Outdoor large structures, such as long-span bridges and high-rise buildings, experience deformation due to various complex loads during use. Structural monitoring plays an important role in ensuring the safety and extending the service life of these structures. Photogrammetry is increasingly used in structure monitoring due to its high precision, non-contact, and dynamic measurement capabilities. However, outdoor camera systems are susceptible to environmental influences. Temperature fluctuations can induce internal thermal effects within the camera, leading to image point drift. This drift becomes more pronounced with long-term temperature variations spanning years and seasons. Experiments have shown that a camera temperature fluctuation of 50 °C can cause an image point drift of approximately 7 pixel. Furthermore, due to the optical lever principle, this error is significantly amplified with increasing observation distances, limiting the application of high-precision visual measurement. In this study, we derive a camera image point drift model based on temperature-induced image plane motion. This model establishes a mathematical relationship between image point drift and changes in key camera parameters. Subsequently, we use regression analysis to obtain the camera's temperature drift effect model and implement compensation for temperature-induced image point drift. We aim to provide strong support for applying photogrammetry technology in long-term structural monitoring.

We derive the camera image point drift model from the image plane using the line of sight principle of camera imaging. This model clarifies the mathematical relationship between the image point drift and the changes in key camera parameters. To analyze the effects of wide temperature ranges and varying temperature rates on image drift, we utilize a temperature control chamber environment and systematically collect experimental data. This approach enriches the model's verification basis and improves image drift prediction accuracy. We use regression analysis to build a mapping model between temperature and variations in camera parameters, predicting and compensating for temperature-induced image point drift in both indoor and outdoor environments.

Starting from the camera image plane, we decompose internal temperature-induced changes into translations and rotations of the image plane. This approach eliminates the need to calculate camera pose during the solution process, avoiding errors from pose estimation and simplifying computations. Compared to image point drift models derived directly from the pinhole imaging model, our proposed model exhibits a reduction of approximately 2% in solution error (Table 3), demonstrating the feasibility. In indoor temperature variation experiments, multiple sets of temperature variation tests with different temperature ranges and rates are conducted to observe the temperature drift phenomenon in cameras. We find that the change in principal point coordinate and temperature are not simple linear relationship, whereas the relationship between temperature and focal length variation exhibits a strong linear trend, consistent with the understanding that the thermal expansion coefficient of solids is constant. By utilizing the camera temperature effect model to correct the image point drift phenomenon, we reduce the average error of image point drift by 89.34% (using Gaussian process regression as an example) (Fig. 8), effectively demonstrating the model's compensation effectiveness. However, a comprehensive and detailed analysis of the specific trends and mechanisms of camera parameter changes under different temperature ranges and temperature variation rates has yet to be undertaken for the designed multi-group temperature-controlled experiments. To test the compensation effect of the model in real-world environments, we conduct outdoor experiments. Over a nearly 24-hour monitoring period, the average displacement errors in the two experimental groups are reduced by 79.31% and 85.71% respectively (Fig. 11), demonstrating the strong effectiveness of the proposed camera temperature effect model even in outdoor settings. The displacement errors in the outdoor experiments are effectively controlled below the sub-millimeter level, proving that the method can meet high-precision measurement requirements for long-term structural monitoring, providing robust support for structural safety assessment and maintenance decision-making. Nevertheless, the experimental environment does not fully simulate complex natural variations, and the assessment of the model's stability and reliability over long-term monitoring remains insufficient. Future research should focus on real engineering structures, extend the monitoring duration, comprehensively evaluate model performance, and optimize the model to enhance its applicability and accuracy in complex environments.

We propose an image point drift model for cameras, derived from the camera’s image plane, establishing a relationship between image point coordinate variation and camera parameter changes. Subsequently, we validate the model's effectiveness through multiple indoor temperature-controlled and outdoor experiments. In addition, a complete camera temperature drift effect model is constructed by fitting the relationship between camera parameter variations and temperature using regression algorithms. Compensation results show a reduction of 89.34% in image point drift in indoor environments and average displacement errors are reduced by 79.31% and 85.71% in outdoor environments. This demonstrates the model's effectiveness in compensating for temperature-induced image point drift, providing a solid foundation for temperature effect correction in long-term monitoring.