Template matching is the search for a known object, represented by a template image, at an arbitrary location within a larger image. The local measure of match is often desired to be invariant to certain transforms, such as rotation and dilation, of the template. While a variety of solutions have been proposed, most are designed to provide invariance to a specific transform or set of transforms, and often involve significant computational demands. When invariance to ``small'' transformations of the template (e.g. rotation by a small angle) is sufficient, local linear approximations to these transforms may be used to allow template matching with invariance to arbitrary transforms, without significantly increased computational requirements.