cs.CVOct 20, 2025
SaveJoint Multi-Condition Representation Modelling via Matrix Factorisation for Visual Place Recognition
Organizations: School of Electronics and Computer Science, University of Southampton, SO17 1BJ Southampton, U.K. · Department of Computer Science and Engineering, Hanyang University, Seoul, South Korea. · QUT Centre for Robotics, School of Electrical Engineering and Robotics, Brisbane, QLD 4000, Australia. · School of Computer Science and Electronic Engineering, University of Essex, Colchester, CO4 3SQ, U.K.
Abstract
We address multi-reference visual place recognition (VPR), where reference sets captured under varying conditions are used to improve localization performance. While deep learning with large-scale training improves robustness, increasing data diversity and model complexity incur extensive computational cost during training and deployment. Descriptor-level fusion via voting or aggregation avoids training, but often targets multi-sensor setups or relies on heuristics with limited gains under appearance and viewpoint change. We propose a training-free, descriptor-agnostic approach that jointly models places using multiple reference descriptors via matrix decomposition into basis representations, enabling projection-based residual matching. We also introduce SotonMV, a benchmark for multi-viewpoint VPR captured over time. Our method improves Recall@1 by up to 18% over conventional single-reference set matching on appearance-change datasets, and matches or outperforms existing multi-reference baselines across most appearance-change settings. For viewpoint-change datasets, our method supports matching when viewpoint is distributed among the references, with the benefit depending on reference set coverage of the query conditions. On unconstrained reference sets, we additionally observe gains of 5%, demonstrating strong generalization while remaining computationally lightweight.
Figures & tables
Fig. 1: Top : Each place is represented by multiple images with different conditions, whose descriptors are stacked and subspace is formed using matrix factorization, here QR decomposition, to construct the map. Bottom : At inference, the query is projected and reconstructed using each subspace, with the smallest residual determining the match.
Fig. 2: Example places from datasets we evaluate. These datasets cover multi-reference sets with varying viewpoints, illumination, seasons and weather. Notably, the GLDv2-micro dataset contains irregular reference imagery with varying conditions, size and channel compositions.
Fig. 3: (Left) The area considered in Southampton. Each point is a cluster of scenes across multiple dates, with each scene encompassing four images at regularly spaced orientation. (Right) Example places from SotonMV. Each place is observed multiple times (appearance change), and captured at four headings (viewpoint change). The query images are taken at intermediate headings, representing VPR under challenging viewpoint with non-trivial spatial overlap.
Fig. 4: (Left, Middle) Distribution of scenes in SotonMV over years and months. (Right) Number of unique dates per place. Each place is composed of multiple scenes at different dates, where each scene consists of 4 images at different orientations.
| Queries | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter |
| References | EigenPlaces (2048D) | CosPlace (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||
| Fall | — | 88.9 | 93.3 | 62.7 | — | 85.9 | 91.2 | 58.4 | — | 95.3 | 95.9 | 81.6 | — | 47.2 | 69.0 | 17.4 |
| Spring | 80.6 | — | 73.5 | 67.6 | 76.4 | — | 68.3 | 68.2 | 88.0 | — | 83.2 | 89.6 | 42.5 | — | 37.4 | 21.0 |
| Summer | 94.3 | 82.6 | — | 59.3 | 92.8 | 79.5 | — | 53.8 | 95.8 | 91.6 | — | 78.4 | 69.1 | 42.9 | — | 18.2 |
| Winter | 51.8 | 70.7 | 47.1 | — | 46.4 | 66.2 | 41.4 | — | 70.2 | 86.9 | 64.8 | — | 14.3 | 22.8 | 13.9 | — |
| Pooling | 96.3 | 92.9 | 93.6 | 70.1 | 95.1 | 90.7 | 92.1 | 70.5 | 97.7 | 98.4 | 96.4 | 91.8 | 72.0 | 54.6 | 70.2 | 23.9 |
TABLE I: Recall@1 with Nordland retrieval using CNN-based Models.
| Queries | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter |
| References | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||
| Fall | — | 97.2 | 97.1 | 94.9 | — | 97.5 | 97.3 | 88.9 | — | 98.6 | 98.4 | 96.1 | — | 97.9 | 97.2 | 93.1 |
| Spring | 96.6 | — | 93.8 | 98.1 | 95.2 | — | 93.2 | 92.3 | 98.1 | — | 95.8 | 98.1 | 96.4 | — | 94.8 | 95.9 |
| Summer | 97.0 | 94.3 | — | 91.3 | 97.6 | 95.1 | — | 87.0 | 98.1 | 96.9 | — | 94.5 | 97.4 | 95.7 | — | 90.0 |
| Winter | 93.1 | 97.9 | 90.1 | — | 86.6 | 93.9 | 84.7 | — | 93.5 | 97.4 | 92.7 | — | 89.8 | 96.9 | 88.7 | — |
| Pooling | 99.0 | 99.4 | 97.9 | 98.5 | 99.0 | 99.0 | 97.8 | 94.0 | 99.4 | 99.4 | 98.6 | 99.0 | 99.2 | 99.3 | 97.7 | 97.0 |
TABLE II: Recall@1 with Nordland retrieval using Transformer-based Models.
| Queries | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow |
| References | EigenPlaces (2048D) | CosPlace (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||||||||||
| Sun | — | 61.3 | 94.4 | 96.7 | 44.2 | 86.7 | — | 52.4 | 90.0 | 93.7 | 23.0 | 81.7 | — | 59.6 | 96.0 | 96.8 | 70.5 | 89.0 | — | 22.9 | 74.5 | 86.4 | 14.4 | 68.2 |
| Dusk | 57.9 | — | 54.6 | 58.8 | 35.0 | 62.0 | 49.0 | — | 42.4 | 49.6 | 17.7 | 50.7 | 51.8 | — | 49.2 | 52.9 | 55.8 | 57.0 | 16.3 | — | 14.6 | 17.8 | 16.5 | 25.6 |
| Rain | 95.2 | 57.7 | — | 94.7 | 44.9 | 84.8 | 89.7 | 48.2 | — | 89.9 | 25.8 | 78.5 | 95.8 | 55.7 | — | 95.4 | 68.2 | 85.2 | 78.5 | 23.4 | — | 80.4 | 15.9 | 57.8 |
| Overcast | 96.3 | 63.6 | 94.2 | — | 49.2 | 89.7 | 94.0 | 55.3 | 90.6 | — | 24.4 | 85.4 | 96.8 | 61.8 | 96.0 | — | 75.4 | 90.5 | 89.3 | 25.4 | 78.4 | — | 19.2 | 69.1 |
| Night | 62.4 | 47.2 | 60.9 | 66.6 | — | 60.5 | 41.9 | 32.2 | 38.4 | 45.2 | — | 37.4 | 69.6 | 58.2 | 70.2 | 74.5 | — | 69.9 | 14.8 | 17.0 | 11.4 | 15.0 | — | 17.7 |
TABLE III: Recall@1 with Oxford RobotCar retrieval using CNN-based Models.
| Queries | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow | Sun | Dusk | Rain | Overcast | Night | Snow |
| References | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||||||||||
| Sun | — | 69.9 | 94.2 | 95.4 | 77.2 | 84.6 | — | 72.4 | 95.5 | 96.2 | 83.0 | 89.1 | — | 71.4 | 96.1 | 97.2 | 79.8 | 89.0 | — | 77.0 | 97.4 | 97.5 | 88.9 | 90.5 |
| Dusk | 64.7 | — | 59.8 | 67.2 | 68.3 | 64.6 | 66.7 | — | 60.6 | 68.1 | 68.9 | 65.4 | 65.2 | — | 61.7 | 66.0 | 68.8 | 66.4 | 74.4 | — | 67.3 | 75.3 | 74.5 | 72.2 |
| Rain | 93.6 | 62.6 | — | 93.0 | 76.2 | 81.1 | 94.8 | 63.4 | — | 95.1 | 81.8 | 87.1 | 96.4 | 65.6 | — | 96.2 | 79.5 | 86.0 | 97.0 | 70.5 | — | 96.8 | 88.8 | 88.5 |
| Overcast | 95.3 | 69.0 | 93.0 | — | 77.6 | 86.7 | 96.2 | 71.8 | 94.4 | — | 84.4 | 90.8 | 96.7 | 71.4 | 95.0 | — | 82.6 | 90.1 | 97.3 | 79.0 | 96.3 | — | 90.2 | 92.4 |
| Night | 72.5 | 67.7 | 73.1 | 74.0 | — | 67.9 | 79.9 | 70.1 | 79.1 | 80.2 | — | 77.8 | 79.8 | 69.9 | 80.4 | 83.0 | — | 75.7 | 87.4 | 77.0 | 86.1 | 88.3 | — | 82.9 |
TABLE IV: Recall@1 with Oxford RobotCar retrieval using Transformer-based Models.
| Approach | CosPlace (2048D) | Eigenplaces (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 34.2 | 50.7 | 57.3 | 64.3 | 70.7 | 82.0 | 88.0 | 91.3 | 72.0 | 84.0 | 88.0 | 92.3 | 32.3 | 55.0 | 61.7 | 73.0 |
| dMat. Avg. | 20.7 | 38.7 | 47.0 | 60.7 | 54.7 | 71.3 | 79.3 | 86.3 | 59.3 | 77.7 | 82.0 | 89.3 | 26.7 | 44.0 | 52.3 | 65.3 |
| LogSumExp | 36.7 | 54.0 | 59.0 | 64.3 | 75.7 | 85.7 | 90.0 | 91.3 | 72.7 | 86.3 | 90.3 | 92.3 | 33.7 | 56.3 | 64.3 | 73.0 |
| Sum Descriptors | 32.3 | 53.0 | 60.7 | 71.3 | 67.3 | 83.7 | 88.0 | 92.3 | 67.3 | 82.3 | 88.3 | 91.3 | 28.7 | 54.7 | 63.7 | 74.7 |
| QR-FullVP (Ours) | 43.7 | 61.7 | 67.0 | 75.3 | 80.7 | 90.7 | 93.0 | 94.7 | 76.3 | 89.7 | 93.0 | 95.7 | 40.3 | 62.3 | 70.0 | 80.0 |
TABLE V: Retrieval performance on SotonMV using CNN-based Models.
| Approach | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 78.7 | 91.3 | 94.7 | 96.7 | 76.3 | 88.3 | 93.0 | 96.7 | 57.7 | 74.7 | 81.3 | 90.0 | 85.7 | 94.3 | 97.3 | 98.7 |
| dMat. Avg. | 74.0 | 86.3 | 91.7 | 95.3 | 67.3 | 82.0 | 88.3 | 94.0 | 32.0 | 50.3 | 60.3 | 71.3 | 84.0 | 94.7 | 96.3 | 98.3 |
| LogSumExp | 78.3 | 92.0 | 95.3 | 96.7 | 77.7 | 89.0 | 92.3 | 96.7 | 56.0 | 73.3 | 82.0 | 90.0 | 87.3 | 94.7 | 98.7 | 98.7 |
| Sum Descriptors | 76.0 | 89.7 | 93.3 | 97.3 | 74.0 | 88.0 | 92.7 | 94.3 | 42.7 | 62.3 | 72.7 | 82.0 | 85.0 | 94.3 | 97.7 | 98.7 |
| QR-FullVP (Ours) | 81.7 | 93.7 | 96.3 | 97.3 | 81.3 | 91.3 | 95.3 | 97.7 | 60.3 | 78.0 | 85.3 | 90.0 | 87.7 | 96.7 | 98.7 | 99.0 |
TABLE VI: Retrieval performance on SotonMV using Transformer-based Models.
| Approach | CosPlace (2048D) | Eigenplaces (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 74.2 | 92.2 | 95.5 | 98.6 | 89.0 | 97.7 | 98.9 | 99.8 | 89.2 | 96.3 | 98.2 | 99.3 | 55.6 | 76.4 | 84.4 | 91.0 |
| dMat. Avg. | 54.1 | 77.5 | 86.3 | 96.3 | 73.6 | 89.9 | 93.9 | 98.0 | 77.7 | 90.8 | 95.2 | 98.4 | 37.0 | 59.1 | 71.5 | 84.8 |
| LogSumExp | 76.4 | 92.9 | 95.8 | 98.6 | 90.7 | 96.5 | 98.4 | 99.8 | 88.8 | 96.8 | 97.5 | 99.3 | 55.4 | 73.6 | 83.1 | 91.0 |
| Sum Descriptors | 62.9 | 85.8 | 93.3 | 97.9 | 80.3 | 94.1 | 97.4 | 98.8 | 81.2 | 93.7 | 96.8 | 98.7 | 42.9 | 67.1 | 77.2 | 87.5 |
| QR-FullVP (Ours) | 82.7 | 95.9 | 98.0 | 99.3 | 93.5 | 98.6 | 99.3 | 99.8 | 91.4 | 97.9 | 99.0 | 99.6 | 60.3 | 81.8 | 88.6 | 94.0 |
TABLE VII: Retrieval performance on Pitts250k-Test using CNN-based Models.
| Approach | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 94.4 | 99.6 | 99.8 | 99.9 | 90.3 | 97.9 | 99.0 | 99.4 | 79.1 | 95.8 | 98.0 | 99.8 | 94.9 | 99.7 | 99.9 | 99.9 |
| dMat. Avg. | 88.4 | 98.9 | 99.8 | 99.8 | 83.0 | 95.6 | 97.8 | 99.0 | 62.6 | 84.6 | 90.1 | 94.7 | 92.9 | 98.7 | 99.5 | 99.9 |
| LogSumExp | 93.8 | 98.8 | 99.6 | 99.9 | 91.5 | 97.6 | 98.5 | 99.4 | 81.8 | 94.0 | 97.3 | 99.8 | 96.2 | 99.0 | 99.4 | 99.9 |
| Sum Descriptors | 90.6 | 99.4 | 99.8 | 99.8 | 87.2 | 97.5 | 98.5 | 99.1 | 68.5 | 88.5 | 93.7 | 97.4 | 94.2 | 99.3 | 99.8 | 99.9 |
| QR-FullVP (Ours) | 95.6 | 99.6 | 99.9 | 99.9 | 93.7 | 98.6 | 99.1 | 99.7 | 82.3 | 97.1 | 98.6 | 99.8 | 97.0 | 99.6 | 99.8 | 99.9 |
TABLE VIII: Retrieval performance on Pitts250k-Test (non-default split, as elsewhere - see Section V ) using Transformer-based Models.
| Approach | CosPlace (2048D) | Eigenplaces (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 53.3 | 69.2 | 75.2 | 84.4 | 71.8 | 83.2 | 88.3 | 93.7 | 75.9 | 87.3 | 90.8 | 93.0 | 22.9 | 40.6 | 54.6 | 63.8 |
| dMat. Avg. | 23.2 | 47.0 | 58.1 | 71.1 | 39.4 | 57.8 | 65.1 | 77.5 | 42.5 | 65.4 | 70.5 | 81.0 | 16.2 | 28.3 | 36.2 | 49.8 |
| LogSumExp | 53.0 | 69.8 | 74.9 | 84.4 | 70.5 | 83.2 | 87.9 | 93.7 | 71.4 | 83.2 | 88.9 | 93.0 | 22.5 | 37.5 | 49.8 | 63.8 |
| Sum Descriptors | 37.5 | 60.6 | 66.4 | 78.4 | 47.3 | 68.3 | 76.2 | 82.9 | 51.4 | 70.8 | 77.8 | 83.8 | 19.1 | 34.3 | 40.0 | 58.4 |
| QR-FullVP (Ours) | 55.9 | 73.7 | 81.3 | 89.5 | 75.6 | 85.7 | 90.8 | 94.9 | 76.5 | 87.0 | 89.2 | 92.4 | 25.4 | 44.8 | 56.5 | 67.0 |
TABLE IX: Retrieval performance on Tokyo24/7 using CNN-based Models.
| Approach | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 95.9 | 98.4 | 99.1 | 99.7 | 88.9 | 96.5 | 97.1 | 99.1 | 80.0 | 90.2 | 93.3 | 95.6 | 94.0 | 97.8 | 98.4 | 98.7 |
| dMat. Avg. | 85.1 | 94.3 | 98.4 | 99.4 | 61.3 | 83.5 | 89.2 | 93.7 | 32.4 | 53.7 | 64.8 | 75.9 | 87.3 | 97.1 | 98.7 | 98.7 |
| LogSumExp | 94.0 | 98.4 | 99.1 | 99.7 | 87.9 | 94.6 | 97.1 | 99.1 | 71.8 | 86.4 | 90.8 | 95.6 | 94.3 | 98.1 | 98.4 | 98.7 |
| Sum Descriptors | 88.3 | 96.2 | 98.7 | 99.1 | 74.6 | 90.2 | 93.3 | 97.1 | 39.7 | 61.3 | 72.1 | 81.0 | 89.8 | 97.1 | 98.7 | 98.7 |
| QR-FullVP (Ours) | 94.8 | 99.1 | 99.7 | 99.7 | 91.4 | 96.8 | 97.5 | 98.4 | 76.5 | 88.9 | 92.1 | 94.9 | 94.6 | 97.8 | 98.4 | 98. 7 |
TABLE X: Retrieval performance on Tokyo24/7 (non-default split, as elsewhere - see Section V ) using Transformer-based Models.
