  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.
