Single View Geometry Research Articles

Positioning Using Visible Light Communications: A Perspective Arcs Approach

Visible light positioning (VLP) is an accurate indoor positioning technology that uses luminaires as transmitters. In particular, circular luminaires are a common source type for VLP, which are typically treated only as point sources for positioning, while ignoring their geometry characteristics. In this paper, the arc feature of the circular luminaire and the coordinate information obtained via visible light communication (VLC) are jointly used for positioning, and a novel perspective arcs approach is proposed for VLC-enabled indoor positioning. The proposed approach does not rely on any inertial measurement unit and has no tilted angle limitation at the user. First, a VLC assisted perspective circle and arc algorithm (V-PCA) is proposed for a scenario in which a complete luminaire and an incomplete one can be captured by the user. Based on plane and solid geometry theory, the relationship between the luminaire and the user is exploited to estimate the orientation and the coordinate of the luminaire in the camera coordinate system. Then, the pose and location of the user in the world coordinate system are obtained by single-view geometry theory. Considering the cases in which parts of VLC links are blocked, an anti-occlusion VLC assisted perspective arcs algorithm (OA-V-PA) is proposed. In OA-V-PA, an approximation method is developed to estimate the projection of the luminaire’s center on the image and, then, to calculate the pose and location of the user. Simulation results show that the proposed indoor positioning algorithm can achieve a 90th percentile positioning accuracy of around 10 cm. Moreover, an experimental prototype is implemented to verify the feasibility. In the established prototype, a fused image processing method is proposed to simultaneously obtain the VLC information and the geometric information. Experimental results in the established prototype show that the average positioning accuracy is less than 5 cm for different tilted angles of the user.

Computer Vision-Based Localization With Visible Light Communications

Visible light positioning and computer vision-based localization have the potential to be cost-effective technologies for accurate indoor localization. However, the feasibility of existing methods in this domain is limited. In this paper, a novel visible light communication (VLC)-assisted perspective-four-line algorithm (V-P4L) is proposed for practical indoor localization. The basic idea of V-P4L is to jointly use VLC and computer vision techniques to achieve high localization accuracy regardless of LED height differences. In particular, the space-domain information is first exploited to estimate the orientation and coordinate information of a single rectangular LED luminaire in the camera coordinate system based on plane geometry theory and solid geometry theory. Then, by using time-domain information transmitted by VLC and the estimated luminaire information, the proposed V-P4L can estimate the position and pose of the camera using single-view geometry theory and the linear least square (LLS) method. To further mitigate the effect of height differences among LEDs on localization accuracy, a correction algorithm based on the LLS method and a simple optimization method is proposed. Due to the combination of time- and space-domain information, V-P4L can achieve accurate localization using a single luminaire without limitation on the correspondences between the features and their projections in conventional perspective-n-line (PnL) algorithms. Simulation results show that the position error caused by the proposed V-P4L algorithm is always less than 15 cm and the orientation error is always less than 4° using popular indoor luminaires. Experimental results with real hardware show that the average position error is less than 3 cm under both similar and different heights for the LEDs.

A High-Coverage Camera Assisted Received Signal Strength Ratio Algorithm for Indoor Visible Light Positioning

A high-coverage algorithm termed enhanced camera assisted received signal strength ratio (eCA-RSSR) positioning algorithm is proposed for visible light positioning (VLP) systems. The basic idea of eCA-RSSR is to utilize visual information captured by the camera to estimate first the incidence angles of visible lights. Based on the incidence angles, eCA-RSSR utilizes the received signal strength ratio (RSSR) calculated by the photodiode (PD) to estimate the ratios of the distances between the LEDs and the receiver. Based on an Euclidean plane geometry theorem, eCA-RSSR transforms the ratios of the distances into the absolute values. In this way, eCA-RSSR only requires three LEDs for both orientation-free 2D and 3D positioning, implying that eCA-RSSR can achieve high coverage. Based on the absolute values of the distances, the linear least square method is employed to estimate the position of the receiver. Therefore, for the receiver having a small distance between the PD and the camera, the accuracy of eCA-RSSR does not depend on the starting values of the non-linear least square method and the complexity of eCA-RSSR is low. Furthermore, since the distance between the PD and camera can significantly affect the performance of eCA-RSSR, we further propose a compensation algorithm for eCA-RSSR based on the single-view geometry. Experiment results show that positioning errors of less than five centimeters is achievable for eCA-RSSR. Simulation results show that eCA-RSSR can achieve 80th percentile accuracy of about four centimeters and can improve the coverage ratio at low cost.

