant merit of the algorithm is that it can be applied to a wide range of image pairs including those with large disparities, with or without rectification. And it may involve both textured part and less textured part of the images. Our dense matching begins from a number of seed points, which are reliably matched by feature tracking. Then corresponding relations are propagated from all of the seeds respectively. The decomposition of the images into Voronoi diagram restricts bad propagations within a single cell. It improves the performance of dense matching both in efficiency and accuracy.
3. A novel 3D reconstruction algorithm with missing data is presented, by which the complete structure of the target can be recovered. Firstly, images taken around the target are divided into several subsets. Each subset has common feature points. Secondly, Euclidean reconstruction is performed by iterative factorization with all of these points visible in each image of a certain subset. Then results coming from different subset are brought into a common coordinate frame by similarity transformations. Finally, global optimization is applied to minimize the back projection errors, which can refine the data and produce a jointly optimal 3D
structure. A significant merit of the algorithm is that it can deal with occlusions and a complete 3D model is recovered from the long image sequence.
4. A new global optimization algorithm with missing data is proposed. To remedy the drawback of cutting a long image sequence into several subsets in our 3D reconstruction algorithm, global optimization with a weighting matrix is applied to refine the results, in which the visible and missing data are arranged together. The back projection error is minimized over the estimated camera matrices and 3D points. In our optimization, the visible points and the missing data are treated uniformly by adding different weights. Experiments demonstrate that the algorithm
is both effective and accurate.
5. The 3D reconstruction algorithm with constrained triangulation has been tested on both simulate data and real images with satisfactory results. The long image sequence is taken from 360 degrees around the target. Each point is visible in about 10 consecutive images and occluded in the rest of the images. The complete structure of the building is recovered with realistic textures and we also generate an augmented scene to demonstrate the good performance of our algorithm. The structures recovered in this way have better visualization effect than that of the virtual scenes.
Future researches on this topic include: go on the work with missing data to further improve its accuracy and feasibility; decrease human interactions in the computation; improve the robustness of self-calibration by prior knowledge of orthogonal / parallel lines and ort
1．提出了一种新的用于种子点可靠匹配的两层算法，该算法在图像边缘提取的基础上，首先比较目标点匹配的边缘相似性，这种特征匹配具有简单可靠的优点。在此基础上，在一个相对较小的搜索范围内比较其灰度相似性，从而得到目标点的精确匹配。该算法可以有效地避免由于重复图案所引起的匹配误差。
2．提出了一种基于图像划分的传播式稠密匹配算法，该算法不仅适用于未经校正的图像对，而且适用于存在大视差的图像对，以及图像中纹理稀疏的区域。通过用种子点的Voronoi图对图像划分，并以特征跟踪的结果作为匹配传播的起点，有效地消除了匹配误差的积累。传播算法在极大提高匹配效率的同时，也增加了算法的准确性。
3．提出了一种新的三维重建算法，该算法可以恢复目标物体完整的三维结构。首先将整个图像序列划分为几个子序列，使每个子序列中的重建点均不被遮挡；然后利用迭代分解算法求出物体局部的射影重建；接着通过自定标将射影重建升级至欧氏重建。这时由每个子序列得到的不同部分的重建结果是相对于不同的坐标系而言的。我们将它们通过一组相似变换转移至同一坐标系下，就得到了物体整体的三维结构。最后通过最小化重投影误差对投影矩阵和空间点坐标进行全局优化。该重建算法的突出优点在于它可以从一个长图像序列中恢复物体的完整结构，从而克服由遮挡(occlusion)引起的数据点的丢失问题。
4．提出了一种适用于存在丢失数据(missing data)的全局优化算法。为了弥补重建算法将一个长图像序列划分为几个子序列所带来的不足，我们对结构整合后的数据进行带有加权矩阵的全局优化，最小化重投影误差以提高数据(包括投影矩阵和重建点三维坐标)的整体精度。该算法通过引入加权矩阵，将可见点和被遮挡点同等处理，提高了数据的一致性。
5．采用带边缘约束的三角剖分算法，对模拟数据和存在遮挡的真实图像序列进行三维重建，这里的长图像序列是围绕目标物体一周拍摄得到的。每一个重建点在大约连续的10幅图像中均可见，而在其余的图像中被遮挡。我们的重建算法很好地恢复出了物体完整的几何结构。最后，通过构造相应的虚拟与真实混
由手提相机获得的序列图像进行二维重建
合的场景，进一步说明了该算法具有很好的准确性与实用性。这样重建出的三
维场景与纯虚拟场景相比，具有更好的真实感。
今后工作中需要进一步研究的问题有:继续研究存在遮挡问题的三维重建算
法，进一步提高算法的准确性与实用性，减少其中一些需要手工干预的步骤:继
续研究相机定标算法，增加外部约束条件以提高其准确性。另外，相机的内外参
数会因为投影矩阵的微小差异而发生较大变化，其求解稳定性也有待于进一步研
究。
