Scalable Fiducial Tag Localization on a 3D Prior Map
via Graph-Theoretic Global Tag-Map Registration
Kenji Koide1 , Shuji Oishi1 , Masashi Yokozuka1 , and Atsuhiko Banno1
Abstract— This paper presents an accurate and scalable
method for fiducial tag localization on a 3D prior environmental
map. The proposed method comprises three steps: 1) visual
odometry-based landmark SLAM for estimating the relative
poses between fiducial tags, 2) geometrical matching-based
global tag-map registration via maximum clique finding, and3) tag pose refinement based on direct camera-map alignment
with normalized information distance. Through simulationbased evaluations, the proposed method achieved a 98 % global
tag-map registration success rate and an average tag pose
estimation accuracy of a few centimeters. Experimental results
in a real environment demonstrated that it enables to localize
over 110 fiducial tags placed in an environment in 25 minutes
for data recording and post-processing.

I. I NTRODUCTION
In recent years, map-based visual localization methods
have been actively studied and widely used for autonomous
navigation systems [1], [2] and user interaction applications(e.g., augmented reality [3]). These methods employing
precise 3D maps enable accurate localization and navigation
in a large variety of environments with affordable equipment.
These visual localization methods are, however, still errorprone in feature-less and dynamic environments, and it issometimes necessary to rely on visual fiducial tags [4], [5]for initialization and fail-safe. Deploying a number of fiducial
tags in the environment and combining them with visual
localization methods allows us to build a robust and accurate
localization and navigation system [6], [7], [8].
Deploying many fiducial tags on a 3D prior map is,
however, sometimes difficult and tedious. Because the tag
localization accuracy directly affects the navigation accuracy,
we need to precisely determine the tag positions as accurate
as possible. Furthermore, we need to place many fiducial tags
(several hundreds, possibly) to cover the entire environment.
However, fiducial tag positions on a prior map are often
measured by hand in many works, which results in large
human effort and inaccurate localization.
In this work, we propose an automatic method for fiducial
tag localization on a 3D prior map. The proposed method
enables to accurately determine the poses of many fiducial
tags on a 3D prior map in a short time (e.g., more than 100
tags in less than 25 minutes) as a pre-installation process
of automatic navigation and user interaction systems. We
consider utilizing the precisely localized fiducial tags makes*This work was supported in part by a project commissioned by the New
Energy and Industrial Technology Development Organization (NEDO).
1 All the authors are with the Department of Information Technology
and Human Factors, the National Institute of Advanced Industrial Science and Technology, Umezono 1-1-1, Tsukuba, 3050061, Ibaraki, Japan,

k.koide@aist.go.jp

Fig. 1: With the proposed fiducial tag localization method,
we aim to make it easy to develop a system based on robust
vision-based localization using precisely localized tags on a
precise 3D environmental map.

it easy to build a system based on vision-based localization
like that shown in Fig. 1.
The proposed method comprises three steps: 1) We firstestimate the relative poses between fiducial tags via visual
inertial odometry (VIO)-based landmark pose graph SLAM.
We observe each fiducial tag with an agile camera andconstruct a pose graph in which fiducial tag poses arebridged by VIO trajectory edges. 2) We then roughly alignthe fiducial tags with a 3D prior map (i.e., global tag-map
registration). Inspired by the recent graph-theoretic global
registration methods [9], [10], [11], we propose a tag-map
matching method based on robust tag-plane correspondence
estimation via maximum clique finding. 3) Finally, we refine
the estimated tag poses by directly aligning agile camera
images with the prior map using normalized information
distance (NID), a mutual-information-based cross-modal distance metric.
The main contribution of this work is three-fold:
1) We propose an accurate and scalable fiducial tag
localization method that enables deploying a massive
amount of tags on a 3D prior map in a short time.
2) To robustly perform global tag-map registration, agraph-theoretic tag-plane correspondence estimation
method is proposed.
3) We show that the combination of NID-based directcamera-map alignment and maximum clique finding-1. Tag relative pose estimation

