3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since -- without additional prior assumptions -- it permits infinitely many solutions leading to accurate projection to the input 2D images. Non-rigid reconstruction is a foundational building block for downstream applications like robotics, AR/VR, or visual content creation. The key advantage of using monocular cameras is their omnipresence and availability to the end users as well as their ease of use compared to more sophisticated camera set-ups such as stereo or multi-view systems. This survey focuses on state-of-the-art methods for dense non-rigid 3D reconstruction of various deformable objects and composite scenes from monocular videos or sets of monocular views. It reviews the fundamentals of 3D reconstruction and deformation modeling from 2D image observations. We then start from general methods -- that handle arbitrary scenes and make only a few prior assumptions -- and proceed towards techniques making stronger assumptions about the observed objects and types of deformations (e.g. human faces, bodies, hands, and animals). A significant part of this STAR is also devoted to classification and a high-level comparison of the methods, as well as an overview of the datasets for training and evaluation of the discussed techniques. We conclude by discussing open challenges in the field and the social aspects associated with the usage of the reviewed methods.

翻译：可变形（或非刚性）场景从一组单目二维图像观测中进行三维重建，是计算机视觉与图形学领域一个长期且活跃的研究方向。由于缺乏额外的先验假设，这一问题具有病态逆问题的特性——存在无穷多个解能精确投影到输入二维图像。非刚性重建是机器人技术、AR/VR、视觉内容创作等下游应用的基础构建模块。使用单目相机的核心优势在于其普遍性、终端用户可获取性，以及相比立体相机或多视角系统等更复杂的相机设置更易于使用。本综述聚焦于从单目视频或单目视角集合中实现各类可变形物体与复合场景的密集非刚性三维重建的最先进方法。它回顾了基于二维图像观测进行三维重建与变形建模的基本原理。我们首先讨论处理任意场景且仅需少量先验假设的通用方法，继而转向对观测对象及变形类型（如人脸、人体、手部及动物）做出更强假设的技术。本综述的重要部分还涉及方法的分类与高层次对比，以及用于训练和评估所述技术的数据集概览。最后，我们讨论了该领域存在的开放性挑战以及与所综述方法相关的社会问题。