Determining the relative pose of an object between two images is pivotal to the success of generalizable object pose estimation. Existing approaches typically approximate the continuous pose representation with a large number of discrete pose hypotheses, which incurs a computationally expensive process of scoring each hypothesis at test time. By contrast, we present a Deep Voxel Matching Network (DVMNet) that eliminates the need for pose hypotheses and computes the relative object pose in a single pass. To this end, we map the two input RGB images, reference and query, to their respective voxelized 3D representations. We then pass the resulting voxels through a pose estimation module, where the voxels are aligned and the pose is computed in an end-to-end fashion by solving a least-squares problem. To enhance robustness, we introduce a weighted closest voxel algorithm capable of mitigating the impact of noisy voxels. We conduct extensive experiments on the CO3D, LINEMOD, and Objaverse datasets, demonstrating that our method delivers more accurate relative pose estimates for novel objects at a lower computational cost compared to state-of-the-art methods. Our code is released at: https://github.com/sailor-z/DVMNet/.

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in small and arbitrary groups, doing so has no theoretical basis and makes its impossible to exploit the power of ED to the full. In this paper, we introduce a numerically stable and differentiable approach to leveraging eigenvectors in deep networks. It can handle large matrices without requiring to split them. We demonstrate the better robustness of our approach over standard ED and PI for ZCA whitening, an alternative to batch normalization, and for PCA denoising, which we introduce as a new normalization strategy for deep networks, aiming to further denoise the network's features.