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Pose registration is critical in vision and robotics. This paper focuses on the challenging task of initialization-free pose registration up to 7DoF for homogeneous and heterogeneous measurements. While recent learning-based methods show promise using differentiable solvers, they either rely on heuristically defined correspondences or are prone to local minima. We present a differentiable phase correlation (DPC) solver that is globally convergent and correspondence-free. When combined with simple feature extraction networks, our general framework DPCN++ allows for versatile pose registration with arbitrary initialization. Specifically, the feature extraction networks first learn dense feature grids from a pair of homogeneous/heterogeneous measurements. These feature grids are then transformed into a translation and scale invariant spectrum representation based on Fourier transform and spherical radial aggregation, decoupling translation and scale from rotation. Next, the rotation, scale, and translation are independently and efficiently estimated in the spectrum step-by-step using the DPC solver. The entire pipeline is differentiable and trained end-to-end. We evaluate DCPN++ on a wide range of registration tasks taking different input modalities, including 2D bird's-eye view images, 3D object and scene measurements, and medical images. Experimental results demonstrate that DCPN++ outperforms both classical and learning-based baselines, especially on partially observed and heterogeneous measurements.

Monocular visual-inertial odometry (VIO) is a critical problem in robotics and autonomous driving. Traditional methods solve this problem based on filtering or optimization. While being fully interpretable, they rely on manual interference and empirical parameter tuning. On the other hand, learning-based approaches allow for end-to-end training but require a large number of training data to learn millions of parameters. However, the non-interpretable and heavy models hinder the generalization ability. In this paper, we propose a fully differentiable, and interpretable, bird-eye-view (BEV) based VIO model for robots with local planar motion that can be trained without deep neural networks. Specifically, we first adopt Unscented Kalman Filter as a differentiable layer to predict the pitch and roll, where the covariance matrices of noise are learned to filter out the noise of the IMU raw data. Second, the refined pitch and roll are adopted to retrieve a gravity-aligned BEV image of each frame using differentiable camera projection. Finally, a differentiable pose estimator is utilized to estimate the remaining 3 DoF poses between the BEV frames: leading to a 5 DoF pose estimation. Our method allows for learning the covariance matrices end-to-end supervised by the pose estimation loss, demonstrating superior performance to empirical baselines. Experimental results on synthetic and real-world datasets demonstrate that our simple approach is competitive with state-of-the-art methods and generalizes well on unseen scenes.