When using a camera as a position sensor, the measurement is limited in bandwidth, mainly due to the blur effects. The knowledge of an accurate model of the camera is then necessary to reconstruct the trajectory from the measurements given by the camera. This paper deals with the reconstruction of the continuous-time trajectory from the discrete-time measurements provided by the camera and shows the improvement obtained by using an accurate camera model. In the proposed methodology, a Kalman filter is used for the data fusion between the model and the measurement. The tuning and implementation of the filter are discussed in the specific context of the camera measurement. The system is evaluated in the context of a biomedical application: the reconstruction of the movement of a beating-heart.