Spectral Geometric Veriﬁcation Re-Ranking Point Cloud Retrieval for Metric Localization Kavisha Vidanapathirana12 Peyman Moghadam12 Sridha Sridharan2 Clinton Fookes2

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Spectral Geometric Veriﬁcation: Re-Ranking Point Cloud Retrieval for

Metric Localization

Kavisha Vidanapathirana1,2, Peyman Moghadam1,2, Sridha Sridharan2, Clinton Fookes2

Abstract— In large-scale metric localization, an incorrect

result during retrieval will lead to an incorrect pose estimate or

loop closure. Re-ranking methods propose to take into account

all the top retrieval candidates and re-order them to increase

the likelihood of the top candidate being correct. However, state-

of-the-art re-ranking methods are inefﬁcient when re-ranking

many potential candidates due to their need for resource

intensive point cloud registration between the query and each

candidate. In this work, we propose an efﬁcient spectral method

for geometric veriﬁcation (named SpectralGV) that does not

require registration. We demonstrate how the optimal inter-

cluster score of the correspondence compatibility graph of two

point clouds represents a robust ﬁtness score measuring their

spatial consistency. This score takes into account the subtle

geometric differences between structurally similar point clouds

and therefore can be used to identify the correct candidate

among potential matches retrieved by global similarity search.

SpectralGV is deterministic, robust to outlier correspondences,

and can be computed in parallel for all potential candidates.

We conduct extensive experiments on 5 large-scale datasets to

demonstrate that SpectralGV outperforms other state-of-the-

art re-ranking methods and show that it consistently improves

the recall and pose estimation of 3 state-of-the-art metric lo-

calization architectures while having a negligible effect on their

runtime. The open-source implementation and trained models

are available at: https://github.com/csiro-robotics/SpectralGV.

I. INTRODUCTION

Accurate 6 Degrees of Freedom (DoF) metric localization

is an essential component in many applications in em-

bodied intelligence. For an embodied agent (mobile robot,

autonomous car etc.) to autonomously operate in any en-

vironment, it must ﬁrst be able to estimate its pose. The

task of robust global localization in large-scale environments

remains an open problem as current methods struggle to

differentiate between structurally similar places with subtle

differences and fail to handle degenerate scenes which lack

distinct geometric structure. When scaling this problem to

city-scale environments (or larger), this task is made efﬁcient

through a hierarchical two-step formulation. This includes

the retrieval-based place recognition step, which estimates a

set of coarse place candidates, and a pose estimation step

which estimates the alignment between the query and the

top place candidate to obtain the 6DoF pose.

In the point cloud domain, the tasks of place recognition

and 6DoF alignment (i.e., registration) have been explored

largely in isolation [1]–[3]. Recently, several methods have

1Robotics and Autonomous Systems Group, DATA61, CSIRO, Australia.

E-mails: firstname.lastname @data61.csiro.au

2Signal Processing, AI and Vision Technologies (SAIVT), Queens-

land University of Technology (QUT), Brisbane, Australia. E-mails:

{s.sridharan, c.fookes}@qut.edu.au

combined the two tasks to offer a complete solution for

metric localization [4]–[6]. They follow a correspondence-

based approach, where local-features are used to estimate

correspondences between the query point cloud and the top-

candidate returned by global-descriptor matching, and the

pose is obtained using the estimated correspondences. The

top place candidate retrieved from place recognition via

global descriptor matching may not always be correct due

to the challenges outlined above, and an incorrect place

candidate will result in an infeasible pose estimation task.

To address such limitations in retrieval, re-ranking meth-

ods take into consideration many top retrieval candidates

and re-order them such that correct candidates will be

ranked higher. Re-ranking is performed using pre-deﬁned

criteria speciﬁc to each re-ranking method and often involves

utilizing additional information complementary to the global

descriptors. Fig. 1 shows an example scenario where an

incorrect top-1 candidate can be replaced with the correct

candidate using a re-ranking method. Re-ranking has become

popular in other domains of information retrieval [7], [8] but

has limited utility in point cloud retrieval due to current re-

ranking methods either lacking robustness or being inefﬁcient

in handling large-scale outdoor point clouds. While re-

ranking methods used in other domains can be adopted, these

methods are not suited to efﬁciently utilize the precise 3D

geometry information present in point clouds.

In this paper, we ﬁrst demonstrate that geometric-

veriﬁcation is necessary to ensure robust point cloud re-

ranking, but these methods are inefﬁcient due their reliance

on resource intensive point cloud registration. To address

this, we introduce an efﬁcient spectral method for geometric

veriﬁcation based re-ranking, named SpectralGV. Using the

correspondence compatibility graph introduced in Spectral

Matching [9], we demonstrate how the optimal inter-cluster

score of this graph represents a robust conﬁdence score on

the spatial consistency of two point clouds, and utilize it to

formulate registration-free geometric veriﬁcation.