2. Global tag-map registration

3. Tag pose refinement

Landmark pose graph SLAM
based on VIO and fiducial tags

Establishing tag plane correspondences
via maximum clique finding

NID-based direct camera-map alignment
and joint factor graph optimization

Fig. 2: Processing flow of the proposed system.

based outlier filtering enables to further improve thefiducial tag localization accuracy.
II. R ELATED WORK
There have been proposed many monocular camera localization methods in a 3D prior map for vision-basednavigation. Caselitz et al. reconstructed the surrounding
environment from camera images using a visual SLAM
technique and estimated the camera pose in a given map by
matching reconstructed points with map points [1]. Pascoe
et al., used the NID metric, a mutual-information-based
cross-modal distance metric, to directly align camera images
with the 3D prior map [12]. Ye et al., combined surfelbased map rendering and direct photometric comparison tokeep tracking the camera trajectory on a prior map [13].
While these methods enable accurate map-referenced camera
localization and affordable vision-based navigation with asingle camera, they can sometimes be unreliable in featureless and dynamic environments. Several practical systems
thus often combine vision-based camera localization withfiducial tag detection for reliability and for fail-safe [6], [14],[15].
As we can robustly detect fiducial tags on an image,by using a visual odometry technique, their poses withrespect to the visual odometry reference frame can easily
be estimated in the form of the landmark pose graph SLAM
[16], [17]. However, aligning the estimated tag poses witha 3D prior map (i.e., tag-map global registration) is notstraightforward because of the difference of modalities between visually detected fiducial tags and a 3D point cloudmap. The modality difference makes it difficult to apply
image-to-image matching methods [18], [19] nor geometrybased global registration methods [9], [20] to estimate thetransformation between tag and map reference frames.
If a 3D prior map is recorded in an ordered point cloudformat (e.g., PTX format), it would be possible to generate
images from points and perform visual image matching(e.g., [21]). However, many 3D map datasets provide only
unordered point clouds that make it difficult to generate
images with good quality resulting in deteriorated accuracyof visual image matching.
The proposed method robustly determines the tag-map
transformation across different modalities by combining
geometry-based tag-plane correspondence hypothesis mak-ing and graph-theoretic outlier hypothesis rejection. While
the geometrical hypothesis making yields many false correspondences, the graph-theoretic algorithm robustly filtersout wrong hypotheses and finds the best subset of correspondence hypotheses that gives the best explanation for thetag placement in the map.
III. M ETHODOLOGY
Fig. 2 shows an overview of the proposed method. In the
tag relative pose estimation step, we observe each fiducial tag
using an agile camera and estimate the relative poses between
fiducial tags in the form of the landmark visual SLAM.
In the following step, we roughly align fiducial tags witha 3D prior map by establishing tag-plane correspondences
via maximum clique finding. We then refine tag and camera
poses by directly aligning camera images with the map.
A. Tag Relative Pose Estimation based on Landmark Pose
Graph SLAM
In this step, we use an agile camera to observe fiducial tags
placed in an environment, and reconstruct the relative poses
between tags with a standard landmark pose graph SLAM
approach [22]. We estimate the camera ego-motion using
a VIO algorithm (e.g., VINS-Mono [23]) while detecting
fiducial tags on images [24]. Let TW C (t) be the camerai(t) be the pose
pose estimated by VIO at time t, and TCT
of a detected fiducial tag with tag ID = i. We estimate thecamera pose at every time step TeW C (t) and fiducial tag posesi
TeW
T by minimizing the following objective function thatcombines odometry factors eodom and tag observation factors
etag :
eslam = eodom + etag ,
(1)
N
−1


X
eodom =
k log TeW C (t, t + 1)−1 TW C (t, t + 1) k2 ,t=1

(2)
etag =

N X
M
X
t=1



i
i
−1
k log TeW C (t)−1 TeW
k2 , (3)
M TCM (t)iwhere TW C (t, t + 1) = TW C (t)−1 TW C (t) is the relative
camera pose between t and t + 1, and log is the SE3 logarithmic map. Here, we intentionally decouple VIO estimationand tag pose estimation and fuse them on a pose graphso that we can easily change the VIO algorithm depending

erot( TiWM )-1 TkWM
pj

ti

tk
pl
etrans(a) Planes in a map (left) and fiducial tag poses (right)

Fig. 3: Tag-plane correspondence consistency.

on the use scenario (e.g., using another VIO running on asmartphone [25] instead of VINS-Mono).

