Template matching based object recognition with unknown geometric parameters

We examine the problem of locating an object in an image when size and rotation are unknown. Previous work has shown that with known geometric parameters, an image restoration method can be useful by estimating a delta function at the object location. When the geometric parameters are unknown, this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient. We propose a new approach where a smooth approximation of the template is used to minimize a well-behaved likelihood surface. A coarse-to-fine approximation of the original template using a diffusion-like equation is used to create a library of templates. Using this library, we can successively perform minimizations which are locally well-behaved. As detail is added to the template, the likelihood surface gains local minima, but previous estimates place us within a well-behaved "bowl" around the global minimum, leading to an accurate estimate. Numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters.