The perspective camera and the isometric surface prior have recently gathered
increased attention for Non-Rigid Structure-from-Motion (NRSfM). Despite the
recent progress, several challenges remain, particularly the computational
complexity and the unknown camera focal length. In this paper we present a
method for incremental Non-Rigid Structure-from-Motion (NRSfM) with the
perspective camera model and the isometric surface prior with unknown focal
length. In the template-based case, we provide a method to estimate four
parameters of the camera intrinsics. For the template-less scenario of NRSfM,
we propose a method to upgrade reconstructions obtained for one focal length to
another based on local rigidity and the so-called Maximum Depth Heuristics
(MDH). On its basis we propose a method to simultaneously recover the focal
length and the non-rigid shapes. We further solve the problem of incorporating
a large number of points and adding more views in MDH-based NRSfM and
efficiently solve them with Second-Order Cone Programming (SOCP). This does not
require any shape initialization and produces results orders of times faster
than many methods. We provide evaluations on standard sequences with
ground-truth and qualitative reconstructions on challenging YouTube videos.
These evaluations show that our method performs better in both speed and
accuracy than the state of the art.

本文提出了一种基于透视相机模型和等距表面先验进行增量式非刚性运动结构的方法，并通过局部刚性以及最大深度启发式方法来同时恢复焦距和非刚性形状，并利用二阶锥规划高效地解决了一次添加大量点以及视角增加的问题。

未知焦距的非刚性结构增量运动恢复

Incremental Non-Rigid Structure-from-Motion with Unknown Focal Length

The optimal power flow (OPF) problem determines power generation/demand that
minimize a certain objective such as generation cost or power loss. It is
nonconvex. We prove that, for radial networks, after shrinking its feasible set
slightly, the global optimum of OPF can be recovered via a second-order cone
programming (SOCP) relaxation under a condition that can be checked a priori.
The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two
real-world networks, and has a physical interpretation.

通过将可行集合轻微缩小，针对径向网络，可以在先验可检查的条件下通过二阶锥规划 (SOCP) 松弛恢复 OPF 的全局最优解。针对 IEEE 13、34、37、123 节点总线网络和两个实际网络，该条件成立并具有物理解释。

径向网络中最优功率流的精确凸松弛

Exact Convex Relaxation of Optimal Power Flow in Radial Networks

Elfving's Theorem is a major result in the theory of optimal experimental
design, which gives a geometrical characterization of $c-$optimality. In this
paper, we extend this theorem to the case of multiresponse experiments, and we
show that when the number of experiments is finite, $c-,A-,T-$ and $D-$optimal
design of multiresponse experiments can be computed by Second-Order Cone
Programming (SOCP). Moreover, our SOCP approach can deal with design problems
in which the variable is subject to several linear constraints.
We give two proofs of this generalization of Elfving's theorem. One is based
on Lagrangian dualization techniques and relies on the fact that the
semidefinite programming (SDP) formulation of the multiresponse $c-$optimal
design always has a solution which is a matrix of rank $1$. Therefore, the
complexity of this problem fades.
We also investigate a \emph{model robust} generalization of $c-$optimality,
for which an Elfving-type theorem was established by Dette (1993). We show with
the same Lagrangian approach that these model robust designs can be computed
efficiently by minimizing a geometric mean under some norm constraints.
Moreover, we show that the optimality conditions of this geometric programming
problem yield an extension of Dette's theorem to the case of multiresponse
experiments.
When the number of unknown parameters is small, or when the number of linear
functions of the parameters to be estimated is small, we show by numerical
examples that our approach can be between 10 and 1000 times faster than the
classic, state-of-the-art algorithms.

本文将 Elfving 定理扩展到多响应实验的情况，并证明了多响应设计问题可通过二阶圆锥规划的方法得到 $c-,A-,T-$ 和 $D-$ 优化设计；同时研究了模型强健的 $c-$ 优化，证明了几何均值可以有效地计算模型强健设计，并且优化条件的最优解可以推广 Dette 定理到多响应实验。