In this work, we study the perception problem for garments using tools from
computational topology: the identification of their geometry and position in
space from point-cloud samples, as obtained e.g. with 3D scanners. We present a
reconstruction algorithm based on a direct topological study of the sampled
textile surface that allows us to obtain a cellular decomposition of it via a
Morse function. No intermediate triangulation or local implicit equations are
used, avoiding reconstruction-induced artifices. No a priori knowledge of the
surface topology, density or regularity of the point-sample is required to run
the algorithm. The results are a piecewise decomposition of the surface as a
union of Morse cells (i.e. topological disks), suitable for tasks such as
noise-filtering or mesh-independent reparametrization, and a cell complex of
small rank determining the surface topology. This algorithm can be applied to
smooth surfaces with or without boundary, embedded in an ambient space of any
dimension.

使用计算拓扑的工具研究服装的感知问题，通过直接拓扑研究样本化纺织物表面的重建算法，得到适用于降噪或网格独立参数化等任务的表面分块分解和确定表面拓扑的小秩细胞复合结构。

基于莫尔斯理论的采样纺织品表面重建

Surface reconstruction of sampled textiles via Morse theory

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。