In this paper, we propose LF-PGVIO, a Visual-Inertial-Odometry (VIO)
framework for large Field-of-View (FoV) cameras with a negative plane using
points and geodesic segments. Notoriously, when the FoV of a panoramic camera
reaches the negative half-plane, the image cannot be unfolded into a single
pinhole image. Moreover, if a traditional straight-line detection method is
directly applied to the original panoramic image, it cannot be normally used
due to the large distortions in the panoramas and remains under-explored in the
literature. To address these challenges, we put forward LF-PGVIO, which can
provide line constraints for cameras with large FoV, even for cameras with
negative-plane FoV, and directly extract omnidirectional curve segments from
the raw omnidirectional image. We propose an Omnidirectional Curve Segment
Detection (OCSD) method combined with a camera model which is applicable to
images with large distortions, such as panoramic annular images, fisheye
images, and various panoramic images. Each point on the image is projected onto
the sphere, and the detected omnidirectional curve segments in the image named
geodesic segments must satisfy the criterion of being a geodesic segment on the
unit sphere. The detected geodesic segment is sliced into multiple
straight-line segments according to the radian of the geodesic, and descriptors
are extracted separately and recombined to obtain new descriptors. Based on
descriptor matching, we obtain the constraint relationship of the 3D line
segments between multiple frames. In our VIO system, we use sliding window
optimization using point feature residuals, line feature residuals, and IMU
residuals. Our evaluation of the proposed system on public datasets
demonstrates that LF-PGVIO outperforms state-of-the-art methods in terms of
accuracy and robustness. Code will be open-sourced at
this https URL

本文提出了 LF-PGVIO，这是一种用于具有负平面的大视场（FoV）相机的视觉惯性里程计（VIO）框架，支持点和大圆线段，该方法可以在具有大畸变的图像上提供线约束，直接从原始全向图像中提取全向曲线段，并在公共数据集上的实验表明，在准确性和稳健性方面，LF-PGVIO 优于最先进的方法。

LF-PGVIO: 使用点和测地线段的大视场相机视觉惯性测距框架

LF-PGVIO: A Visual-Inertial-Odometry Framework for Large Field-of-View  Cameras using Points and Geodesic Segments

Given a family of probability measures in P(X), the space of probability
measures on a Hilbert space X, our goal in this paper is to highlight one ore
more curves in P(X) that summarize efficiently that family. We propose to study
this problem under the optimal transport (Wasserstein) geometry, using curves
that are restricted to be geodesic segments under that metric. We show that
concepts that play a key role in Euclidean PCA, such as data centering or
orthogonality of principal directions, find a natural equivalent in the optimal
transport geometry, using Wasserstein means and differential geometry. The
implementation of these ideas is, however, computationally challenging. To
achieve scalable algorithms that can handle thousands of measures, we propose
to use a relaxed definition for geodesics and regularized optimal transport
distances. The interest of our approach is demonstrated on images seen either
as shapes or color histograms.

本文探讨了在概率测度空间 P（X）中，使用最优传输（Wasserstein）几何将被限制为该度量下的测地线段的曲线，以高效地总结该系列测度。我们展示了在最优传输几何中，重要概念可以通过使用 Wasserstein 平均值和微分几何，找到自然的等效物。然而，应用这些想法是具有挑战性的。为了处理数千个测度和实现可扩放的算法，我们建议使用放松的测地线定义和正则化的最优传输距离。本文的方法在将图像视为形状或颜色直方图方面具有重要意义。