Homotopy Continuation Made Easy: Regression-based Online Simulation of Starting Problem-Solution Pairs

While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to intractability. In recent years, homotopy continuation has been introduced as a plausible alternative. However, the method currently depends on expensive parallel tracking of all possible solutions in the complex domain, or a classification network for starting problem-solution pairs trained over a limited set of real-world examples. Our innovation consists of employing a regression network trained in simulation to directly predict a solution from input correspondences, followed by an online simulator that invents a consistent problem-solution pair. Subsequently, homotopy continuation is applied to track that single solution back to the original problem. We apply this elegant combination to generalized camera resectioning, and also introduce a new solution to the challenging generalized relative pose and scale problem. As demonstrated, the proposed method successfully compensates the raw error committed by the regressor alone, and leads to state-of-the-art efficiency and success rates while running on CPU resources, only.

EVIT: Event-based Visual-Inertial Tracking in Semi-Dense Maps Using Windowed Nonlinear Optimization

Event cameras are an interesting visual exteroceptive sensor that reacts to brightness changes rather than integrating absolute image intensities. Owing to this design, the sensor exhibits strong performance in situations of challenging dynamics and illumination conditions. While event-based simultaneous tracking and mapping remains a challenging problem, a number of recent works have pointed out the sensor's suitability for prior map-based tracking. By making use of cross-modal registration paradigms, the camera's ego-motion can be tracked across a large spectrum of illumination and dynamics conditions on top of accurate maps that have been created a priori by more traditional sensors. The present paper follows up on a recently introduced event-based geometric semi-dense tracking paradigm, and proposes the addition of inertial signals in order to robustify the estimation. More specifically, the added signals provide strong cues for pose initialization as well as regularization during windowed, multi-frame tracking. As a result, the proposed framework achieves increased performance under challenging illumination conditions as well as a reduction of the rate at which intermediate event representations need to be registered in order to maintain stable tracking across highly dynamic sequences. Our evaluation focuses on a diverse set of real world sequences and comprises a comparison of our proposed method against a purely event-based alternative running at different rates.