Our research is focused on the problems of the recovery of a realistic textured model from image sequences and some critical issues related to this subject, such as dense matching to stereo images. The thesis investigates both the theoretical and practical feasibility in recovering the complete structure of an object from a long image sequence captured around it with occlusions. In this case, some points may be visible in a number of frames and then disappear in the following several frames. The main contributions of the thesis are as follows:
1. We propose a new two level matching algorithm for seed points in propagation. Firstly, our algorithm compares edge similarity around the target pixel based on edge extraction. This level of feature matching is both simple and reliable. Then intensity similarity is compared within a small search window, which is constrained by the results of the first level matching. In this way, the corresponding point is located accurately. This algorithm efficiently avoids mismatches caused by the repetitive patterns.
2. A novel and efficient dense matching method is proposed, which is based on the propagation by the Voronoi decomposition of the images. The significant merit of the algorithm is that it can be applied to a wide range of image pairs including those with large disparities, with or without rectification. And it may involve both textured part and less textured part of the images. Our dense matching begins from a number of seed points, which are reliably matched by feature tracking. Then corresponding relations are propagated from all of the seeds respectively. The decomposition of the images into Voronoi diagram restricts bad propagations within a single cell. It improves the performance of dense matching both in efficiency and accuracy.
3. A novel 3D reconstruction algorithm with missing data is presented, by which the complete structure of the target can be recovered. Firstly, images taken around the target are divided into several subsets. Each subset has common feature points. Secondly, Euclidean reconstruction is performed by iterative factorization with all of these points visible in each image of a certain subset. Then results coming from different subset are brought into a common coordinate frame by similarity transformations. Finally, global optimization is applied to minimize the back projection errors, which can refine the data and produce a jointly optimal 3D
structure. A significant merit of the algorithm is that it can deal with occlusions and a complete 3D model is recovered from the long image sequence.
4. A new global optimization algorithm with missing data is proposed. To remedy the drawback of cutting a long image sequence into several subsets in our 3D reconstruction algorithm, global optimization with a weighting matrix is applied to refine the results, in which the visible and missing data are arranged together. The back projection error is minimized over the estimated camera matrices and 3D points. In our optimization, the visible points and the missing data are treated uniformly by adding different weights. Experiments demonstrate that the algorithm
is both effective and accurate.
5. The 3D reconstruction algorithm with constrained triangulation has been tested on both simulate data and real images with satisfactory results. The long image sequence is taken from 360 degrees around the target. Each point is visible in about 10 consecutive images and occluded in the rest of the images. The complete structure of the building is recovered with realistic textures and we also generate an augmented scene to demonstrate the good performance of our algorithm. The structures recovered in this way have better visualization effect than that of the virtual scenes.
Future researches on this topic include: go on the work with missing data to further improve its accuracy and feasibility; decrease human interactions in the computation; improve the robustness of self-calibration by prior knowledge of orthogonal / parallel lines and ort
引文
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