Deep networks have recently seen significant application to the analysis of medical image data, particularly for segmentation and disease classification. However, there are many situations in which the purpose of analysing a medical image is to perform parameter estimation, assess connectivity or determine geometric relationships. Some of these tasks are well served by probabilistic trackers, including Kalman and particle filters. In this work, we explore how the probabilistic outputs of a single-architecture deep network may be coupled to a probabilistic tracker, taking the form of a particle filter. The tracker provides information not easily available with current deep networks, such as a unique ordering of points along vessel centrelines and edges, whilst the construction of observation models for the tracker is simplified by the use of a deep network. We use the analysis of retinal images in several datasets as the problem domain, and compare estimates of vessel width in a standard dataset (REVIEW) with manually determined measurements.