ARTag, AprilTag and CALTag Fiducial Marker Systems: Comparison in

a Presence of Partial Marker Occlusion and Rotation

Artur Sagitov

, Ksenia Shabalina

, Leysan Sabirova

, Hongbing Li

and Evgeni Magid

Intelligent Robotics Department, Higher School of Information Technology and Information Systems,

Kazan Federal University, Kremlyovskaya str. 35, Kazan, Russian Federation

Department of Instrument Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

Keywords:

Fiducial Marker, ARTag, AprilTag, CALTag, Occlusion, Experimental Comparison.

Abstract:

Fiducial marker systems consist of patterns that are placed in environment and are automatically detected

with a camera using appropriate for the marker detection algorithm. Marker systems are useful for many

modern visual applications such as augmented reality, robot navigation and collaboration, industrial and space

robotics, and human-robot interaction. A variety of applications demands certain quality assurance for marker

properties. Among the most common criteria are resistance to partial occlusion and rotation, sensitivity to

lightning conditions, marker size, false positive and false negative rates. This paper compares three types of

markers for their resistance to partial occlusion in various types of occlusion and resistance to normal, lateral,

and longitudinal rotations. Intensive experimental comparison of tags is presented with analysis. Detection of

markers was performed with a common Web camera. Based on our experimental results, we have selected a

marker system, which should be preferred for real world applications when only simple inexpensive hardware

is available and appearance of rotation and occlusion disturbances are expected in the environment. Our long

term goal is to calibrate humanoid robot manipulators in real-world environment applying a pre-calibrated

camera of the robot, while the presented in this paper results help selecting a most suitable marker system for

further calibration procedures.

1 INTRODUCTION

Fiducial markers, also referred as tags, are placed

in a physical environment to provide object track-

ing, alignment, and identiﬁcation. The application

of marker systems ranges from industrial marker sys-

tems, where markers are designed to label parts in

manufacturing and store certain information e.g ship-

ping data, to systems where markers are used for lo-

calization, e.g augmented reality and others. Exam-

ples of the ﬁrst case are Maxicode marker system,

which is used by the US Postal Service, DataMa-

trix and QR (Quick Response) systems. In turn, for

augmented reality ARToolKit and ARTag marker sys-

tems were integrated into Mars Science Laboratory,

NASA’s Spacecraft 3D smartphone app and other AR

Unity applications. Fiducial markers are also popu-

lar and useful in multiple ﬁelds of robotics. Mark-

ers allow to calibrate cameras and mechanical parts of

robotic systems, which are required for industrial ap-

plications (Klimchik et al., 2016), social human-robot

interaction (Pipe et al., 2014) and humanoids (Khu-

sainov et al., 2015), SLAM (Buyval et al., 2017), res-

cue robotics (Magid and Tsubouchi, 2010), robot col-

laboration (Panov and Yakovlev, 2017), swarm con-

trol (Ronzhin et al., 2016) and other ﬁelds.

Tag design directly depends on its application. For

example, Maxicode, Qr and DataMatrix are appli-

cable for locating on train cars, that allow machin-

ery to automatically identify and route them through

stations; CyberCode has 2D grid of black and white

squares, and could communicate digital information.

Most markers that are used in augmented reality ap-

plications have at least four feature points that help

determining position and orientation of the markers

and cameras (Hirzer, 2008). Typically, these markers

have square edges and four corner points are used to

calculate a position in three-dimensional space.

This paper we brieﬂy overview various ﬁducial

marker systems and focus on comparing ARTag,

AprilTag, and CALTag marker systems in presence

of occlusion. The three selected tags are paired with

182

Sagitov, A., Shabalina, K., Sabirova, L., Li, H. and Magid, E.

ARTag, Apr ilTag and CALTag Fiducial Marker Systems: Comparison in a Presence of Partial Marker Occlusion and Rotation.

DOI: 10.5220/0006478901820191

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 2, pages 182-191

ISBN: Not Available

corresponding error correction methods to recover the

data when some of the bits are incorrectly read (Fiala,

2004). As a comparison benchmark, we use marker

reliability and detection rate in presence of occlusions

of various types and intensity as well as resistance to

normal, lateral, and longitudinal rotations. The ex-

periments were performed with a simple inexpensive

Web camera. Based on our experiments, we con-

cluded that among the three selected marker systems

CALTag system should be preferred for real world

applications when only simple inexpensive hardware

is available and we expect the appearance of rotation

and occlusion disturbances in the environment. As a

global goal, we plan to select the most suitable tag for

camera calibration of the humanoid robot hardware in

real-world environment.

The rest of the paper if organized as follows.

Section 2 describes ARTag, AprilTag, and CALTag

marker systems in details but the details of the under-

lying algorithms and their implementation are out of

scope of this paper due to space limitations. Sections

3 and 4 present experiment design and experimental

results respectively. Finally, we conclude and discuss

future work directions in Section 5.

