# Experimental Validation of Non-Marker Simple Image Displacement Measurements for Railway Bridges
## 1 Introduction  
There is a long history of railway construction, and railway bridges exist that were constructed over 100 years ago [1]. In addition, in developed countries, there has been a decrease in the number of personnel available to manage these bridges. Thus, improvement is required in the efficiency of bridge management systems based on existing periodic visual inspection. In particular, a transition to condition-based maintenance (CBM) has been proposed. CBM aims at improving the efficiency of maintenance while ensuring safety by appropriately evaluating the structural performance of railway bridges and optimizing the types and implementation times of measures [2, 3]. The efficient and quantitative evaluation of bridge performance based on measurements is indispensable for realizing CBM. One of the typical property indicators of railway bridges is the deflection (vertical displacement) under the passage of trains [4, 5]. However, the traditional contact-type or wire-type deflection measurement methods are required to work at large heights and may not be possible depending on the conditions under the bridge (e.g., river bridges). Because of this problem, several developments of simple deflection measurement techniques have been conducted [6, 7, 8]. This study contributes to the realization of CBM from the perspective of improving the efficiency of the measurement method by focusing on the displacement measurement method of bridges via image processing.  
This study's concept for image displacement measurements is based on the premise that it will be used for patrols and visual inspections of existing bridges. This point differsfrom previous studies aimed at developing highly accurate measurement techniques. Therefore, non-marker image displacement measurements that use only the minimum portable image measurement items (i.e., camera and tripod only) and do not require access to the bridge will be considered in this study. This concept aims at realizing primary screening based on bridge performance by establishing a simple bridge displacement measurement method that can be applied in the current inspection and patrol system. Furthermore, the quantitative records of structural performance are maintained in daily patrol visual inspections, which provide vital and objective data for future managers' decision making in the long-term management of bridges.  
The measurement accuracy and applicable conditions are critical issues for this type of simple measurement method. In this study, the displacement measurement accuracy and brightness conditions for non-marker image measurement were confirmed by a laboratory model test [9]. The applicable scope was then determined based on the accumulated deflection data of railway bridges during the passage of a train. Furthermore, field tests using two bridges, on a local low- and a high-speed railway, indicate the effectiveness of non-maker image measurement in real-world situations.  
In this paper, Section 2 reviews the related works and Section 3 explains the non-marker image measurement method. Section 4 describes the results of accuracy verification tests using model bridges and the calculation results of the applicable scope. Section 5 presents the results from the application on two bridges and additional considerations.