Title: FlatVPR: A Plug-and-Play Geo-linear Residual Adapter for Geometric Rectification of Foundation Model Feature Manifolds

Abstract: This study introduces "FlatVPR," an innovative approach to geometric rectification designed to resolve the tension between maintaining lightweight mapping and achieving high localization accuracy in visual place recognition (VPR). The core of this paradigm involves structuring feature manifolds such that any descriptor located between two neighboring anchors, $\mathbf{z}A$ and $\mathbf{z}_B$, can be precisely reconstructed through linear interpolation. This process is defined by the equation $\hat{\mathbf{z}}{pseudo} = (1-t)\mathbf{z}_A + t\mathbf{z}_B$, where the parameter $t \in [0,1]$ signifies the relative position. Although leading foundation models like DINOv2-ViT-S/14 yield robust semantic features, their latent manifolds suffer from significant curvature. This characteristic causes uniform linear movement in the physical world to map onto complex, non-linear paths within the feature space, making accurate reconstruction difficult when anchor points are sparse.

To facilitate this interpolation-based reconstruction, we apply a residual transformation, $\hat{\mathbf{z}} = \mathbf{z} + \text{Res}(\mathbf{z})$, to the raw foundation features $\mathbf{z}$, utilizing $\text{Res}(\cdot)$ as a learnable adapter. We employ a mathematically derived Pullback Flatness Loss to explicitly reduce manifold curvature. This loss function minimizes the deviation of intermediate features from the straight line segment linking adjacent anchors, effectively reducing the manifold's intrinsic curvature. By flattening the spatial representation, we frame map construction within an Expectation-Maximization (EM) framework. This approach separates the process into a continuous M-step for adapting the manifold and a conceptual E-step that provides guidelines for selecting optimal anchors. Testing on the NCLT dataset reveals that our adapter yields substantial performance gains, even in scenarios characterized by extreme seasonal variations and very sparse anchor intervals of 100 meters.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC