We consider a category-level perception problem, where one is given 3D sensor
data picturing an object of a given category (e.g. a car), and has to
reconstruct the pose and shape of the object despite intra-class variability
(i.e. different car models have different shapes). We consider an active shape
model, where -- for an object category -- we are given a library of potential
CAD models describing objects in that category, and we adopt a standard
formulation where pose and shape estimation are formulated as a non-convex
optimization. Our first contribution is to provide the first certifiably
optimal solver for pose and shape estimation. In particular, we show that
rotation estimation can be decoupled from the estimation of the object
translation and shape, and we demonstrate that (i) the optimal object rotation
can be computed via a tight (small-size) semidefinite relaxation, and (ii) the
translation and shape parameters can be computed in closed-form given the
rotation. Our second contribution is to add an outlier rejection layer to our
solver, hence making it robust to a large number of misdetections. Towards this
goal, we wrap our optimal solver in a robust estimation scheme based on
graduated non-convexity. To further enhance robustness to outliers, we also
develop the first graph-theoretic formulation to prune outliers in
category-level perception, which removes outliers via convex hull and maximum
clique computations; the resulting approach is robust to 70%-90% outliers. Our
third contribution is an extensive experimental evaluation. Besides providing
an ablation study on a simulated dataset and on the PASCAL3D+ dataset, we
combine our solver with a deep-learned keypoint detector, and show that the
resulting approach improves over the state of the art in vehicle pose
estimation in the ApolloScape datasets.

本文提出了一个主要解决物体类别感知问题的非凸优化模型，其中包括针对模型内部变异性的解决方案，将图形学和优化算法相结合，以提高汽车姿态估计等领域的精度和鲁棒性。

基于类别的三维物体感知的最优姿态和形状估计

Optimal Pose and Shape Estimation for Category-level 3D Object  Perception

We present a general paradigm for dynamic 3D reconstruction from multiple
independent and uncontrolled image sources having arbitrary temporal sampling
density and distribution. Our graph-theoretic formulation models the
Spatio-temporal relationships among our observations in terms of the joint
estimation of their 3D geometry and its discrete Laplace operator. Towards this
end, we define a tri-convex optimization framework that leverages the geometric
properties and dependencies found among a Euclideanshape-space and the discrete
Laplace operator describing its local and global topology. We present a
reconstructability analysis, experiments on motion capture data and multi-view
image datasets, as well as explore applications to geometry-based event
segmentation and data association.

本论文提出了一种通用的范式来处理来自多个独立和不受控制的图像来源的 3D 动态重建问题，该问题具有任意时间采样密度和分布，通过图表论的方法建立空间 - 时间关系，通过三重凸优化框架来进行重建，在运动捕捉数据和多视图图像数据集上进行实验，并探讨几何事件分割和数据关联的应用。