(b) Consistency graph (tag-plane correspondence hypotheses)

B. Tag-Map Global Registration via Graph-Theoretic TagPlane Correspondence Establishment
Given the estimated relative poses between fiducial tags,
we roughly align the reference frame of the tags (i.e.,
VIO origin) with the map reference frame (i.e., tag-map
global registration). The challenge here is that we need todeal with the difference of modalities between the sparse
point cloud map and visually detected fiducial tags. Due tothe difference of modalities, traditional vision-based image
matching methods [18], [19] are not applicable.
In this work, we assume that most of the fiducial tags
are placed on a plane in the environment, and solve theglobal registration problem by establishing tag-plane correspondences. This assumption can naturally be held inmany practical use scenarios because most fiducial tags are
required to be placed on a flat surface for accurate detection
and localization [24].
Inspired by the recent success of graph-theoretic approaches for global registration [9], [10], [11], we robustly
estimate tag-plane correspondences via maximum clique
finding. We first construct a consistency graph, in which
vertices represent a hypothesis of tag-plane correspondence,and edges represent the consistency between two tag-plane
correspondence hypotheses. By finding the largest subsetof hypotheses that are all mutually consistent (i.e., themaximum clique in the consistency graph), we can robustly
filter out outlier correspondences and determine a set of tagplane correspondences that gives the best explanation for thetag placement in the prior map.
To construct a consistency graph, we first extract planes
from the map point cloud using region growing segmentation[26] and then list all possible tag-plane correspondences. We
evaluate the geometrical consistency of every combination ofcorrespondence hypotheses as illustrated in Fig. 3. Let hij =(ti , pj ) be a hypothesis that a fiducial tag ti corresponds
to a plane pj in the map and consider its consistency withanother hypothesis hkl = (tk , pl ). We transform the pose ofti such that its normal becomes aligned with the normal of
pj . Given the relative pose between ti and tk , we shift androtate ti on the plane pj such that the distance between tk
and pl is minimized. If the distance between tk and pl issmaller than thtrans and the angle error of their normals is
smaller than throt (e.g., 0.4 m and 10°), we consider hij and(c) Maximum clique in the consistency graphFig. 4: Tag-plane correspondence estimation via maximum
clique finding.

hkl are mutually consistent. For the algorithmic detail of theconsistency check procedure, see the appendix.
With all combinations of tag-plane correspondence hypotheses that pass the mutual geometrical consistency check,we construct a consistency graph and find the maximum
clique using the parallel heuristic maximum clique finding
algorithm [27].
Fig. 4 shows an example of tag-plane correspondence
estimation results. For all possible combinations of planes
and tags, we evaluated the correspondence consistency andconstructed a consistency graph (Fig. 4 (b)) and then foundthe maximum clique (Fig. 4 (c)). While the consistency graphcontained a massive amount of tag-plane correspondence
hypotheses (429,735 hypothesis pairs), the maximum clique(56 tag-plane correspondences) was efficiently found in 92
msec.
Given the tag-plane correspondences, we estimate thetransformation between the tag and map reference frames
by minimizing the symmetric point-to-normal ICP distance[28] between corresponding tags and planes.
C. Estimation Refinement via Information-theoretic Direct
Camera-Map Alignment
We then refine the tag and camera pose estimates bydirectly aligning each camera image with the global map
using the NID [12], a mutual-information-based cross-modal
distance measure. We insert the camera poses aligned withthe map into the landmark pose graph as prior factors, andre-optimize the graph to improve the camera and tag pose
estimates.
Let P be a map point cloud, Ir be a camera image, and
TeW C (t) be the camera pose with respect to the map reference
frame. Given an initial estimate of TeW C (t), we first remove

points from P that should not be visible from the current
viewpoint using direct visibility assessment [29], and thenestimate TeW C (t) by minimizing the NID metric between P
and Ir using the BFGS algorithm. The NID is defined asfollows:
H(Ir , Is ) − MI(Ir ; Is ),H(Ir , Is )MI(Ir ; Is ) = H(Ir ) + H(Is ) − H(Ir , Is ),NID(Ir , Is ) =

