Motion Tracking with Finite Elements Meshes and Image Models

Motion tracking plays an important role in many domains including biomedical and mechanical engineering. Numerous methods have been proposed in the literature. While recent machine learning-based approaches provide fairly robust and accurate results, classical methods —combining statistical analysis of image intensity with a model of the underlying motion— remain widely used, as they offer greater control over the obtained results. Such approaches may handle highly complex motions; however, any artifact in the images (e.g.., partial voluming, local decrease of signal-to-noise ratio or even local signal void), may drastically affect the tracking. In order to reduce the impact of such artifacts, this paper extends a recently proposed motion tracking approach that relies on both a geometrical model of the tracked object and a model of the images themselves. The problem is thus formulated in terms of finding the displacement of the object such that the generated images, obtained with the image model, best match the acquired images. That way, if any artifact is present in the acquired images but also well represented in the image model, precise motion information can still be recovered from the acquired images. The performance of the proposed method is illustrated on tagged magnetic resonance images, for which acquired images are usually low-resolution, generating significant partial voluming. A simple model of such images is formulated. The method is applied to 2D synthetically generated image series representing various kinematics, with resolutions as low as those found in in vivo acquisitions, and compared to a classical tracking method. In order to avoid computing the cost function gradient, a derivative-free algorithm is used to solve the optimization problem. On the considered examples, the proposed method performs better than the classical tracking method.