2 FIDUCIAL MARKERS

Most markers have a common design feature an out-

lining square shape frame with a pattern image in-

side, which encodes information. The square shape

is popular due to four special points (that correspond

to the square corners) detection, which allow cam-

era calibration and marker position calculation. To

reduce light sensitivity, conﬁguration planar marker

systems use monochrome (bitonal) markers (Hirzer,

2008). This way the need to identify shades of grey

is avoided, and a per pixel decision is reduced to a

threshold decision only. In this section, we intro-

duce ARTag, AprilTag and CALTag marker systems.

These markers have two stages of detection: unique

features detection and identiﬁcation (or recognition)

stage (Fiala, 2005b). First stage searches an image

for a unique feature (quadrilateral shapes). The sec-

ond stage validates an interior of the shape to deter-

mine if the feature is a marker or another object. The

markers have different design, detection and recogni-

tion algorithms, which determine their strengths and

weaknesses in different situations. Typical metrics

for marker systems performance evaluation are: oc-

clusion resistance (marker partial or complete overlap

by other objects), inter-marker confusion (probability

of confusion between markers), resistance to lighting

conditions changes, size of the marker (or distance to

Figure 1: ARTag, AprilTag and CALTag markers example.

the marker) (Fiala, 2005a) etc. Figure 1 demonstrates

examples of ARTag, AprilTag and CALTag.

2.1 ARTag

ARTag (Fig. 1, left) is planar marker system, which

was presented by Mark Fiala in 2004 (Fiala, 2004)

and was inspired by ARToolKit - a library in C and

C++ languages, which was created for Augmented

Reality applications in 1999 by Hirokazu Kato and

Mark Billinghurst (Kato and Billinghurst, 1999). AR-

Toolkit marker is a square shape with a black border

and user-deﬁned image inside. The system has a sim-

ple detection and recognition algorithm: the use of

image binarization for detection and mapping of po-

tential markers with a set of marker patterns. If a

marker is successfully mapped, its internal value is

read. However, this system has a number of draw-

backs that include false positive effect (falsely report-

ing the presence of a marker when none is present)

and inter marker confusion (when a marker is de-

tected, but the wrong ID was given, i.e. one marker

was mistaken for another) (Fiala, 2005a).

The ARTag system uses the same concept of

squares with an internal image inside, but unlike AR-

ToolKit, the system uses a digital approach to read

an internal pattern that is a binary code (barcode).

ARTag system contains 2002 individual tags of square

shape, 1001 markers have a white frame and 1001

markers have a black frame with an image (barcode)

inside. Marker system detects tags with edge points

based approach: edge point detector ﬁnds edge pix-

els that form segments, which are then grouped into

quadrilaterals. A marker internal image forms a 6x6

cell grid, which is composed of black and white cells,

each representing 36 bit-values of ”1” and ”0” . First

10 bits of 36 constitute marker ID, remaining 26 bits

are redundant and are used to detect and correct er-

rors and to insure uniqueness of four possible marker

orientations (Fiala, 2005a). ARTag system ensures

fast marker identiﬁcation as it does not require match-

ing its internal marker image with a library of stored

templates, as it was previously implemented in AR-

ToolKit.

ARTag, AprilTag and CALTag Fiducial Marker Systems: Comparison in a Presence of Partial Marker Occlusion and Rotation

183

2.2 AprilTag

AprilTag marker system (Fig. 1, center) was devel-

oped by April Robotics Laboratory at the University

of Michigan (Olson, 2011). AprilTag is applicable for

a wide range of tasks: camera calibration, robotics,

augmented reality etc. It allows to calculate exact po-

sition, orientation and identity of a marker relatively

to a camera. The detection process consists of sev-

eral stages: searching for linear segments, detecting

squares, calculating the position and orientation of the

tag, decoding the barcode.

The detection process consists of several stages:

searching for linear segments, detecting squares, cal-

culating the position and orientation of the tag, decod-

ing the barcode. Directed linear segments search uses

similar to the ARTag approach, and then sequences of

segments are processed to form a square. Square de-

tection applies a recursive 4-level depth search and at

each level, the tree adds one side of the square. At the

identiﬁcation stage the validity of the barcode inside

the discovered marker is veriﬁed. To encode an inter-

nal picture, AprilTag uses a lexicode system charac-

terized by two parameters: number of codeword (in-

ternal pattern) bits and minimal Hamming distance

between any two codes. Lexicode generates codes

for tags, which allows detecting and ﬁxing bits errors.

AprilTag has several marker families that differ in two

parameters: the number of bits to encode and the min-

imal Hamming distance. For example, ”Tag36h11”

means a 36-bit marker (6x6 array) with a minimal

Hamming distance of 11 bits between any two codes;

”Tag16h5” refers to a 16-bit marker (4x4 array) with

a minimal Hamming value of 5 bits between any two

codes.

AprilTag system is characterized by an increased

number of different codes (barcodes), an increased

number of bit errors that could be detected and cor-

rected, reduced false positives and confusion between

the tags, a reduced total number of bits in the tag, and

a decreased marker size.

2.3 CALTag

After analysis of classical chessboard-based camera

calibration and ﬁducial markers approach, CALTag

marker was proposed as a specially designed for cam-

era calibration solution (Atcheson et al., 2010). This

system consists of two components: marker design

and detection algorithm. A calibration marker is used

in a proposed calibration grid, which is externally

identical to a chessboard. The tags layout within this

grid has two variations on tags density. A grid with a

highest markers density provides a larger number of

Figure 2: Other ﬁducial marker systems. MaxiCode , Rune-

Tag and Blur tag (top set of images, from left to right). ART-

Tag, CanTag and Fourier tag (bottom set of images, from

left to right).

calibration points and is thus more reliable and efﬁ-

cient for recognition. Each marker consists of M x N

matrix of black and white squares, which are encapsu-

lated with a border that contains strictly black or white

pixels (Fig. 1, right). After initial detection of poten-

tial markers, they are ﬁltered and veriﬁed by access-

ing their binary codes. Any missed calibration points

of the template are restored as the chessboard layout is

known by CALTag system. The binary marker code is

validated by calculating the ﬁrst P bits checksum and

comparing it with a checksum that is obtained from

four possible marker positions.

2.4 Other Fiducial Marker Systems

Examples

Below we present several other examples from a huge

variety of existing marker systems in order to famil-

iarize a reader with other approaches to marker sys-

tem design and applications. Figure 2 demonstrates

examples of the presented in this subsection markers.

• MaxiCode is a high-capacity, two-dimensional

machine-readable code, that were created for

shipper and load-receiving systems. The code

is reduced to one standard size - one inch per

one inch, with tolerances corresponding to ther-

mal laser printing. The US Postal Service uti-

lizes Maxicode marker in order to handle shipping

information regarding the product: in query any

product information may be included, e.g., prod-

uct weight, serial number, material type, classiﬁ-

cation, degree of danger. Yet, Maxicode is not rec-

ommended for the use as a ﬁducial marker system

because it does not perform satisfactorily under

the perspective distortion and large ﬁeld of view

cameras (Fiala, 2005a).

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• RuneTag is a marker system, that was pro-

posed by University of Venice (Bergamasco et al.,

2011). The marker is characterized by a circular

arrangement of dots at ﬁxed angles containing one

or several concentric rings. The marker is built by

partitioning a disk into several evenly distributed

sectors. Each sector, in turn, can be divided into

several concentric rings - levels and the level de-

termines a slot where a dot can be placed. Each

dot has a radius that is proportional to the level

at which the dot is located. With a help of the

generated design, some information could be en-

crypted into a tag, and also allows to easily local-

ize it. RuneTag authors emphasize that it is a high

resistance to occlusion tag, and claim that it was

successfully detected with up to 70% of its area

occlusions in their experiments.

• BlurTag system algorithm relies on the ability to

detect blurred patterns. For this reason, the au-

thors (Reuter et al., 2012) designed a checker-

board pattern that is well suited to estimate point

spread functions (PSFs) and could be robustly de-

tected in a presence of blur. The idea of mak-

ing an out-of-focus pattern with a wide range of

possible focus settings while maintaining a full

coverage of an image and a comparable apparent

resolution of a target at different distances with-

out changing the target pattern. In (Reuter et al.,

2012) the authors presented the dependence of

square detection on the level of blur kernel size

(sigma) and camera resolution, and claimed that

BlurTag demonstrated its strengths with gradually

increasing amount of blur at sufﬁcient image reso-

lution, while CALTag marker system failed to re-

sist equivalent levels of blur.

• ARTTag is an aesthetic ﬁducial marker system,

which actually can be designed in any colour,

shape and other features with circle pairs, that

allow camera detection, identiﬁcation and pose

estimation. Fiducial can be placed in everyday

environment and guarantee high level of robust-

ness and accuracy with a help of circle pairs (Hi-

gashino et al., 2016).

• Cantag is an open source software toolkit for

building Marker-based Vision (MBV) systems

that can identify and locate markers (Rice et al.,

2006). System implements two design types of

tags: circle shape (CircleTag) and square border

(SquareTag). Square tags carry a larger symbolic

data payload than a circular marker of the same

size, whereas circular tags offer better location

and pose accuracy.