(4)
(5)

where Is is a map image created by projecting P on theimage space of Ir , H(Ir , Is ), H(Ir ), H(Is ) are the joint andmarginal entropies of Ir and Is , and MI(Ir , Is ) is the mutual
information between Ir and Is . Because this metric does
not directly compare pixel and point colors but measureco-occurrence of them, it enables to measure the distance
between data across different modalities. Following [12], we
use B-spline based weighted histogram voting to make Eq.
4 differentiable.
The NID enables to accurately determine the camera
pose with respect to a map point cloud. It is, however,very sensitive to the initial guess and often gets corrupted.
Because the NID is a dimensionless quantity, it is not easy
to remove corrupted results with simple thresholding of the
NID value.
To robustly filter out corrupted camera-map alignment
results, we again use a graph-theoretic approach to find the
maximum mutually consistent subset of them. Let ht =(TeW C (t), TbW C (t)) be a pair of initial and refined camera
poses. To determine the consistency between ht and hk , wecalculate the camera pose displacements they are declaring:−1b∆TbW C (t) = TeW
C (t)TW C (t),∆TbW C (t, k) = ∆TbW C (t)−1 ∆TbW C (k).

(6)i(b) Outlier filtering result

Fig. 5: Camera-map alignment and outlier filtering results.
Red: initial camera poses, Blue: refined camera poses.

Fig. 6: Fiducial tags randomly placed on the Replica dataset.

(7)

If the translational and rotational errors of ∆TbW C (t, k)
are smaller than threshold values (e.g., 0.5 m and 5°), we
consider ht and hk are mutually consistent. We constructa consistency graph for all combinations of camera-map
alignment results and find the maximum clique to filter out
corrupted results (i.e., outliers).
Fig. 5 (a) shows an example of NID-based camera-map
alignment results. Red frustums show the initial camera posesof frames where the BFGS optimization converges whileblue ones show estimated camera poses. We can see that the
NID-based optimization sometimes gets corrupted. Fig. 5 (b)shows a result of outlier filtering, in which corrupted cameramap alignment results are filtered out and only mutuallyconsistent results remain.
We insert the refined camera poses in the factor graphcreated in the tag relative pose estimation as pose priorfactors, and re-optimize tag and camera poses with all theconstraints:
erefine = eodom + etag + eNID ,NXeNID =
k log TeW C (t)−1 TbW C (t) k2 .

(a) Camera alignment results

(8)
(9)

IV. E XPERIMENTS
A. Evaluation in a Simulated Environment
1) Global registration evaluation: To evaluate the proposed method, we used apartment 0 model in the Replica
dataset [30], [31]. We generated 50 camera trajectories byrandomly sampling waypoints in the map and interpolatingthem using SE3 B-spline interpolation. Along with camera
images, we synthesized IMU data using [32]. For eachtrajectory, we randomly placed 200 fiducial tags on planes in
the map and estimated the poses of fiducial tags, which wereobserved by the camera more than once, using the proposed
method.
As a baseline, we compared the proposed method withfeature-based global registration methods. We first ran
colmap [21] on the camera image stream to obtain a dense
3D point cloud of the environment. We then extracted FPFH
features [33] respectively from the reconstructed point cloud
TABLE I: Global registration success rate
MethodRANSAC [20]Teaser [9]Proposed

Success rate

26% (13 / 50)

70% (35 / 50)

98% (49 / 50)

(a) Replica model(b) Reconstructed modelFig. 7: Prior environmental map and reconstructed point
cloud for apartment 0 model.

and the 3D prior model and estimated the transformation
between them using RANSAC [20] and Teaser [9].
We first evaluated the global registration success rate ofeach method. If the translational and rotational errors of a
global registration result are smaller than threshold values(1.0 m and 15°), we consider the registration is succeeded.
Table I shows the success rate of each global registration
method. We can see that, even with Teaser [9], a stateof-the-art transformation estimation algorithm, the global
registration failed for 30 % of the sequences. Fig. 7 shows
the 3D prior map model and the reconstructed model. While
the reconstructed model well captures the overall shape ofthe environment, the detailed shapes and densities of points
are largely different from those of the prior map model. We
consider that these differences make it difficult to obtainconsistent features between the reconstructed and the priormodels, which results in the global registration failures.
The proposed tag-plane matching method successfully
estimated the tag-map transformation except for a sequence
where fiducial tags were placed very symmetrically andwrong tag-plane correspondences were given via maximum
clique finding.
2) Fiducial tag localization accuracy: We calculated tag
localization errors for sequences where global registration
succeeded. For RANSAC and Teaser, assuming the perfecttag localization accuracy is given on the reconstructed model,
we calculated transformation errors of point cloud registration results as fiducial tag localization errors.
Table II summarizes the fiducial tag localization accuracy of each method. We can see that Teaser exhibited
better localization errors (0.180 m and 2.807°) than that of
RANSAC (0.416 m and 7.847°) thanks to its robust feature
matching mechanism. The proposed method showed the best
localization accuracy among compared methods (0.110 m
and 1.870°) owing to the robust tag-plane matching. With
the refinement step, the localization accuracy was further
improved, and we achieved an average translation error of afew centimeters (0.039 m and 1.021°).
3) Robustness to outliers: To evaluate the robustness ofthe proposed method to outlier fiducial tags that are notlying on a plane, we evaluated the global registration successrate while changing the number of inlier tags. For each
inlier tag rate setting Rin , we generated 100Rin fiducial

Fig. 8: Fiducial tag inlier rate vs global registration successrate. The proposed method is robust to outlier tags that do
not lie on a plane.

tags on randomly selected planes in the environment and100(1 − Rin ) tags with random poses, and repeated random
tag placement and global registration for 100 times. To see
how the global registration success rate changes dependingon tag relative pose estimation errors, we added two levels of
random pose noise (σt = 0.05m / σr = 1.0°, and σt = 0.2m
/ σr = 4.0°) to the tag poses.
Fig. 8 shows a plot of global registration success rate vsinlier rate. We can see that the proposed method is robust
to outlier tags and achieved a success rate of over 90%
with 60% outlier tags under a low-level noise (0.05 m and1.0°). Even under larger tag pose noise (0.2 m and 4.0°), theproposed method achieved a success rate about 75% with
60% outlier tags.
B. Evaluation in a real environment
To demonstrate that the proposed method enables robust
fiducial tag localization on a 3D prior map with a small
effort, we placed 117 fiducial tags in the environment shownin Fig. 9. The red circles in the figure show the positionsof placed fiducial tags. Note that only tags that are visible
in the figure are drawn just for visualization. We recorded
two environmental map point clouds with and without fiducial tags using a 3D LiDAR (FARO Focus). We manuallyannotated fiducial tag positions on the environmental map
to obtain the ground-truth tag poses. We then estimated thetag poses with the proposed method using the environmental
map without tags.
For VIO, we recorded a stream of monocular images
and IMU measurements using a MYNTEYE camera. Eachfiducial tag was observed by the agile camera at least once
during the recording. The duration of the image stream wasabout 970 s.
Table III summarizes the processing time of each step inthe proposed method. The tag relative pose estimation step
was performed on the fly while recording the image stream.
The global tag-map registration step took only about 1.5 s
thanks to the efficient maximum clique finding algorithm.
The refinement step took about 381.3 s in total, and the NIDbased camera pose estimation was the most computationallydemanding process in this step (379.6 s). Note that thecurrent implementation uses only a CPU, and the processing
time of the NID optimization can be improved by 10 to
50 times faster by using a GPU implementation [2], [12],resulting in reducing the total processing time to about 10
s. Furthermore, because we can independently perform theTABLE II: Fiducial tag localization errors
MethodRANSAC [20]Teaser [9]Translational error [m]Rotational error [°]0.416 ± 0.214
7.847 ± 4.081