SpectralGV allows integration with any architecture that

extracts both local and global features for a given point cloud,

without modifying the architectures and without further train-

ing of learning-based methods. It is an architecture agnostic

method and shows no bias towards datasets allowing it to

generalize well. We integrate our method with 3 state-of-the-

art architectures and demonstrate improvements in recall and

pose estimation across 5 large-scale datasets in all evaluation

settings. SpectralGV outperforms other re-ranking methods

while being the only geometric veriﬁcation method with sub-

linear time complexity, enabling real-time deployment.

arXiv:2210.04432v2 [cs.CV] 6 Mar 2023

Encode

Pool

Database

1st 2nd

Retrieval

Re-Ranking

Re-ranked result

Retrieved result

Query

Point Cloud

Local Features

Global

Descriptor A

Pose

AQuery Query B

Fig. 1: Overview of our SpectralGV method. Local features are extracted from the query point cloud using an encoder and

then aggregated to form a global descriptor which is used in the ‘Retrieval’ block to ﬁnd the top-k place candidates (k=2

in the diagram). The local features and point cloud are used for re-ranking the retrieved candidates in the ‘Re-Ranking’

module which estimates a matching conﬁdence based on the spatial consistency of point correspondences (black lines).

In this example, retrieved point cloud ‘B’ is more consistent with the query and is therefore ranked higher than ‘A’ after

re-ranking. The 6DoF pose estimate TBis obtained by aligning the query point cloud to the top re-ranked candidate. Point

clouds are coloured based on the t-SNE embeddings of local features to better visualize the point correspondences.

II. RELATED WORK

Point cloud retrieval methods have mainly been proposed

under the two topics of place recognition and metric local-

ization, which we discuss in II-A and II-B respectively. We

review re-ranking methods used in other domains in II-C and

discuss them in relation to our proposal.

A. Place Recognition

Large-scale place recognition is formulated as a retrieval

problem where methods encode point clouds to a compact

global descriptor to be used for querying a database of

previously visited places. Global descriptors can be cate-

gorised as handcrafted [10], [11], hybrid [12], and end-to-

end learning [13]–[17]. While handcrafted methods such as

ScanContext [10] and hybrid methods such as Locus [12]

still act as strong baselines, end-to-end learning methods

have demonstrated superior performance [18], [19]. End-to-

end learning methods deﬁne a neural network to map point

clouds to global descriptors. PointNetVLAD [13] pioneered

the end-to-end trainable global descriptor by combining

PointNet [20] and NetVLAD [21]. Works such as LPD-Net

[14] and MinkLoc3D [15] have addressed the limitations of

PointNetVLAD. Recently, LoGG3D-Net [18] demonstrated

the beneﬁts of using joint constraints on the local and

global embeddings during the training. In this paper, we

demonstrate how the recall of these methods can be improved

by a large margin by our re-ranking method.

B. Metric localization

DH3D [4] pioneered correspondence-based metric local-

ization using LiDAR data by proposing the uniﬁcation of

global place recognition with local 6DoF reﬁnement. They

used a simultaneous detect-and-describe formulation to ex-

tract local features, NetVLAD to generate a global descriptor,

and RANSAC [22] to estimate the 6DoF pose. LCDNet [5]

proposed the use of a differentiable relative pose head based

on Unbalanced Optimal Transport (UOT) [23] to match local

features. EgoNN [6] extended the MinkLoc3D architecture

for the task of metric localization with the addition of

keypoint detection and saliency prediction modules. Global

descriptors formed by GeM [7] pooling were used for

retrieval and RANSAC was used for pose estimation.

Our proposed SpectralGV can be readily integrated into

all the above metric localization methods [4]–[6] as well

as place recognition methods such as [18] which produce

discriminative local features. We demonstrate how this inte-

gration results in an improvement of both recall and pose

estimation for all architectures across all datasets, while

having an insigniﬁcant effect on their runtime.

C. Re-ranking

In many retrieval problems, re-ranking methods take the

initial retrieved candidates and re-order them such that cor-

rect candidates will be ranked higher. These methods can be

categorised as those which use only the global descriptors

and those which use both global and local embeddings. Re-

ranking methods which use only global descriptors can be

classiﬁed under Query Expansion (QE) [7] methods that

use ﬁrst-order neighbour information and methods that use

higher-order neighbour information such as k-reciprocal [24],

[25] and region-diffusion [26]. QE methods take the nearest

neighbours of the query and generate an updated query which

is used to retrieve a new set of candidates. The updated

query is an aggregation of the initial top-candidates (e.g.,

average-QE, alpha-QE [7]). Higher-order methods consider

the neighbours-of-neighbours of the query and are non-

trivial to extend to large-scale scenarios [8]. In this paper,

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SpectralGeometricVerication:Re-RankingPointCloudRetrievalforMetricLocalizationKavishaVidanapathirana1;2,PeymanMoghadam1;2,SridhaSridharan2,ClintonFookes2AbstractInlarge-scalemetriclocalization,anincorrectresultduringretrievalwillleadtoanincorrectposeestimateorloopclosure.Re-rankingmethodsproposeto...

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Spectral Geometric Veriﬁcation Re-Ranking Point Cloud Retrieval for Metric Localization Kavisha Vidanapathirana12 Peyman Moghadam12 Sridha Sridharan2 Clinton Fookes2

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