In face tracking, geometry refers to the spatial configuration of a predefined set of points that correspond to physically consistent locations on the human face (such as eye corners, nose tips, and eyebrow edges). A particular choice of these points is application dependent, with some applications requiring a dense set of over 100 points and others requiring only a sparser selection. However, the robustness of face-tracking algorithms generally improves with an increased number of points, as their separate measurements can reinforce each other through their relative spatial dependencies. For example, the location of an eye corner is a good indication of where to expect the nose to be located. However, there are limits to improvements in robustness gained by increasing the number of points, where performance typically plateaus after around 100 points. Furthermore, increasing the point set used to describe a face carries with it a linear increase in computational complexity...