In this paper, we propose the first minimal solutions for estimating the
semi-generalized homography given a perspective and a generalized camera. The
proposed solvers use five 2D-2D image point correspondences induced by a scene
plane. One of them assumes the perspective camera to be fully calibrated, while
the other solver estimates the unknown focal length together with the absolute
pose parameters. This setup is particularly important in structure-from-motion
and image-based localization pipelines, where a new camera is localized in each
step with respect to a set of known cameras and 2D-3D correspondences might not
be available. As a consequence of a clever parametrization and the elimination
ideal method, our approach only needs to solve a univariate polynomial of
degree five or three. The proposed solvers are stable and efficient as
demonstrated by a number of synthetic and real-world experiments.

该论文提出了从场景平面引出的五个二维 - 二维图像点对应所能获得的对于半广义单应性的第一种最小解决方案。其中一个解决器假设透视相机完全校准，而另一个解决器则估计未知的焦距和绝对姿态参数。

经过校准或部分校准的半广义单应矩阵

Calibrated and Partially Calibrated Semi-Generalized Homographies

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。