Changes in video data recorded by a static camera can be caused by structural scene changes like motion and by illumination changes. We describe an algorithm which discriminates reliably between structural scene changes and illumination, thus detecting only true scene changes. To this end, we derive a new test statistic for change detection based on a Total Least Squares (TLS) approach. The basic idea is to design a test to decide whether or not two vectors observed in noise are collinear. The TLS statistic reacts to structural scene changes, while it is insensitive to varying illumination. Moreover, we integrate the TLS statistic into a Bayesian framework for change detection, which uses prior knowledge via Markov random fields. The resulting change detection algorithm combines the benefits of Bayesian detection with robustness against both fast and slow variations of illumination.