Recent progress in two-view geometry increasingly emphasizes enforcing smoothness and global consistency priors when estimating motion fields between pairs of images. However, in complex real-world scenes, characterized by extreme viewpoint and scale changes as well as pronounced depth discontinuities, the motion field often exhibits diverse and heterogeneous motion patterns. Most existing methods lack targeted modeling strategies and fail to explicitly account for this variability, resulting in estimated motion fields that diverge from their true underlying structure and distribution. We observe that Mixture-of-Experts (MoE) can assign dedicated experts to motion sub-fields, enabling a divide-and-conquer strategy for heterogeneous motion patterns. Building on this insight, we re-architect motion field modeling in two-view geometry with GeoMoE, a streamlined framework. Specifically, we first devise a Probabilistic Prior-Guided Decomposition strategy that exploits inlier probability signals to perform a structure-aware decomposition of the motion field into heterogeneous sub-fields, sharply curbing outlier-induced bias. Next, we introduce an MoE-Enhanced Bi-Path Rectifier that enhances each sub-field along spatial-context and channel-semantic paths and routes it to a customized expert for targeted modeling, thereby decoupling heterogeneous motion regimes, suppressing cross-sub-field interference and representational entanglement, and yielding fine-grained motion-field rectification. With this minimalist design, GeoMoE outperforms prior state-of-the-art methods in relative pose and homography estimation and shows strong generalization.

As a long-range prior, motion consensus essentially forces the overall spatial transformation between a pair of images to be smooth and consistent, which is naturally well-suited for two-view correspondence learning. However, such precious property remains under-explored by most existing studies due to the modeling challenges posed by the sparsity and uneven distributions of putative correspondences. In this paper, we propose DeMo, a novel and cutting-edge network for outlier rejection, which possesses the capacity to fully capture global motion consensus clues by way of consensus interpolation over the entire high-dimensional motion field generated by putative correspondences. Specifically, through incorporating regularization techniques into a Reproducing Kernel Hilbert Space (RKHS), a concise interpolation formula can be derived for the high-dimensional motion field, which inherently allows a closed-form solution. Subsequently, learnable deep kernels are collaboratively used to flexibly and efficiently capture the relationships between global inputs, thus maintaining the entire motion field consensus. In addition, to remedy the cubic computational overhead of explicit interpolation, a scene-adaptive sampling strategy is introduced, which implicitly selects the more scene-representative motions, reducing the computational complexity of motion consensus interpolation to be approximately linear while maintaining the accuracy. Moreover, to deal with underlying depth discontinuities caused by complicated scene variations, a local consensus complementation block is designed, which maintains local bilateral consensus across both feature and spatial channels. Without bells and whistles, DeMo achieves superior performance in various geometric tasks, including relative pose estimation, homography estimation, and visual localization.