| Approach | Eigenplaces (2048D) | CosPlace (2048D) | MixVPR (4096D) | NetVLAD (4096D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 53.6 | 64.7 | 69.6 | 75.3 | 48.1 | 60.0 | 65.2 | 72.1 | 59.7 | 71.0 | 75.4 | 80.9 | 41.1 | 54.9 | 61.0 | 69.6 |
| dMat. Avg. | 35.2 | 51.3 | 58.0 | 66.7 | 28.4 | 45.0 | 52.8 | 62.4 | 45.2 | 60.6 | 66.7 | 74.6 | 29.1 | 46.6 | 53.9 | 64.7 |
| LogSumExp | 52.6 | 65.5 | 70.7 | 75.3 | 47.2 | 60.9 | 67.1 | 72.1 | 57.1 | 71.0 | 76.5 | 80.9 | 41.1 | 56.5 | 63.8 | 69.6 |
| Sum Descriptors | 46.4 | 61.7 | 67.3 | 74.2 | 39.5 | 56.3 | 62.4 | 70.7 | 54.8 | 67.9 | 73.1 | 79.3 | 40.4 | 55.8 | 62.2 | 71.1 |
| QR-FullVP (Ours) | 58.8 | 70.4 | 74.9 | 80.3 | 53.3 | 66.0 | 71.0 | 77.7 | 64.9 | 76.4 | 79.8 | 84.7 | 48.7 | 62.7 | 68.4 | 75.4 |
TABLE XI: Retrieval performance on the GLDv2-micro dataset using CNN-based Models.
| Approach | MegaLoc (8448D) | SALAD (8448D) | CricaVPR (10752D) | BoQ (12288D) | ||||||||||||
| R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | R@1 | R@5 | R@10 | R@25 | |
| Pooling | 86.8 | 92.3 | 94.0 | 95.9 | 71.8 | 82.2 | 85.3 | 89.1 | 70.2 | 81.4 | 84.8 | 88.8 | 74.2 | 83.6 | 86.5 | 89.9 |
| dMat. Avg. | 80.5 | 89.4 | 92.6 | 94.8 | 59.1 | 74.3 | 79.0 | 85.2 | 52.1 | 67.4 | 73.3 | 80.1 | 67.2 | 80.2 | 84.4 | 88.4 |
| LogSumExp | 85.1 | 92.7 | 94.6 | 95.9 | 70.2 | 82.5 | 86.5 | 89.1 | 66.4 | 79.6 | 84.5 | 88.8 | 71.7 | 83.1 | 86.9 | 89.9 |
| Sum Descriptors | 84.6 | 92.3 | 94.4 | 95.8 | 68.7 | 79.9 | 84.3 | 88.9 | 65.9 | 79.3 | 83.7 | 88.2 | 71.9 | 83.4 | 86.7 | 90.2 |
| QR-FullVP (Ours) | 89.4 | 94.3 | 95.7 | 97.0 | 76.8 | 86.2 | 89.1 | 92.3 | 76.2 | 86.4 | 88.9 | 92.8 | 77.5 | 86.7 | 89.4 | 92.4 |
TABLE XII: Retrieval performance on the GLDv2-micro dataset using Transformer-based Models.
| Nordland | ||||
| Queries | Fall | Spring | Summer | Winter |
| References | SeqVLAD (24576D) | |||
| Fall | — | 85.7 | 95.0 | 68.4 |
| Spring | 78.9 | — | 80.0 | 77.3 |
| Summer | 92.2 | 83.6 | — | 69.4 |
| Winter | 57.9 | 74.2 | 60.9 | — |
TABLE XIII: Retrieval performance using SeqVLAD across datasets.
Fig. 5: QR-FullVP residuals using Eigenplaces for correct (green) and incorrect (red) top-1 matches across all datasets. Correct matches show lower residuals across all conditions. Appearance-challenging datasets (ORC Night, Nordland Winter), show larger overall residuals, reflecting a larger domain gap between query and reference basis. Multi-viewpoint datasets exhibit high residuals (from non-overlapping viewpoints), yet still improve retrieval over pooling, suggesting the subspace is sufficiently discriminative.
Fig. 6: Retrieval comparison on Oxford RobotCar (overcast query) using Eigenplaces. Left shows retrieval outcomes for single reference matching (dusk reference) and QR-FullVP (all references), with green indicating correct and red incorrect top-1 matches. The difference map (center) highlights where QR-FullVP succeeds over single-reference (green), the reverse (red) or both agree (grey). As expected, QR-FullVP resolves ambiguity across large portions of the traverse. (Retrieved images for QR-FullVP show a randomly sampled image from the matched place’s reference collection).
Fig. 7: Retrieval comparison on Oxford RobotCar (snow query) using Eigenplaces. Left shows retrieval outcomes for reference pooling and QR-FullVP, with green indicating correct and red incorrect top-1 matches. The difference map (center) highlights where QR-FullVP succeeds over pooling (green), the reverse (red), or both agree (grey). Overall, QR-FullVP outperforms pooling, and qualitative examples suggest this is often a fine disambiguation, such as the third example where the pooling match falls just outside the ground truth tolerance while QR-FullVP recovers the correct place. (Retrieved images for QR-FullVP show a randomly sampled image from the matched place’s reference collection).
Fig. 8: Retrieval comparison on Oxford RobotCar (night query) using Eigenplaces. Left shows retrieval outcomes for reference descriptor summing and QR-FullVP, with green indicating correct and red incorrect top-1 matches. The difference map (center) highlights where QR-FullVP succeeds over summing (green), the reverse (red), or both agree (grey). Although outperforming pooling, summing produces a more robust aggregate under night conditions, likely because this severe appearance shift is not as well represented by the span of the reference basis, and benefiting from reinforcement of low-variance structure. However, summing relies on viewpoint consistency across references, with performance degrading when viewpoints differ within a place’s collection or where outlier effects such as light refraction are present, as in the third example. (Retrieved images for Summed & QR-FullVP show a randomly sampled image from the matched place’s reference collection).
Fig. 9: Retrieval comparison on Pitts250k-Test using Eigenplaces. Left shows retrieval outcomes for reference pooling and QR-FullVP, with green indicating correct and red incorrect top-1 matches. The difference map (center) highlights where QR-FullVP succeeds over pooling (green), the reverse (red), or both agree (grey). QR-FullVP outperforms pooling, using complementary viewpoint information, and qualitative examples suggest that QR-FullVP improves disambiguation, retrieving places closer to the true location. (Retrieved images for QR-FullVP show a randomly sampled image from the matched place’s reference collection).
Fig. 10: Recall@1 versus descriptor size. Our QR-based approach using smaller descriptor sizes often outperforms other multi-reference approaches at maximum size, offering optimization with map memory. Note: for each plot the y-axis is scaled respectively for clear visualization.
Fig. 11: Change in Recall@1 against pooling ( with the same descriptor size ) using SVD decomposition instead of QR. At full rank (top rows), the performance is equivalent to QR-FullVP.
Fig. 12: Average cumulative variance of SVD-derived principal components for reference representations across the datasets. Nordland and Oxford RobotCar exclude Fall and Sun conditions, respectively.
| Method | Dim | Approach | Extraction Time (ms/query) | SotonMV (300 Query, 63872 Ref. Images) | Pitts250k Test (1000 Query, 20988 Ref. Images) | ||||||
| Match Time (ms/query) | Total Map Time (s) | Map Mem. (GB) | R@1 | Match Time (ms/query) | Total Map Time (s) | Map Mem. (GB) | R@1 | ||||
| CosPlace | 2048 | Pooling | 5.90 | 0.43 | - | 0.523 | 34.2 | 0.15 | - | 0.172 | 74.2 |
| CosPlace | 2048 | QR-FullVP | 5.57 | 1.41 | 3.22 | 0.523 | 43.7 | 0.48 | 0.88 | 0.172 | 82.7 |
| CosPlace | 2048 | SVD (k-1) | 4.78 | 1.20 | 9.25 | 0.392 | 36.9 | 0.39 | 2.50 | 0.143 | 83.5 |
| CosPlace | 256 | Pooling | 6.21 | 0.12 | - | 0.0654 | 32.7 | 0.05 | - | 0.0215 | 69.1 |
| CosPlace | 256 | QR-FullVP | 5.61 | 0.26 | 1.66 | 0.0654 | 42.3 | 0.11 | 0.45 | 0.0215 | 81.9 |
TABLE XIV: Computational overhead of conventional VPR vs QR and SVD-based approach using an Nvidia A100 GPU with a batch size of 1. QR uses all ( ) references for the subspace while SVD truncates to . Note that matching and map construction have asymptotic complexity across approaches, however, measured differences reflect our implementation choices and kernel behavior, with pooling executed as a matrix–vector multiplication, subspace methods using einsum-based projections with reductions, map construction performed via full per-place decompositions and explicit synchronizations, affecting the practical runtime.
