Generalized pattern matching using orbit decomposition

Motion estimation, motion detection and tracking invariably require finding a particular pattern in a set or sequence of images. The task involves finding appearances of a given pattern in an image under various transformations and at various locations. This process is of very high time complexity since a search must be implemented both in the transformation domain and in the spatial domain. Contributing to this complexity is the chosen distance metric that measures the similarity between patterns. The Euclidean distance, for example, may change drastically when a small transformation is applied to the pattern. Applying a different metric distance might be advantageous, though at the expense of loosing the norm structure of the Euclidean space. In this work we present a new method for fast search in the transformation domain, which can also be applied in metric spaces. The method is based on recursive decomposition of the transformation domain, and a rejection scheme, which enables the process to quickly reject as irrelevant large percentages of this decomposition.