• Fourier Tag is synthetic ﬁducial marker used to

Figure 3: ARTag marker system with IDs 2, 3, 6, 34 (from

left to right).

visually encode information and provide control-

lable positioning (Sattar et al., 2007). This marker

could be used for interactive control, e.g., employ-

ing ﬁducial markers to directly facilitate human-

robot interaction. For example, it could be useful

for a scuba driver to communicate with a swim-

ming robot vehicle to indicate desired actions or

behaviours.

3 EXPERIMENTAL SETUP

Our experimental work compares ARTag, AprilTag

and CALTag marker resistance to occlusion and ro-

tations relatively to various axis. We deﬁne occlu-

sion as a partial overlapping of a marker with other

objects. For rotation resistance validation, normal,

lateral, and longitudinal rotations were applied. This

Section presents experiment setup and design.

Each ARTag and AprilTag marker has its own

unique ID, which is encoded in the internal pattern

of the tag. For experiments with ARTag and AprilTag

particular marker IDs were selected randomly.

ARTag ID is encoded in 10 bits of 36 bits and it

determines a unique bit sequence that passes through

several stages to produce a 36-bit binary sequence,

which is encoded in the marker as white and black

cells (Fiala, 2005a). We randomly selected ARTag

markers with IDs 2, 3, 6, and 34 (Fig. 3).

All AprilTags were selected from 36h11 tags fam-

ily, i.e., each of marker ID is encoded in a 36 bit code-

word with a minimum Hamming distance of 11 bits.

Each ID of AprilTag was encoded in a 36 bit code-

word using coding system based on lexicodes (Tracht-

enbert, 1996). Lexicodes are greedily generated error-

correcting codes. Lexicographic code system is char-

acterized by two parameters: number of codeword

(internal pattern) bits n and minimal Hamming dis-

tance between any two codes d. Generation of valid

codewords works as follows: a codeword is added to a

Figure 4: AprilTag marker system with IDs 4, 6, 8, 9 (from

left to right).

ARTag, AprilTag and CALTag Fiducial Marker Systems: Comparison in a Presence of Partial Marker Occlusion and Rotation

185

codebook only when its distance corresponds at least

to the speciﬁed distance d to each previous codeword

added to the codebook. The lexicode always starts

with a zero code. For example, to generate a binary

lexicode of length n=3 and minimum Hamming dis-

tance d=2, we would set up Table 1, where indicates

that the vector is a valid codeword. AprilTag system

uses modiﬁcation of the lexicode algorithm and re-

jects tags with a too simple codewords, which would

produce simple geometric patterns (Olson, 2011). We

utilize arbitrarily selected tags with IDs 4, 6, 8, and 9

(Fig. 4).

Table 1: Lexicode with length n=3 and Hamming distance

d=2.

Vector 000 001 010 011 100 101

Valid c c c

Image capturing during experiments was per-

formed with Genius FaceCam 1000X camera. It

should be noted that a low quality camera for the ex-

periments was selected on purpose in order to ver-

ify the marker capabilities for inexpensive hardware.

Secondly, this selection simpliﬁed the experimental

process as the camera was directly connected to a PC

and we avoided a necessity to collect images from

robot cameras and further transfer them to a PC.

For each marker we provided the same condi-

tions of room illumination and camera posture with

respect to the tag. To analyse the effect of occlu-

sion on marker recognition, we selected four differ-

ent ARTag markers (IDs 2, 3, 6, 34), four AprilTag

markers (IDs 4, 6, 8, 9) and two CALTag tags (4x4

and 9x6 grid size). Four types of experiments were

conducted: pure marker rotation around various axis,

systematic occlusion, arbitrary overlap with an ob-

ject, and a combination of systematic occlusion with

marker rotation.

For the experiments, we set up rotation axis with

regard to the observing camera (Fig. 5,). X -axis (lon-

gitudinal axis), which is responsible for roll rota-

tions of a marker, is orthogonal to the marker plane,

passes through a central point of the contact line of

the marker image and its supporting plane, and points

out in the direction of the camera. Y -axis (lateral

axis), which is responsible for pitch rotations of a

marker, coincides with the contact line of the marker

image and its supporting plane. Z-axis (normal axis),

which is responsible for yaw rotations of a marker,

passes through a central point of the contact line of

the marker image and its supporting plane and points

upward from the in the supporting plane, thus com-

pleting a right-hand coordinate frame.

Figure 5: Marker rotation axis.

3.1 Type 1 Experiments: Marker

Rotation

In the ﬁrst set of experiments (Fig. 5, Type 1A), each

of the markers was ﬁxed at two points that formed

a vertical rotation axis being drawn from a top to a

bottom of a marker and passing through the marker

centre. Then the rotation was performed around this

normal axis, which corresponds to yaw axis. The rota-

tion was performed clockwise and counter-clockwise

for 10, 20, 30 ,45, and 55 degrees in both direc-

tions (Fig. 6 demonstrates an experiment with April-

Tag marker).

