Dealing with 2D translation estimation in log-polar imagery

Abstract

Log-polar mapping has been proposed as a very appropriate space-variant imaging model in active vision applications. This biologically inspired model has several advantages, and facilitates some visual tasks. For example, it provides an efficient data reduction, and simplifies rotational and scaling image transformations. However, simple translations become a difficult transform due to the log-polar geometry. There is no doubt about the importance of translation estimation in active visual tracking. Therefore, in this work, the problem of translation estimation in log-polar images is tackled. Two different approaches are presented, and their performances are evaluated and compared. One approach uses a gradient descent for minimizing a dissimilarity measure, while the other converts the 2D problem into two simpler 1D problems, by using projections. As the experimental results reveal, this second approach, besides being more efficient, can deal with larger translations than the gradient-based search can.