Fig. 13: Match and map construction latency for pooling, QR-FullVP, and SVD (k-1) evaluated on an Apple M4 CPU using SciPy linear algebra with synthetic descriptors. Queries are processed sequentially (batch size 1) with single-threaded BLAS, and all approaches use identical matrix-vector multiplication for matching, differing only in the post-multiplication aggregation. Map construction is performed per place via QR or truncated SVD. Results are reported as median latency over 300 queries across sweeps in descriptor dimension, number of places, and references per place, which, when non-swept are fixed to 512, 500, and 4 respectively.
Fig. 14: Evaluation of orientation estimates with SotonMV. ( Left ) Distribution of absolute angular errors. ( Right ) Predicted vs ground-truth headings.
| Methods | EigenPlaces (2048D) | CosPlace (2048D) | MixVPR (4096D) | |||||||||||||||||||||||||||||||||
| Queries | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | Fall | Spring | Summer | Winter | ||||||||||||||||||||||||
| References | Sp+Su | Sp+Wi | Su+Wi | Fa+Su | Fa+Wi | Su+Wi | Fa+Sp | Fa+Wi | Sp+Wi | Fa+Sp | Fa+Su | Sp+Su | Sp+Su | Sp+Wi | Su+Wi | Fa+Su | Fa+Wi | Su+Wi | Fa+Sp | Fa+Wi | Sp+Wi | Fa+Sp | Fa+Su | Sp+Su | Sp+Su | Sp+Wi | Su+Wi | Fa+Su | Fa+Wi | Su+Wi | Fa+Sp | Fa+Wi | Sp+Wi | Fa+Sp | Fa+Su | Sp+Su |
| Pooling | 96.4 | 80.7 | 94.4 | 91.4 | 91.4 | 87.2 | 93.6 | 93.3 | 73.7 | 69.1 | 67.3 | 69.5 | 95.1 | 76.8 | 93.0 | 88.4 | 89.0 | 85.0 | 92.1 | 91.2 | 68.7 | 69.8 | 61.7 | 69.8 | 97.7 | 88.1 | 95.8 | 97.0 | 97.6 | 95.0 | 96.4 | 95.9 | 83.3 | 90.7 | 85.4 | 91.4 |
| dMat. Avg. | 95.9 | 76.2 | 90.7 | 90.0 | 91.8 | 89.1 | 91.1 | 87.5 | 68.7 | 76.6 | 66.9 | 75.8 | 92.7 | 69.7 | 83.6 | 87.3 | 86.2 | 83.6 | 87.2 | 80.2 | 62.7 | 73.4 | 61.1 | 71.6 | 97.6 | 90.1 | 96.6 | 96.2 | 98.1 | 96.6 | 95.3 | 94.8 | 85.2 | 93.2 | 84.2 | 92.9 |
| LogSumExp | 97.0 | 81.7 | 95.1 | 90.9 | 94.1 | 90.5 | 93.5 | 93.5 | 74.8 | 74.8 | 67.6 | 74.3 | 95.2 | 77.6 | 93.5 | 88.7 | 90.4 | 87.0 | 91.6 | 91.8 | 69.3 | 73.0 | 62.3 | 73.1 | 98.1 | 89.9 | 96.6 | 96.7 | 98.3 | 96.6 | 96.2 | 95.9 | 84.9 | 93.3 | 85.2 | 93.4 |
| Sum Descriptors | 97.8 | 80.4 | 95.4 | 91.5 | 95.8 | 93.9 | 93.3 | 92.3 | 73.2 | 75.2 | 67.6 | 75.0 | 96.3 | 75.3 | 91.5 | 88.7 | 92.6 | 90.7 | 91.4 | 87.7 | 68.2 | 72.4 | 61.5 | 71.8 | 98.6 | 90.9 | 97.7 | 97.3 | 98.5 | 97.7 | 96.5 | 96.1 | 86.3 | 92.7 | 86.4 | 92.9 |
TABLE XV: Recall@1 with Nordland retrieval using pairwise reference-season combinations for place representations.
| Methods | MegaLoc (8448D) | CricaVPR (10752D) | BoQ (12288D) | SALAD (8448D) | ||||||||||||||||||||||||||||||||||||
| Queries | Sun | Overcast | Night | Snow | ||||||||||||||||||||||||||||||||||||
| References | Du+Ra | Du+Ov | Du+Ni | Du+Sn | Ra+Ov | Ra+Ni | Ra+Sn | Ov+Ni | Ov+Sn | Ni+Sn | Su+Du | Su+Ra | Su+Ni | Su+Sn | Du+Ra | Du+Ni | Du+Sn | Ra+Ni | Ra+Sn | Ni+Sn | Su+Du | Su+Ra | Su+Ov | Su+Sn | Du+Ra | Du+Ov | Du+Sn | Ra+Ov | Ra+Sn | Ov+Sn | Su+Du | Su+Ra | Su+Ov | Su+Ni | Du+Ra | Du+Ov | Du+Ni | Ra+Ov | Ra+Ni | Ov+Ni |
| Pooling | 93.1 | 95.8 | 73.2 | 88.8 | 97.0 | 93.6 | 94.3 | 95.4 | 96.4 | 89.4 | 96.6 | 98.2 | 97.2 | 97.8 | 95.5 | 81.0 | 94.0 | 96.3 | 97.9 | 95.1 | 83.7 | 91.4 | 91.3 | 90.5 | 82.8 | 85.2 | 84.3 | 92.1 | 90.2 | 91.2 | 88.3 | 90.4 | 92.5 | 89.6 | 87.1 | 91.1 | 78.2 | 91.8 | 88.0 | 91.4 |
| dMat. Avg. | 91.5 | 93.6 | 75.6 | 87.8 | 97.4 | 93.1 | 95.5 | 95.2 | 96.0 | 90.2 | 94.9 | 98.1 | 97.4 | 98.1 | 93.1 | 84.0 | 90.9 | 96.4 | 98.0 | 95.6 | 88.7 | 91.8 | 92.7 | 92.5 | 89.3 | 88.7 | 88.5 | 92.9 | 92.5 | 93.0 | 86.2 | 90.5 | 92.3 | 89.2 | 86.0 | 87.8 | 79.3 | 91.4 | 88.5 | 90.3 |
| LogSumExp | 93.3 | 96.0 | 76.7 | 89.7 | 97.7 | 94.0 | 95.7 | 95.8 | 96.7 | 90.4 | 96.7 | 98.3 | 97.4 | 98.0 | 95.7 | 83.5 | 92.7 | 97.0 | 98.1 | 95.6 | 87.2 | 92.4 | 92.9 | 92.5 | 87.0 | 88.1 | 87.4 | 93.5 | 92.5 | 93.2 | 89.3 | 91.0 | 92.9 | 90.8 | 88.8 | 91.9 | 80.4 | 92.2 | 89.4 | 91.5 |
| Sum Descriptors | 93.2 | 94.9 | 77.8 | 89.1 | 97.7 | 94.7 | 96.4 | 96.1 | 96.4 | 91.4 | 96.8 | 98.5 | 97.9 | 98.9 | 95.6 | 87.0 | 93.4 | 97.2 | 98.7 | 96.9 | 89.7 | 92.5 | 93.1 | 93.5 | 90.0 | 90.3 | 90.1 | 93.7 | 92.8 | 93.7 | 89.4 | 91.4 | 93.0 | 90.5 | 88.5 | 90.8 | 82.0 | 92.6 | 90.5 | 91.5 |
TABLE XVI: Recall@1 with Oxford Robot Car retrieval using pairwise reference-weather combinations for place representations.
TABLE XVII: Recall@1 comparison of our QR approach, creating one place representation (FullVP) vs multiple representations using pairwise adjacent viewpoints (2VP), on SotonMV and Pitts250k.
TABLE XVIII: Recall@1 using query images aligned with reference map headings. Despite the additional non-overlapping viewpoint information, our approach suffers little to no degradation.
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