With an increased interest in applications that require a clean background image, such as video surveillance, object tracking, street view imaging and location-based services on web-based maps, multiple algorithms have been developed to reconstruct a background image from cluttered scenes. Traditionally, statistical measures and existing image quality techniques have been applied for evaluating the quality of the reconstructed background images. Though these quality assessment methods have been widely used in the past, their performance in evaluating the perceived quality of the reconstructed background image has not been verified. In this work, we discuss the shortcomings in existing metrics and propose a full reference Reconstructed Background image Quality Index (RBQI) that combines color and structural information at multiple scales using a probability summation model to predict the perceived quality in the reconstructed background image given a reference image. To compare the performance of the proposed quality index with existing image quality assessment measures, we construct two different datasets consisting of reconstructed background images and corresponding subjective scores. The quality assessment measures are evaluated by correlating their objective scores with human subjective ratings. The correlation results show that the proposed RBQI outperforms all the existing approaches. Additionally, the constructed datasets and the corresponding subjective scores provide a benchmark to evaluate the performance of future metrics that are developed to evaluate the perceived quality of reconstructed background images.