论文标题
部分可观测时空混沌系统的无模型预测
Deep-MDS Framework for Recovering the 3D Shape of 2D Landmarks from a Single Image
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this paper, a low parameter deep learning framework utilizing the Non-metric Multi-Dimensional scaling (NMDS) method, is proposed to recover the 3D shape of 2D landmarks on a human face, in a single input image. Hence, NMDS approach is used for the first time to establish a mapping from a 2D landmark space to the corresponding 3D shape space. A deep neural network learns the pairwise dissimilarity among 2D landmarks, used by NMDS approach, whose objective is to learn the pairwise 3D Euclidean distance of the corresponding 2D landmarks on the input image. This scheme results in a symmetric dissimilarity matrix, with the rank larger than 2, leading the NMDS approach toward appropriately recovering the 3D shape of corresponding 2D landmarks. In the case of posed images and complex image formation processes like perspective projection which causes occlusion in the input image, we consider an autoencoder component in the proposed framework, as an occlusion removal part, which turns different input views of the human face into a profile view. The results of a performance evaluation using different synthetic and real-world human face datasets, including Besel Face Model (BFM), CelebA, CoMA - FLAME, and CASIA-3D, indicates the comparable performance of the proposed framework, despite its small number of training parameters, with the related state-of-the-art and powerful 3D reconstruction methods from the literature, in terms of efficiency and accuracy.
