Incident detection (ID), or the automatic discovery of anomalies from road traffic data (e.g., road sensor and GPS data), enables emergency actions (e.g., rescuing injured people) to be carried out in a timely fashion. Existing ID solutions based on data mining or machine learning often rely on dense traffic data; for instance, sensors installed in highways provide frequent updates of road information. In this paper, we ask the question: Can ID be performed on sparse traffic data (e.g., location data obtained from GPS devices equipped on vehicles)? As these data may not be enough to describe the state of the roads involved, they can undermine the effectiveness of existing ID solutions. To tackle this challenge, we borrow an important insight from the transportation area, which uses trajectories (i.e., moving histories of vehicles) to derive incident patterns. We study how to obtain incident patterns from trajectories and devise a new solution (called Filter-Discovery-Match (FDM)) to detect anomalies in sparse traffic data. Experiments on a taxi dataset in Hong Kong and a simulated dataset show that FDM is more effective than state-of-the-art ID solutions on sparse traffic data.