0.180 ± 0.190
2.807 ± 3.042

Proposed
w/o refinement
w/ refinement
0.110 ± 0.078
1.870 ± 1.629

0.039 ± 0.060
1.021 ± 1.629

TABLE III: Processing time
Step

Process

Time [s]Tag pose estimation

Visual inertial odometry
Fiducial tag detection
Pose graph optimization

on-the-fly

Consistency graph creation
Maximum clique finding
Transformation optimization

1.395
0.092
0.004

Total

1.491

NID camera alignment
Outlier filtering
Pose graph optimization

379.6
0.072
1.614

Total

381.3

Global registration

Estimation refinement

Fig. 9: Experimental environment. The red circles indicate
the positions of fiducial tags. 117 fiducial tags were placedin the environment.

align the fiducial tags with a 3D prior map using a graphtheoretic tag-plane correspondence estimation. We refine theestimated tag and camera poses by directly aligning camera
images with the environmental map using an informationtheoretic metric. Through simulation-based experiments, theproposed method achieved a global registration success rateof 98% and tag estimation accuracy of a few centimeters.
The real experiment demonstrated that the proposed method
can accurately localize over 100 fiducial tags on a prior map
in 16 minutes for data recording and 6 minutes for postprocessing.
A PPENDIX
Fig. 10: Estimation result. RGB thick lines: estimated tag
poses, Green thin line: camera trajectory, Red frustums:
camera poses where the NID optimization converged, Bluefrustums: NID-based camera-map alignment results.

image alignment frame-by-frame, it can easily be accelerated
by using, e.g., cloud computing.
Fig. 10 shows the estimation result. The thick RGB lines
indicate the estimated fiducial tag poses, and the thin green
line shows the estimated camera trajectory. The averagetranslational and rotational errors of the estimated fiducial
tag poses were respectively 0.019 ± 0.014 m and 2.382 ±4.093 °. This result would be sufficiently accurate for therequirement for vision-based navigation systems.
V. C ONCLUSIONS
We have proposed an accurate and scalable method forfiducial tag localization on a 3D prior environmental map.
We first estimate the relative poses between fiducial tags
using VIO-based landmark graph SLAM, and then roughly

A. Tag-Plane Correspondence Consistency Check
Alg. 1 describes the algorithm to determine the consistencyof two tag-plane correspondence hypotheses. n∗ , R∗ , p∗ are
the normal, rotation, and translation of a tag or plane,
respectively. l∗ is the length of a plane along XYZ axes
(Z = normal). Lines 2 and 3 swap hij and hkl if the normalof pj is almost vertical to avoid indeterminacy of the tagplane rotation (Because we can assume that both ti and pj
are gravity-aligned, the tag-plane rotation can be determinedfrom only their normals as long as the plane normal is
not vertical). Lines 4-7 calculate the transformation thattransforms ti such that its normal is aligned with the normalof pj . Note that we consider only rotation along the gravity
direction assuming tags and planes are gravity-aligned. Line
8 checks if the angle error between the normals of pl androtated tk . If it is larger than a threshold, we consider hij isinconsistent with hkl . Lines 10-13 calculate the translation tominimize the distance between tk and pl such that ti remains
on pj . Then, if the distance between transformed tk and plis smaller than a threshold, we consider hij and hkl aremutually consistent.

Algorithm 1 Tag-plane correspondence consistency check
1: function CONSISTENCY CHECK (hij , hkl )2:
if nj · [0, 0, 1]T > 1 −  then
3:
4:
5:

SWAP(hij , hkl )XY
ni = nti ◦ [1, 1, 0]TTnXY
j = npj ◦ [1, 1, 0]

XY
Rji = ALIGN VECTORS(nXY
i , nj )7:
pji = ppj − Rji pti
8:
if A NGLE(Rji ntk , npl ) > throt then9:
return False10:
plk = ppl − (Rji ptk + pji )11:
pjk = Rp−1
plk
j
12:
p0jk = C LAMP(pjk , −lpj /2, lpj /2)
13:
p0tk = Rji ptk + pji + Rpj p0jk
14:
if D ISTANCE(p0tk , pl ) > thtrans then15:
return False
16:
else
17:
return True
18: function ALIGN VECTORS (a, b)
19:v =a×b20:s = kvk
21:
c=a·b
22:
if s <  then23:
return I
24:
S = skew(v)225:
return I + S + 1−c
s2 S

6:

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