Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

翻译：从单目图像估计物体姿态是计算机视觉中的一个基本逆问题。该问题的不适定性要求结合变形先验进行求解。实践中，许多材料在操作过程中不会发生显著收缩或拉伸，这构成了一个强大且广为人知的先验条件。从数学角度看，这等价于黎曼度量的保持。神经网络为解决表面重建问题提供了理想框架，既能以任意精度逼近曲面，又能支持微分几何量的计算。本文提出了一种从图像序列推断连续可变形表面的方法，该方法与多种技术进行了对比评测，无需离线训练即可获得最先进的性能。