In the second set of experiments (Fig. 5,Type 1B),

each marker was ﬁxed with its bottom on a support

plane and the contact line was used as a horizon-

tal rotation axis (lateral axis), which corresponds to

pitch axis. The rotation was performed clockwise and

counter-clockwise for 10, 20, 30, 45, 55 and 65 de-

grees in both directions (Fig. 7 demonstrates an ex-

periment with AprilTag marker).

In the third set of experiments (Fig. 5,Type 1C),

each marker was ﬁxed at its central point and the rota-

tion was performed clockwise and counter-clockwise

around longitudinal axis for 0, 22.5, 45, 67.5, and 90

degrees in both directions.

3.2 Type 2 Experiments: Systematic

Occlusion

In systematic occlusion experiments a part of each

marker was covered with a white paper template of

a rectangular shape, and the template size was gradu-

ally increased. The template was growing from image

bottom to the top so that it would hide 0%, 10%, 20%,

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Figure 6: AprilTag ID 4 marker rotation around normal axis

for 10, 45 and 65 degrees.

Figure 7: AprilTag ID 9 marker rotation around lateral axis

for 20, 45, and 65 degrees.

50%, and 70% of the markers area. Figure 8 demon-

strates an example of type 4 experiments for CALTag

marker, but it explains well the idea behind template

growth for type 2 experiments.

3.3 Type 3 Experiments: Marker

Rotation with Systematic Occlusion

In marker rotation with systematic occlusion experi-

ments the ﬁrst (Type 1C) and the Type 2 of experi-

ments were combined together. The marker was ro-

tated clockwise and counter-clockwise around longi-

tudinal axis in its plane for 0, 22.5, 45, 67.5, and 90

degrees and simultaneously occluded with the white

paper template for 0%, 10%, 20%, 50%, and 70% of

its area. Figure 8 demonstrates an example of the ex-

periments for CALTag marker. Rotations relatively to

normal and lateral axes with a simultaneous system-

atic occlusion are left for the future work.

3.4 Type 4 Experiments: Arbitrary

Overlap with an Object

In arbitrary overlap with an object experiments each

marker was randomly overlapped with one of three

different objects so that an object was entirely located

within tags area and thus the overlap percentage was

always kept constant. The ﬁrst object was a white

thick paper strip of 13 cm width and 2.5 cm length

Figure 8: CALTag marker rotation around longitudinal axis

for 22.5, 67.5 and 90 degrees in both directions with an oc-

clusion of 20% of its area.

Figure 9: Arbitrary overlap of the ARTag ID3 with the scis-

sors (top set of images) and the white strip object (bottom

set of images).

with 32.5 cm

area. The second object was a metal

scissors with 7.99 cm

area. The third object was a

black plastic strip of 15,7 cm width and 2.6 cm length

with 40.82 cm

area. This way, for each experiment

the constant overlap percentage was always known

in advance. In the case of the black strip, it covers

the interior and also crosses the boundaries of each of

marker (Fig. 10). In the case of the white strip and

the scissors, they cover only the internal pattern of

each marker (Fig. 9). With each of three object for

each marker 25 trials were conducted. We emphasize

a special case for the 4x4 size CALTag: if the black

and the strip white strip is placed strictly along the

marker side, the occupied area percentage decreases

as the width of the strips exceed marker size. In this

case, the overlap percentage varies between 25.5%

and 33.84% in for the white strip and between 26.53%

and 40.20% for the black strip.

4 EXPERIMENTAL RESULTS

For the experiments we used the available for public

use ofﬁcial software of AprilTag and CALTag. For

ARTag we used ArUco library, which allows detect-

ing and recognizing various kinds of marker fami-

lies (Garrido-Jurado et al., 2014). The markers were

ARTag, AprilTag and CALTag Fiducial Marker Systems: Comparison in a Presence of Partial Marker Occlusion and Rotation

187

Figure 10: Arbitrary overlap of the CALTag 4x4 (top set of

images) and AprilTag (bottom set of images) with the black

strip object.

printed on white paper with the following sizes:

• ARTag: 15.2 x 15.2 cm, total area 231.04 cm

• AprilTag: 13.5 x 13.5 cm, total area 182.25 cm

• CALTag 4x4: 9.8 x 9.8 cm, total area 96.04 cm

• CALTag 9x6: 21.7 x 14.7 cm, total area 318.99

It is important to notice that the two types of oc-

clusion, systematic and arbitrary, had slightly differ-

ent experimental implementation. For systematic oc-

clusion, which is reﬂecting a very typical real world

occlusion situation, a marker becomes partially visi-

ble due to its rotation and incline in 3D space. Arbi-

trary occlusion had the overlapping object completely

within internal pattern of the marker, which effected

only the recognition stage of marker pattern detection.

