IEEE Trans Pattern Anal Mach Intell. 2017 Aug;39(8):1648-1661. doi: 10.1109/TPAMI.2016.2605097. Epub 2016 Sep 1.
We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable shape model and a sparse representation is often used to capture complex shape variability. But the model inference is still challenging due to the nonconvexity in the joint optimization of shape and viewpoint. In contrast to prior work that relies on an alternating scheme whose solution depends on initialization, we propose a convex approach to addressing this challenge and develop an efficient algorithm to solve the proposed convex program. We further propose a robust model to handle gross errors in the 2D correspondences. We demonstrate the exact recovery property of the proposed method, the advantage compared to several nonconvex baselines and the applicability to recover 3D human poses and car models from single images.
我们研究了给定单个图像中 3D 地标与其 2D 对应点的情况下，估计由一组 3D 地标定义的物体 3D 形状的问题。一种成功的缓解重建歧义的方法是 3D 可变形形状模型，并且通常使用稀疏表示来捕获复杂的形状变化。但是，由于形状和视点的联合优化中的非凸性，模型推断仍然具有挑战性。与依赖于初始化的交替方案的先前工作不同，我们提出了一种解决此挑战的凸方法，并开发了一种有效的算法来解决所提出的凸规划。我们进一步提出了一种稳健的模型来处理 2D 对应中的粗差。我们证明了所提出方法的精确恢复特性，与几个非凸基线相比的优势以及从单个图像中恢复 3D 人体姿势和汽车模型的适用性。
