Projector Calibration via Overlapping Point Cloud Distance Minimization

Abstract

Projection mapping is a technique that transforms any 3D surface into an interactive display by projecting visuals that conform to the surface’s shape. Camera and projector calibration is a fundamental prerequisite for accurate spatial measurement and perception in projection mapping. The calibration of projectors is necessary to ensure that they correctly map the surface they are projecting onto. An accurately calibrated projector will have the image projected perfectly in line with the intended surface, without any misalignment. Such alignment is important for a number of applications, one of which is projection mapping, in which multiple projectors are used to create immersive visual displays on complex surfaces such as buildings, stages, or statues.

Since projector calibration involves highly nonlinear relationships between the projector's parameters, a nonlinear optimization is required. Typically such optimizations include reprojection error as the objective functions, which is also one of the most commonly used objective function to calibrate projectors. However, in scenarios where there is a lack of ground truth reprojection error fails to accurately align the multiple overlapping projector point clouds, resulting in visible gaps between them instead of forming a continuous surface.

To address this issue, this thesis proposes a multi-step optimization with a novel global objective function. To analyze its robustness, the proposed optimization is tested both on simulated and on multiple real world configurations. Experimental results show that the proposed approach achieves higher calibration accuracy compared to existing methods, while also maintaining low runtime.

The proposed multi-step optimization process parameterizes the calibration problem as a function of the degree of stereo overlap to improve accuracy. The stereo overlap plays a key role in projection mapping, influencing calibration accuracy and system cost. Understanding the relationship between stereo overlap and calibration error allows for reducing overlap while maintaining acceptable accuracy, thus reducing the number of cameras needed and cutting costs.

In summary, this thesis introduces a novel global objective function that minimizes the distance between overlapping projector point clouds, rather than relying solely on reprojection error. It also provides insight into the required overlap between devices, including both cameras and projectors, helping to achieve higher accuracy while efficiently covering an entire projection surface that may not be uniform.