Two-Stage Camera Calibration Method for Multi-Camera Systems Using Scene Geometry

TL;DR

This work tackles the problem of calibrating multi-camera systems in real-world environments where floor plans or synchronized video streams are unavailable. It proposes a two-stage, scene-geometry–based calibration: Stage 1 uses operator-annotated geometric primitives to obtain partial camera parameters and project the EFOV into a common base space; Stage 2 enables interactive adjustment of EFOV projections to recover the remaining extrinsics, with optional use of location plans or virtual calibration elements. Implemented as a web service, the approach demonstrates accuracy and flexibility through comparative analyses and demonstration videos, showing applicability to retail, industrial, and archival settings. The method expands the deployment of precise multi-camera tracking to scenarios previously deemed infeasible.

Abstract

Calibration of multi-camera systems is a key task for accurate object tracking. However, it remains a challenging problem in real-world conditions, where traditional methods are not applicable due to the lack of accurate floor plans, physical access to place calibration patterns, or synchronized video streams. This paper presents a novel two-stage calibration method that overcomes these limitations. In the first stage, partial calibration of individual cameras is performed based on an operator's annotation of natural geometric primitives (parallel, perpendicular, and vertical lines, or line segments of equal length). This allows estimating key parameters (roll, pitch, focal length) and projecting the camera's Effective Field of View (EFOV) onto the horizontal plane in a base 3D coordinate system. In the second stage, precise system calibration is achieved through interactive manipulation of the projected EFOV polygons. The operator adjusts their position, scale, and rotation to align them with the floor plan or, in its absence, using virtual calibration elements projected onto all cameras in the system. This determines the remaining extrinsic parameters (camera position and yaw). Calibration requires only a static image from each camera, eliminating the need for physical access or synchronized video. The method is implemented as a practical web service. Comparative analysis and demonstration videos confirm the method's applicability, accuracy, and flexibility, enabling the deployment of precise multi-camera tracking systems in scenarios previously considered infeasible.

Figures (14)

• Figure 1: Relationship between the base CS (blue) and the camera-associated CS (red). The coordinate systems are linked via the displacement vector (x0, y0, z0) and a sequence of three rotations: yaw, pitch, roll.
• Figure 2: Schematic of the projection of point M', defined in the camera-associated CS (x', y', z') (red), onto the image plane M, defined in the pixel CS of the camera image (green). Point M' is obtained at the intersection of the projection ray from point k to point M with the image plane.
• Figure 3: Finding the vanishing point on the image of annotated lines, vertical in space, and computing the $roll$ angle (left). Using the found vanishing point to construct other vertical lines in space, based on the coordinates of any point lying in the horizontal plane (right).
• Figure 4: First option for annotating visible perspective geometry lines on the camera image.
• Figure 5: Second option for annotating visible perspective geometry lines on the camera image.