An emerging problem in computer vision is the reconstruction of 3D shape and
pose of an object from a single image. Hitherto, the problem has been addressed
through the application of canonical deep learning methods to regress from the
image directly to the 3D shape and pose labels. These approaches, however, are
problematic from two perspectives. First, they are minimizing the error between
3D shapes and pose labels - with little thought about the nature of this label
error when reprojecting the shape back onto the image. Second, they rely on the
onerous and ill-posed task of hand labeling natural images with respect to 3D
shape and pose. In this paper we define the new task of pose-aware shape
reconstruction from a single image, and we advocate that cheaper 2D annotations
of objects silhouettes in natural images can be utilized. We design
architectures of pose-aware shape reconstruction which re-project the predicted
shape back on to the image using the predicted pose. Our evaluation on several
object categories demonstrates the superiority of our method for predicting
pose-aware 3D shapes from natural images.

该论文提出了一种新的、基于 2D 注释的单张图像姿态感知的 3D 形状重建方法，通过设计特定的深度学习模型，实现了姿态感知形状的精准重建，并在多个对象类别的测试中验证了该方法的优越性。

重新思考复投影：从单张图像进行姿势感知形状重建的闭环

Rethinking Reprojection: Closing the Loop for Pose-aware  ShapeReconstruction from a Single Image

The pose of a rigid object is usually regarded as a rigid transformation,
described by a translation and a rotation. However, equating the pose space
with the space of rigid transformations is in general abusive, as it does not
account for objects with proper symmetries -- which are common among man-made
objects.In this article, we define pose as a distinguishable static state of an
object, and equate a pose with a set of rigid transformations. Based solely on
geometric considerations, we propose a frame-invariant metric on the space of
possible poses, valid for any physical rigid object, and requiring no arbitrary
tuning. This distance can be evaluated efficiently using a representation of
poses within an Euclidean space of at most 12 dimensions depending on the
object's symmetries. This makes it possible to efficiently perform neighborhood
queries such as radius searches or k-nearest neighbor searches within a large
set of poses using off-the-shelf methods. Pose averaging considering this
metric can similarly be performed easily, using a projection function from the
Euclidean space onto the pose space. The practical value of those theoretical
developments is illustrated with an application of pose estimation of instances
of a 3D rigid object given an input depth map, via a Mean Shift procedure.

本文提出了一种基于几何考虑的、用于描述刚体物体位姿的不依赖于任何人为调整的、基于刚体对称性的不变度量，可以有效地执行大量姿态的查询，如半径搜索或 k 最近邻搜索，并且可以用于简单的姿态平均，文中还提到了一种基于该度量方法的 3D 刚体姿态估计技术。

定义任意三维刚性物体的姿态及其相关距离

Defining the Pose of any 3D Rigid Object and an Associated Distance

We introduce and evaluate several architectures for Convolutional Neural
Networks to predict the 3D joint locations of a hand given a depth map. We
first show that a prior on the 3D pose can be easily introduced and
significantly improves the accuracy and reliability of the predictions. We also
show how to use context efficiently to deal with ambiguities between fingers.
These two contributions allow us to significantly outperform the
state-of-the-art on several challenging benchmarks, both in terms of accuracy
and computation times.

本文研究使用卷积神经网络结构，预测手的三维关节位置，并通过引入关节先验和有效利用上下文来提高方案的预测精确性和可靠性，在多个基准测试中都表现出了远胜于现有技术的高精度和较快的计算时间。