The experimental results for ARTag (ID 2, ID 3,

ID 6, ID 34), AprilTag (ID 4, ID 6, ID 8, ID 9) and

CALTag (4x4 and 9x6 sizes) are summarized in Ta-

bles 2-12. Tables 2-9 present the results of systematic

occlusion experiments. ”2/2” denotes a successful de-

tection of the marker in both (clockwise and counter-

clockwise) directions for normal axis (Table 2) and

lateral axis (Table 3) rotations. ”1/2” denotes suc-

cessful detection of the marker only in one of the di-

rections, while ”0/2” denotes a failure to detect the

marker in both directions of rotation.

AprilTag and CALTag markers demonstrated

strong resistance to normal and lateral rotations: they

were successfully detected and recognized at any

tested angle (0, 10, 20, 30, 45, 55, and 65 degrees) for

both rotation directions. ARTag markers were sen-

sitive to any normal axis rotations. For lateral axis

rotations the ARTag markers failures started at 10 de-

grees rotation, but showed more resistance for lateral

rotations comparing with normal axis rotations. In

particular, ARTag markers were sensitive to large ro-

tation angles of 55 and 65 degrees. In the case of

lateral rotation for these angles, two markers (ARTag

with ID=3 and ARTag with ID=6) were not detected

in one of the directions.

Tables 4-7 demonstrate the results of marker ro-

tation around longitudinal axis with a simultaneous

systematic occlusion; percentage of marker occlusion

appears in the ﬁrst column of the tables, while rotation

degree appears in the ﬁrst row. Table 8 summarizes

the results of successful detection rate with regard to

the marker occlusion percentage for all markers. Ta-

ble 9 summarizes the results of successful detection

rate with regard to the marker rotation degree around

longitudinal axis for all markers.

Table 2: Systematic approach: rotation around normal axis.

Tag / Rotation percent 0

◦

ARTag (ID 2) 2/2 2/2 2/2 2/2 2/2 1/2 0/2

ARTag (ID 3) 2/2 2/2 2/2 2/2 2/2 2/2 0/2

ARTag (ID 6) 2/2 2/2 1/2 2/2 2/2 0/2 0/2

ARTag (ID 34) 2/2 2/2 2/2 1/2 2/2 1/2 0/2

AprilTag (ID 4) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 6) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 8) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 9) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

CALTag 4x4 2/2 2/2 2/2 2/2 2/2 2/2 2/2

CALTag 9x6 2/2 2/2 2/2 2/2 2/2 2/2 2/2

Table 10 demonstrates the results of arbitrary

overlap with an object experiments for the black strip

object. As the markers have different sizes while

the strip size is constant, the percentage of occluded

marker area differs between the markers.

The strip was arbitrarily placed within an inter-

nal part of the marker. For each marker, twenty ﬁve

experiments were performed so that the position of

the strip on the marker was different in each exper-

iment. The black colour of the strip makes it difﬁ-

cult to read binary code of the marker since all mark-

ers are bitonal (monochrome) and the strip crosses

the marker boundaries. A special case was CAL-

Tag 4x4 marker: because of its small size, the over-

lapped (by the strip) area varied from 25.5 to 33.84

percent. ARTag and AprilTag demonstrated particular

sensitivity to marker edges overlapping when marker

boundaries were overlapped with a black strip. Edge

overlapping disables marker unique feature (edge) de-

tection, which in turn results into a failure of marker

discovery (recognition) stage. At the same time,

CALTag 4x4 and 9x6 were successfully detected al-

most in all experiments (46 out of 50 experiments),

which demonstrates CALTag resistance to overlap-

ping boundaries and a part of it’s internal pattern area.

Table 11 shows the results of arbitrary overlap

with an object experiments for the scissors object.

These experiments demonstrated the dependence of

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188

Table 3: Systematic approach: rotation around lateral axis.

Tag/ Inclination percent 0

◦

ARTag (ID 2) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

ARTag (ID 3) 2/2 2/2 1/2 1/2 1/2 1/2 1/2

ARTag (ID 6) 2/2 2/2 2/2 2/2 1/2 1/2 1/2

ARTag (ID 34) 2/2 1/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 4) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 6) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 8) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

AprilTag (ID 9) 2/2 2/2 2/2 2/2 2/2 2/2 2/2

CALTag 4x4 2/2 2/2 2/2 2/2 2/2 2/2 2/2

CALTag 9x6 2/2 2/2 2/2 2/2 2/2 2/2 2/2

Table 4: Systematic approach: occlusion and rotation

around longitudinal axis of AprilTag.

