Nonlinear constructive observer design for direct homography estimation

Feature-based homography estimation approaches rely on extensive image processing for feature extraction and matching, and do not adequately account for the information provided by the image. Therefore, developing efficient direct techniques to extract the homography from images is essential. This paper presents a novel nonlinear direct homography observer that exploits the Lie group structure of \(\mathbf{SL}(3)\) and its action on the space of image maps. Theoretical analysis demonstrates local asymptotic convergence of the observer. The observer design is also extended for partial measurements of velocity under the assumption that the unknown component is constant or slowly time-varying. Finally, simulation results demonstrate the performance of the proposed solutions on real images.