基于正交匹配追踪及加速近端梯度的人体三维重建

为提高人体三维结构的重建精度,针对重建过程中字典中原子的最佳选择和结构矩阵的优化问题,结合稀疏表示和低秩约束,提出一种正交匹配追踪追踪及加速近端梯度(OMP-APG)算法,以此为医学领域提供丰富的信息,以辅助医生快速精确地制定出治疗方案。首先,对特征点观测矩阵进行奇异值分解(SVD)分解,利用列文伯格-马夸尔特(LM)算法得到唯一确定的相机旋转矩阵;其次,利用稀疏表示中“最大化逼近”思想,通过正交匹配追踪算法对轨迹基系数进行求解,结合预定义的轨迹基求解出人体三维结构矩阵;最后,根据结构矩阵是一个低秩矩阵,将其秩优化问题转化为核范数最小化问题,利用加速近端梯度算法对人体结构矩阵进一步优化处理。将该算法与稀疏逼近算法进行比较,对伸懒腰、瑜伽、拾物、喝水和跳舞等5组不同的人体运动模型进行三维重建,通过其三维重建效果图和三维重建误差的结果显示,其重建精度更高且稳定性更好。在该算法下喝水运动的重建效果最佳,其1 102帧图像序列41个特征点的重建误差为0.030 3,而在稀疏算法下的重建误差为0.017 8。因此,该算法可以有效地提高人体三维结构的重建精度,为医学领域辅助治疗提供相应的技术支持。

3D Reconstruction of Human Body Based on Orthogonal Matching Pursuit and Accelerated Proximal Gradient

In order to improve the reconstruction accuracy of the 3D structure of human body, the optimal selection of atoms and the optimization of structure matrix in the process of reconstruction were investigated in this work. On the basis of the sparse representation and low-rank constraint, we proposed anorthogonal matching pursuit and accelerated proximal gradient (OMP-APG) algorithm to provide a wealth information to assist medical doctors to work out the treatment plan quickly and accurately. First of all, the feature matrix was decomposed by singular value decomposition (SVD), and the uniquely determined camera rotation matrix was obtained by LM (Levenberg-Marquardt) algorithm. Secondly, according to the idea of “maximization approximation” in sparse representation, the trajectory basis coefficients were solved by orthogonal matching pursuit algorithm, combined with a predefined trajectory basis to solve the 3D structure of the human body matrix. Finally, considering that the structure matrix was a low rank matrix, the rank optimization problem was transformed into the nuclear norm minimization problem, and the human body structure matrix was further optimized by the accelerated proximal gradient algorithm. The algorithm and sparse approximation algorithms were compared in five motion models including stretch, yoga, pick up, drink and dance in 3D reconstruction with the 3D reconstruction renderings and 3D reconstruction errors. The results showed that the reconstruction accuracy was higher and had better stability. In this algorithm, the reconstruction of drink motion was the best, and the reconstruction error of the 41 feature points of the 1102 frame image sequence was about 0.0303, while the reconstruction error under the sparse algorithm was about 0.0178. In conclusion, the algorithm improved the reconstruction accuracy of the human three-dimensional structure.