Occl. / Rot. 0

◦

0% 2/2 0/2 0/2 0/2 0/2

10% 2/2 0/2 0/2 0/2 0/2

20% 2/2 0/2 0/2 0/2 0/2

50% 2/2 0/2 0/2 0/2 0/2

70% 2/2 0/2 0/2 0/2 0/2

marker recognition algorithm on overlap only the in-

terior of marker with a complex object. CALTag 9x6

and 4x4 showed the best results and high resistance to

any overlap of the interior within an object of a com-

plex shape (scissors). ARTag demonstrated high relia-

bility to occlusion of interior within a complex object

as well. At the sane time, in the case of AprilTag, the

marker system exposed sensitivity to overlapping of

the interior with a complex object: of the one hundred

experiments 15 markers were not recognized, but the

overall results were still satisfactory.

Table 12 shows the result of arbitrary overlap

with an object experiments for the white strip ob-

ject. These experiments demonstrated the dependence

of marker recognition algorithm on overlap of the

marker interior. ARTag system showed the lowest re-

sult relative to other marker systems: of the one hun-

dred experiments only two were successful. This re-

sult conﬁrms that white colour of the strip makes it

difﬁcult to read binary code of the marker as all mark-

ers contain monochrome colours. In case of AprilTag

only 7 experiments were successful out of 100. CAL-

Tag 4x4 markers successful rate was 88% and 9x6

markers successful rate was 96%. CALTag marker

system demonstrated the best resistance to overlap-

Table 5: Systematic approach: occlusion and rotation

around longitudinal axis of ARTag.

Occl. / Rot. 0

◦

0% 2/2 0/2 0/2 0/2 0/2

10% 2/2 0/2 0/2 0/2 0/2

20% 2/2 0/2 0/2 0/2 0/2

50% 2/2 0/2 0/2 0/2 0/2

70% 2/2 0/2 0/2 0/2 0/2

Table 6: Systematic approach: occlusion and rotation

around longitudinal axis of CALTag 9x6.

Occl. / Rot. 0

◦

0% 2/2 2/2 2/2 2/2 2/2

10% 2/2 1/2 2/2 2/2 2/2

20% 2/2 0/2 1/2 2/2 2/2

50% 2/2 1/2 2/2 2/2 2/2

70% 0/2 1/2 1/2 1/2 2/2

Table 7: Systematic approach: occlusion and rotation

around longitudinal axis of CALTag 4x4.

Occl. / Rot. 0

◦

0% 2/2 2/2 2/2 2/2 2/2

10% 2/2 2/2 2/2 2/2 2/2

20% 2/2 1/2 2/2 2/2 2/2

50% 2/2 1/2 2/2 2/2 2/2

70% 2/2 0/2 1/2 2/2 1/2

Table 8: Successful detection rate with regard to the marker

occlusion percentage.

0% 10% 20% 50% 70%

ARTag 100% 0% 0% 0% 0%

AprilTag 100% 0% 0% 0% 0%

CALTag 4x4 100% 100% 90% 90% 50%

CALTag 9x6 100% 90% 70% 100% 30%

Table 9: Successful detection rate with regard to the marker

rotation degree around longitudinal axis.

◦

ARTag 100% 0% 0% 0% 0%

AprilTag 100% 0% 0% 0% 0%

CALTag 4x4 100% 60% 90% 100% 80%

CALTag 9x6 100% 50% 80% 90% 90%

Table 10: Results of arbitrary overlap experiments with a

black strip object.

Tag Occlusion percent % Recognition rate

ARTag (ID 2) 17.66 0%

ARTag (ID 3) 17.66 0%

ARTag (ID 6) 17.66 0%

ARTag (ID 34) 17.66 0%

AprilTag (ID 4) 22.39 0%

AprilTag (ID 6) 22.39 0%

AprilTag (ID 8) 22.39 0%

AprilTag (ID 9) 22.39 0%

CALTag 4x4 26.53 –40.20 92%

CALTag 9x6 12.79 92%

ping of interior due to markers design and recogni-

tion algorithm (Atcheson et al., 2010). Yet, these re-

sults supported the claim that white colour of the strip

makes it difﬁcult to read binary code of the marker as

all markers contain monochrome colours.

ARTag, AprilTag and CALTag Fiducial Marker Systems: Comparison in a Presence of Partial Marker Occlusion and Rotation

189

Table 11: Results of arbitrary overlap experiments with a

scissors object.

Tag Occlusion percent % Recognition rate

ARTag (ID 2) 3.45 100%

ARTag (ID 3) 3.45 92%

ARTag (ID 6) 3.45 100%

ARTag (ID 34) 3.45 96%

AprilTag (ID 4) 4.38 76%

AprilTag (ID 6) 4.38 92%

AprilTag (ID 8) 4.38 92%

AprilTag (ID 9) 4.38 80%

CALTag 4x4 8.32 100%

CALTag 9x6 2.5 100%

Table 12: Results of arbitrary overlap experiments with a

white strip object.

Tag Occlusion percent % Recognition rate

ARTag (ID 2) 14.06 4%

ARTag (ID 3) 14.06 4%

ARTag (ID 6) 14.06 0%

ARTag (ID 34) 14.06 0%

AprilTag (ID 4) 17.83 4%

AprilTag (ID 6) 17.83 4%

AprilTag (ID 8) 17.83 20%

AprilTag (ID 9) 17.83 0%

CALTag 4x4 25.5 –32.5 88%

CALTag 9x6 10.18 96%

5 CONCLUSIONS AND FUTURE

WORK

In this paper we described three marker system in de-

tails: ARTag, AprilTag and CALTag. We conducted

experiments with this marker systems to evaluate their

sensitivity for partial occlusion in various types of oc-

clusion and resistance to normal, lateral, and longi-

tudinal rotations. For the given marker types we ran-

domly selected particular markers: four ARTag mark-

ers with IDs 2, 3, 6, 34; four AprilTag markers with

IDs 4, 6, 8, and 9; and two CALTag markers of 4x4

and 9x6 grid size. Occlusion experiments were de-

signed to validate resistance to a systematic occlusion

of a marker and an arbitrary overlap with an object.

For systematic occlusion experiments, which reﬂects

a very typical real world occlusion situation, a marker

was occluded with a rectangular shaped white colour

template that covered from 0 to 70 percent of total

marker area in a such manner that both marker in-

terior and edges were occluded. For arbitrary over-

lap experiments an object that covers up to 40 percent

of marker area was arbitrarily placed within marker’s

area. Three object were utilized: black strip, white

strip and scissors. The ﬁrst object crossed the bound-

aries of markers and overlapped interior; the second

and the third objects overlapped only markers interior,

which affected only the recognition stage of marker

pattern detection. Rotation experiments considered

normal, lateral, and longitudinal rotations of a marker

for 0, 10, 20, 30, 45, 55, and 65 degrees. Com-

bined experiments of simultaneous marker rotation

with systematic occlusion were performed only for

rotation around longitudinal axis.

ARTag and AprilTag markers demonstrated high

sensitivity to edge occlusions, which limits their ef-

fective use only to the cases where it could be guar-

anteed that no edge occlusions occur. These mark-

ers performed at satisfactory level for the cases when

the object occluded only the internal part of the mark-

ers. ARTag showed high resistance to overlapping its

interior, while AprilTag demonstrated a greater level

of sensitivity in the same situation. AprilTag demon-

strated high reliability under rotation around normal

and lateral axes in all one hundred experiments. At

the same time, ARTag demonstrated a high vulnera-

bility to rotations, especially with regard to the normal

axis. CALTag showed high resistance to all types of

occlusion. This marker is more resistant to overlap-

ping of interior due to markers design and recogni-

tion algorithm. CALTag was also resistant to rotations

within the complete range of the selected angles. The

lowest recognition rate was within white strip object

experiments, where CALTag 4x4 showed 88% recog-

nition rate (3 experiments out of 25 had failed).

Based on our experiments, we conclude that

among the three selected marker systems CALTag

have demonstrated signiﬁcantly better results than

ARTag and AprilTag markers. Thus, among the three

systems, CALTag marker system should be preferred

for real world applications when only simple inexpen-

sive hardware is available and we expect the appear-

ance of rotation and occlusion disturbances in the en-

vironment.

As a part of our future work, we plan to conduct

occlusion resistance experiments using different qual-

ity cameras and to identify the strengths and weak-

nesses of the markers using an increased set of cri-

teria, which includes inter-marker confusion, resis-

tance to lighting conditions changes and inﬂuence of

marker size (or distance to a marker). Special atten-

tion will be paid to the behaviour of CALTag marker,

which have demonstrated the best performance in our

current empirical research. Our long term goal is to

calibrate cameras and manipulators of a humanoid

robot and of a crawler mobile robot in real-world en-

vironments. The presented in this paper results help

selecting a most suitable marker system for further

calibration procedures. Our on-going experimental

work concentrates on veriﬁcation of the markers with

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

190

AR-601M robot hardware (Khusainov et al., 2015) in

both laboratory and real-world environments. In ad-

dition to ARTag, AprilTag and CALTag markers, we

are interested to verify the performance of BlurTag

marker system. The later stages of experimental work

will include veriﬁcation of the markers with Servosila

Engineer robot hardware (Sokolov et al., 2016).

ACKNOWLEDGEMENTS

This work was partially supported by the Russian

Foundation for Basic Research (RFBR) and Min-

istry of Science Technology and Space State of Israel

(project IDs 15-57-06010 and 17-48-160879). Part

of the work was performed according to the Rus-

sian Government Program of Competitive Growth of

Kazan Federal University.

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