A Differential–Algebraic Projective Framework for the Deformable Single-View Geometry of the 1D Perspective Camera

Single-View Geometry (SVG) studies the world-to-image mapping or warp, which is the relationship that exists between a body’s model and its image. For a rigid body observed by a projective camera, the warp is described by the usual camera matrix and its properties. However, it is clear that for a body whose deformation state changes between the body’s model and its image, the ‘simple,’ globally parameterized warp described solely by the camera matrix, breaks down. Existing work has exploited deformation to reconstruct the deformed body from its image, but did not establish the properties of the deformable warp. Studying these properties is part of deformable SVG and forms a recent research topic. Because deformations may take place anywhere in the object’s body, and because they may be uncorrelated, the warp is local in nature. Using a differential framework is thus an obvious choice. We propose a differential–algebraic projective framework based on modeling the body’s surface by a locally rational projective embedding and on the 1D projective camera. We show that this leads, via the study of univariate rational functions, to differential invariants that the warp must satisfy. It may seem surprising, given the generic hypothesis made on the observed body, hardly stronger than mere local smoothness, that constraints can still be found. Our framework generalizes the Schwarzian derivative, the first-order projective differential invariant, which holds under the assumption that the body’s shape is locally linear. Our invariants may be used to construct regularizers to be used in warp estimation. We report experimental results of two types on simulated and real data. The first type shows that the proposed invariants hold well for an independently estimated warp. The second type shows that the proposed regularizers improve warp estimation from point correspondences compared to the classical derivative-penalizing regularizers.

People Watching: Human Actions as a Cue for Single View Geometry

We present an approach which exploits the coupling between human actions and scene geometry to use human pose as a cue for single-view 3D scene understanding. Our method builds upon recent advances in still-image pose estimation to extract functional and geometric constraints on the scene. These constraints are then used to improve single-view 3D scene understanding approaches. The proposed method is validated on monocular time-lapse sequences from YouTube and still images of indoor scenes gathered from the Internet. We demonstrate that observing people performing different actions can significantly improve estimates of 3D scene geometry.

Robust single-view geometry and motion reconstruction

We present a framework and algorithms for robust geometry and motion reconstruction of complex deforming shapes. Our method makes use of a smooth template that provides a crude approximation of the scanned object and serves as a geometric and topological prior for reconstruction. Large-scale motion of the acquired object is recovered using a novel space-time adaptive, non-rigid registration method. Fine-scale details such as wrinkles and folds are synthesized with an efficient linear mesh deformation algorithm. Subsequent spatial and temporal filtering of detail coefficients allows transfer of persistent geometric detail to regions not observed by the scanner. We show how this two-scale process allows faithful recovery of small-scale shape and motion features leading to a high-quality reconstruction. We illustrate the robustness and generality of our algorithm on a variety of examples composed of different materials and exhibiting a large range of dynamic deformations.

Backpropagation in turbid media

We extend the backpropagation algorithm of standard diffraction tomography to backpropagation in turbid media. We analyze the behavior of the backpropagation algorithm both for a single-view geometry, as is common in mammography, and for multiple views. The most general form of the algorithm permits arbitrary placement of sources and detectors in the background medium. In addition, we specialize the algorithm for the case of a planar array of detectors, which permits the backpropagation algorithm to be implemented with fast-Fourier-domain noniterative algebraic methods. In this case the algorithm can be used to reconstruct three-dimensional images in a minute or less, depending on the number of views. We demonstrate the theoretical results with computer simulations.