Title: A Universal Method for Camera Pose Estimation Using Lamé Curve LEDs in Visible Light Positioning

Camera-based visible light positioning (VLP) has emerged as a highly promising solution for achieving precise and cost-effective indoor camera pose estimation (CPE). To minimize the infrastructure cost by reducing the number of required light-emitting diodes (LEDs), contemporary approaches often leverage the geometric features of LEDs for positioning tasks. However, while these methods are intriguing, they are generally limited to specific LED geometries, which causes them to fail in environments with heterogeneous LED shapes.

To overcome this limitation, this study introduces Lamé curves as a unified mathematical representation for common LED geometries. Building on this concept, we propose a generic VLP algorithm known as LC-VLP, which utilizes Lamé curve-shaped LEDs. In this system, several ceiling-mounted LEDs periodically transmit their specific curve parameters through visible light communication. These signals are captured by a receiver equipped with a camera. By analyzing the received LED images alongside the transmitted curve parameters, the receiver can determine the camera's pose using the LC-VLP method.

The proposed framework involves constructing an LED database offline to store relevant curve parameters. Online positioning is then modeled as a nonlinear least-squares problem, which is resolved through iterative solving. Furthermore, to ensure robust initialization, we developed a perspective-n-points (FreePnP) algorithm that does not require correspondences. This innovation allows for approximate CPE without the need for any pre-calibrated reference points.

The efficacy of LC-VLP was validated through both simulations and real-world experiments. Simulation results demonstrate that LC-VLP surpasses existing state-of-the-art techniques in scenarios involving both circular and rectangular LEDs. Specifically, when compared to a perspective arcs algorithm, LC-VLP reduces average position and rotation errors by more than 30%. Experimental trials further confirm the system's high precision, achieving an average position accuracy of under 4 cm.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC