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Hyperbolic Geometry for Open-World Object Detection in Remote Sensing Imagery

Wuzhou Li, Jiawei Zhou, Shenghang Wang, Xiang Li

arXiv:2609.09626v1cs.CVcs.AI

TL;DR

Remote-sensing OWOD must discover unknown objects and incrementally learn novel classes, while hierarchical category relationships are poorly represented by common Euclidean spaces. HyRS-OWOD uses hyperbolic geometry through DOL and HUL for unknown discovery and HML for incremental learning, with experiments reporting consistent improvements across three benchmarks.

  • Problem

    Unknown-object recall and incremental learning in remote-sensing OWOD are challenged by unlabeled unknowns, semantic similarity, and catastrophic forgetting.

  • Method

    HyRS-OWOD combines DOL and HUL for foreground separation and hyperbolic uncertainty-based known–unknown discrimination, with HML for incremental representation learning.

  • Results

    Experiments on three remote sensing benchmarks improve unknown-object recall, reduce known–unknown confusion, and retain previously acquired knowledge during incremental learning.

  • Takeaways & Limitations

    Hyperbolic geometry supports a unified remote-sensing OWOD framework spanning unknown discovery and incremental learning.

Abstract

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Open-world object detection (OWOD) extends closed-set detection by requiring models to identify unknown objects and incrementally learn them once annotations become available. In remote sensing imagery, object categories often exhibit latent hierarchical relationships that may be inadequately represented in the Euclidean spaces commonly adopted by existing methods, limiting unknown-object recall and incremental-learning performance. To address this issue, we investigate hyperbolic geometry for OWOD in remote sensing imagery and propose HyRS-OWOD. To improve unknown object recall, we design a two-step unknown-object discovery mechanism: a Decoupled Objectness Learning (DOL) module that disentangles foreground perception from semantic information to separate foreground proposals from background regions, followed by a Hyperbolic Uncertainty Learning (HUL) component that leverages the radius of hyperbolic embeddings as an uncertainty-aware cue for known-unknown discrimination. For incremental learning, we develop a Hyperbolic Metric Learning (HML) strategy that enhances inter-class separability, facilitating the incorporation of novel categories while mitigating catastrophic forgetting. Experiments on three remote sensing benchmarks demonstrate consistent improvements in unknown recall and incremental learning over state-of-the-art OWOD methods.

I. INTRODUCTION

OWOD in remote sensing must discover unseen objects and incrementally learn them, but unknown-object recall and retention of known classes remain challenging. HyRS-OWOD introduces hyperbolic geometry with dedicated discovery and metric-learning components to address these challenges.

  • Open-World Object Detection: OWOD identifies unseen objects as unknown and incrementally incorporates them as novel classes once annotations become available.
  • Challenges: Unknown-object recall is limited by unlabeled unknowns being confused with background or semantically similar known categories.
  • Proposed Framework: HyRS-OWOD is presented as a unified framework for known-class detection, unknown-object discovery, and incremental learning in remote sensing imagery.
  • Unknown-Object Discovery: DOL separates class-agnostic foreground objectness from semantic classification, while HUL uses hyperbolic embedding radius to discriminate known and unknown objects.
  • Incremental Learning: HML combines hyperbolic metric learning with a class-balanced proposal buffer and hard-negative weighting to improve class separation and reduce interference during incremental learning.
  • Evaluation: Experiments on three remote sensing benchmarks report improvements over existing approaches for unknown-object discovery and incremental learning.

C. Hyperbolic Geometry

Hyperbolic geometry is used to represent hierarchical relationships in remote sensing categories and to provide uncertainty information through embedding radius. The section introduces its foundations, Poincaré ball formulation, and relevance to visual representation learning.

  • Motivation: Hyperbolic representations model hierarchical and tree-like visual structures with low distortion and provide an alternative to Euclidean representations.
  • Related Applications: Prior work has applied hyperbolic geometry to continual learning, few-shot learning, classification, segmentation, and object detection.
  • Uncertainty: In the Poincaré model, embedding radius—the distance to the origin—can serve as a measure of model uncertainty.
  • Remote Sensing Motivation: Remote sensing imagery contains semantically related categories with implicit hierarchical structures, motivating hyperbolic modeling for remote sensing OWOD.
  • Poincaré Ball Model: The Poincaré ball is introduced as a conformal model of hyperbolic space with constant negative curvature and an open-ball domain embedded in Euclidean space.
  • Poincaré Ball Model: As a point approaches the ball boundary, the conformal factor grows without bound, supporting exponentially expanding capacity for hierarchical structures.

C. M¨obius addition

The paper adopts Möbius gyrovector-space operations to perform algebraic computations in the Poincaré ball. The section introduces Möbius addition and the exponential-map setting for hyperbolic representations.

  • Möbius gyrovector spaces generalize Euclidean operations to hyperbolic geometry within the Poincaré ball model.
  • For x, y ∈ B_n^c, Möbius addition ⊕_c is defined as a hyperbolic analogue of vector addition.
  • The exponential map is introduced for x ∈ B_n^c and v ∈ T_xB_n^c to map tangent-space information into the hyperbolic space.

E. Distance and Hyperbolic Radius

The section defines hyperbolic distance and radius in the Poincaré ball and explains how radius provides an uncertainty cue. It also introduces relative δ-hyperbolicity as a scale-invariant measure of hierarchical structure.

  • The hyperbolic radius of a point is its Poincaré distance to the ball origin.
  • Higher-confidence proposals lie farther from the origin, whereas lower-confidence proposals lie closer to it in hyperbolic space.
  • The evaluation computes Gromov δ-hyperbolicity from region-level embeddings sampled across NWPU VHR-10, DIOR, and DOTA.
  • Relative δ-hyperbolicity ranges from 0 to 1, with values closer to 0 indicating stronger hierarchical structure.
  • Relative δ-hyperbolicity is used to estimate the manifold curvature of the Poincaré ball model.

IV. METHODOLOGY

HyRS-OWOD combines foreground–background separation, hyperbolic known–unknown discrimination, and hyperbolic metric learning within one OWOD architecture. Proposal features support box regression, classification, objectness estimation, and hyperbolic embedding.

  • A. Problem Formulation: The OWOD formulation uses known classes K_t and an unbounded set of unknown classes U_t that may appear during inference.
  • A. Problem Formulation: At each time step, the model detects known objects, labels unknown objects, and incorporates oracle-annotated novel classes into later training.
  • Overall Architecture: HyRS-OWOD introduces DOL for foreground–background separation, HUL for known–unknown discrimination, and HML for novel-class learning with reduced catastrophic forgetting.
  • Overall Architecture: Proposal features are used for bounding-box regression and are mapped into the Poincaré ball through the exponential map.
  • Overall Architecture: At inference, proposals with high objectness and high hyperbolic uncertainty are identified as unknown, while HML supports incremental training.

C. Decoupled Objectness Learning

DOL separates class-agnostic foreground perception from known-class semantics, while HUL uses hyperbolic radius to estimate proposal uncertainty. Together, they identify unknown proposals using objectness and uncertainty cues.

  • Objectness Learning: Objectness is trained as a binary foreground/background prediction for each proposal.
  • Objectness Learning: Known-class-only supervision can correlate objectness with semantic confidence and suppress proposals containing unknown objects.
  • Objectness Learning: DOL reduces dependence between objectness and known-class predictions so objectness captures class-agnostic foreground cues.
  • Hyperbolic Uncertainty Learning: Proposal embeddings are projected into a negatively curved Poincaré ball, where their radial position is used to estimate uncertainty.
  • Hyperbolic Uncertainty Learning: Image-wise radius normalization produces an uncertainty score whose larger values indicate greater uncertainty.
  • Hyperbolic Uncertainty Learning: HUL encourages candidate unknown proposals toward the high-uncertainty region near the origin using a radius threshold and smooth margin.
  • Hyperbolic Uncertainty Learning: Confident known proposals near the boundary receive smaller uncertainty scores than proposals close to the origin.

E. Hyperbolic Metric Learning for Incremental Learning

HML mitigates catastrophic forgetting by emphasizing confusing inter-class proposal pairs in hyperbolic space and using a balanced memory buffer during incremental learning.

  • HML assigns larger weights to hard-negative proposal pairs from different classes that lie close together.The weighting uses their Poincaré distances, so smaller distances receive larger weights.
  • The metric-learning set combines current-batch foreground proposal embeddings with embeddings retained in a class-balanced buffer.The buffer stores labeled foreground embeddings and retains at most Kmax embeddings per class using first-in-first-out updates.
  • Only anchors with non-empty positive sets participate in metric learning.
  • HML pulls same-class proposal embeddings closer in the Poincaré ball while pushing hard negatives from different classes apart.This objective is intended to learn more discriminative class boundaries during incremental learning.

F. Overall Training Objective

The framework combines known-object detection, objectness, decoupling, and hyperbolic uncertainty losses, then adds weighted HML during incremental learning.

  • Known-object detection uses classification and bounding-box regression losses.The classification term is focal loss, while regression uses smooth L1 loss.
  • The overall base-training objective combines known-object detection with objectness, decoupling, and hyperbolic uncertainty terms.The corresponding contributions are controlled by λobj, λdec, and λHUL.
  • Incremental training further introduces a weighted HML loss.λHML controls the contribution of this objective.

V. EXPERIMENTS

The experiments evaluate the method across three remote-sensing object-detection benchmarks with varied dataset sizes, category counts, and image resolutions.

  • The experiments cover NWPU VHR-10, DIOR, and DOTA remote-sensing datasets.
  • NWPU VHR-10 contains 650 positive images across ten geospatial object classes.Its spatial resolution ranges from 0.5 to 2 m.
  • DIOR comprises 23,463 aerial images with 192,472 instances across 20 categories.Its spatial resolution ranges from 0.5 m upward, as reported in the passage.
  • DOTA contains 2,806 large-scale aerial images and 402,089 annotated instances across 16 categories.Image dimensions range from 800 × 800 to 4,000 × 4,000 pixels.

4) Dataset Splits for OWOD:

The evaluation uses established OWOD class splits and metrics across DIOR, DOTA, and NWPU VHR-10, with comparisons showing gains in unknown recall, retention of known classes, and overall incremental performance.

  • Dataset Splits for OWOD: The study adopts 16+4, 10+10, and 4+16 splits on DIOR, 8+8 on DOTA, and 8+2 on NWPU VHR-10.It also establishes a progressive OWOD protocol on NWPU VHR-10 for sequential category discovery.
  • Evaluation Metrics: Evaluation reports mAP for known and novel classes, U-Recall for unknown classes, and wilderness impact for unknown-object influence.
  • Open-world object detection: The method achieves the best performance in four of five settings, exceeding previous best results by 10.00, 7.39, 0.41, and 3.04 percentage points.These gains correspond to DIOR 16+4, DIOR 10+10, DOTA 8+8, and NWPU VHR-10 8+2, respectively.
  • Open-world object detection: After incremental learning, previously known-class performance improves by 14.36, 4.05, 3.45, 1.88, and 5.07 percentage points across the five settings.
  • Unknown-object confusion: Unknown-object recall exceeds competing methods by 19.07, 20.11, and 23.66 percentage points in NWPU VHR-10 Tasks 1–3.WI remains 0.000578 and 0.000214 in Tasks 1 and 2 and decreases to zero in Task 3.
  • Incremental object detection: Overall mAP improves by 1.7 and 4.9 percentage points under the two DIOR class-incremental settings.

E. Qualitative Results

HyRS-OWOD discovers more unknown objects while preserving known-class detection, and its components improve unknown recall and incremental learning. Ablations attribute these gains to complementary objectness, uncertainty, and metric-learning mechanisms.

  • Qualitative comparison: HyRS-OWOD identifies more unknown objects than RandBox while maintaining accurate detection of known classes on NWPU VHR-10.The qualitative comparison highlights more tennis courts detected as unknown and correct detection of known basketball courts and baseball diamonds.
  • Unknown-object discovery: DOL alone raises U-Recall from 45.2% to 48.1%, while HUL alone raises it from 45.2% to 51.2% and reduces WI and A-OSE to zero.These ablations isolate the contributions of class-agnostic objectness and hyperbolic-radius uncertainty.
  • Unknown-object discovery: Combining DOL and HUL increases U-Recall to 58.9%, outperforming the baseline by 13.7 percentage points, while WI remains zero and A-OSE decreases from 8 to 1.K-mAP decreases from 91.9% to 89.1%, indicating a trade-off between unknown discovery and known-class detection.
  • Incremental learning: HML increases newly introduced-class mAP from 76.9% to 91.2% and overall mAP from 88.5% to 91.5%, while previously known-class mAP changes from 91.5% to 91.6%.The results support improved learning of novel classes without degrading previously learned performance.
  • Representation analysis: With HML, proposal embeddings form more compact intra-class clusters and clearer inter-class separation than embeddings learned without HML.The t-SNE visualization supports improved proposal discriminability during incremental learning.
  • Overall findings: Across remote sensing benchmarks, HyRS-OWOD improves unknown-object recall, reduces known–unknown confusion, and retains previously acquired knowledge during incremental learning.The conclusion attributes these outcomes to DOL, HUL, and HML within the hyperbolic OWOD framework.
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