We present a new approach to the general problem of template-based segmentation, detection, and registration. This joint problem is highly nonlinear and high dimensional, due to the large space of possible geometric transformations between a given template and its observed signature. Hence, any attempt to directly solve it inevitably leads to a high dimensional, nonlinear, non-convex optimization procedure. We propose a novel parametric solution to this problem, by showing that it can be equivalently represented by a low dimensional model, that is linear in the deformation parameters, and biased by the unknown observation background. Classical linear methods are then employed to estimate the deformation parameters, providing an explicit solution for the joint segmentation and registration problem.