The speed and quality of imaging cardiac structures (coronary arteries, cardiac valves etc) in MR can be improved by tracking and predicting their motion in MR images. The problem is challenging not only due to the complex motion of these structures that significantly changes the appearance of the region of interest, but also the ability to track at different spatial and temporal resolutions depending on the application. We have developed a multiple template-based tracking method to track these cardiac structures reliably and accurately in MR images. Depending on the cardiac structure being imaged, we have proposed subject-specific approaches that provide better motion compensation.

In MR coronary angiography, we proposed an approach to track coronary artery in high speed, low-resolution MR images, and to use the extracted motion information to 'servo' the MR imaging slice to compensate for motion, thereby acquiring the data as if the structure was stationary (see top two figures on the left).

In cardiac valve MR imaging, we developed an image-based tracking approach that estimates the valve plane motion through the cardiac cycle in high-resolution cine images taken during a pre-scan, which can then be used to adaptively re-position the acquisition slice during data acquisiton. Also, real-time tracking of the valve planes can be employed to account for shifts between pre-scan and data acqusiition (see bottom two figures on the left).

Multiple Kernel SSD tracking
Kernel-based tracking methods have recently gained popularity primarily due to their broad range of convergence and their robustness to unmodelled spatial deformations. We demonstrated a connection between kernel-based algorithms and more traditional template tracking methods. There is a well known equivalence between the kernel-based objective function and an SSD-like measure on kernel-modulated histograms, that can be optimized using Newton-style iterations. This method of optimization is more efficient (requires fewer steps to converge) than gradient descent mean shift and makes fewer assumptions on the form of the underlying kernel structure. In addition, the method naturally extends to objective functions optimizing more elaborate parametric motion models using multiple spatially distributed kernels. The multi-kernel methods are demonstrated on a variety of examples ranging from tracking of unstructured objects in image sequences to stereo tracking of structured objects.

Optimal Kernel Tracking
In practice, the design and development of tracking algorithms is still relatively ad-hoc leading to sub-optimal performance. The two primary drawbacks of the current kernel-based tracking approaches are 1) the same kernel is used for all image projections, and 2) kernel parameters (location and scale) are chosen in ad-hoc manner. The location is chosen at the center of the image with the scale equal to the size of target. We present an objective approach for developing optimal tracking methods, and have demonstrated this approach for the specific case of kernel-based tracking. We have shown that this optimization can be performed using effective approximations for one-dimensional and two-dimensional cases. In addition, the optimization can be easily generalized to higher-dimensional problems. The results on several examples illustrate the potential advantages of the optimizing a target-specific kernel. Finally, we believe these results point the way towards a more principled and consistent methodology for the design of visual tracking algorithms.