Automatic tracking of blood vessels in images of retinal fundus is an important and non-invasive procedure for the diagnosis of many diseases. Tracking techniques often present a high rate of false positives. This paper presents six methods to discriminate false detections from true positives, each based on a different model of the vessel. They describe a candidate vessel in terms of its average geometric and grayscale properties considered along the full trajectory of the vessel itself. The rationale is that false vessels are caused by the small scale of the tracking algorithm necessary during the tracking phase. Once tracking has been completed, we can gather information from the full vessel trajectory and solve ambiguities that cannot be fixed during tracking. We apply Fisher linear discriminant analysis to these features to get the desired discrimination. Results on 28 images show satisfactory rejection of false positives and better results when using more complex models.