Equivariant Observer Design on SL(3) for Image Intensity-Based Homography Estimation
For robotics and computer vision, this provides a featureless homography estimation method with theoretical convergence guarantees, though it is an incremental improvement over existing direct methods.
This paper introduces a nonlinear observer on SL(3) for homography estimation using direct image registration, achieving local exponential convergence without feature extraction. Simulations on real images validate the approach.
This paper addresses the problem of homography estimation using a nonlinear observer designed on the Lie group $\mathbf{SL}(3)$ that exploits the full image information through direct image registration. Unlike traditional feature-based methods, which rely on extensive feature extraction and matching, the proposed approach formulates an observer that minimises a cost function defined directly in terms of image pixel intensities. Explicit conditions ensuring the non-degeneracy of the cost function are derived, and a comprehensive analysis is conducted to characterise and generate degenerate (unobservable) image configurations. Theoretical results demonstrate local exponential convergence of the observer. To improve local convergence properties, a second-order observer variant is introduced by incorporating the Hessian of the cost function into the correction term. Simulation results demonstrate the performance of the proposed solutions on real images.