ROBUST DETECTION AND IDENTIFICATION OF PARTIALLY

OCCLUDED CIRCULAR MARKERS

Johannes Koehler, Alain Pagani and Didier Stricker

DFKI GmbH, Trippstadter Strasse 122, 67663 Kaiserslautern, Germany

Keywords:

Circular markers, Ellipse ﬁtting, Marker design, Robustness.

Abstract:

In this paper we present a pipeline for the robust detection of partially occluded circular markers. Compared

to square markers, occluded circular tags can be tracked in a more robust way, since the camera pose is in

this case computed from the whole contour instead of only the four corners. We introduce a new ellipse

detection technique based on a constrained RANSAC algorithm and pre-ellipse ﬁt outlier removal to detect

tag candidates with damaged borders. Digital codes are used to identify the actual markers afterwards, since

correlation based marker identiﬁcation approaches are not capable of handling occlusion. The key to error

detection and correction is a suitable Reed Solomon code together with a proper code layout on the marker.

We show that markers covered up to 30% can be detected, our tracker moreover has a very low risk of false

positive marker detection.

1 INTRODUCTION

In the context of computer vision and augmented re-

ality, markers can be used to provide easily detectable

visual cues for e.g. robot navigation (Sattar et al.,

2007), indoor tracking (Naimark and Foxlin, 2002),

marking important or interesting points in 2D/3D and

deﬁning coordinate systems for placing augmenta-

tions (Fiala, 2004). The tags should be detectable

within a certain distance to the camera and even in

a simple, “tidy” scenario an object can quickly get

between the camera and the tag, covering parts of it.

Successful detection under partial occlusion is there-

fore an important use case (Figure 1). Most of the

existing marker systems either use square- and/or cir-

cular markers. We believe that circular tags provide

a higher robustness to occlusion, since the camera

pose used for accessing the marker content can be

computed from the whole elliptic contour. In case of

square markers, the pose computation relies only on

the four vertices. The tag can not be detected any-

more as soon as a whole edge is covered, whereas

the ellipse-shaped contour resulting from a circle still

contains enough information to obtain a good pose

estimation. The ellipse resulting from the perspective

projection of the marker however yields two possi-

ble poses only one of which is correct. We use the

error detection capabilities of the marker code to re-

trieve the correct pose, since the code cannot be read

Figure 1: The successful identiﬁcation of an occluded

marker is visualized by rendering the coordinate frame it

deﬁnes.

correctly from the wrong pose for most angles. Cir-

cular markers additionally need special features for

determining their orientation, which is not naturally

induced by the tag’s shape as it is the case with square

markers. We address the degenerated ellipse contours

resulting from occlusion with a RANSAC-based el-

lipse ﬁtting technique that allows for successful ﬁtting

even if the ellipse’s contour contains large damages.

We assume that a total amount of 255 markers is

sufﬁcient for most AR applications and use a non-

redundant digital ID composed of 8 bits on our mark-

ers together with a suitable Reed Solomon (“RS” in

the following) code (Moon, 2005) for error correc-

tion and a CRC code for error detection, inspired by

387

Koehler J., Pagani A. and Stricker D. (2010).

ROBUST DETECTION AND IDENTIFICATION OF PARTIALLY OCCLUDED CIRCULAR MARKERS.

In Proceedings of the International Conference on Computer Vision Theory and Applications, pages 387-392

DOI: 10.5220/0002850603870392

 SciTePress

ARTag (Fiala, 2004). Since RS codes are symbol ori-

ented polynomial codes, we recommend a construc-

tion of the code over a small ﬁeld, such that symbol-

chunks on the marker do not contain too many bits.

We also optimize the code to maximize the error cor-

rection capabilities.

The remainder of this paper is organized as fol-

lows: Section 2 reviews marker tracking and ellipse

ﬁtting approaches. Sections 3 and 4 cover error tol-

erant ellipse ﬁtting and digital marker identiﬁcation,

the essentials of our processing pipeline. We ﬁnally

conclude with an outlook to future work.

2 RELATED WORK

Robustness characteristics for a marker tracker have

already been discussed in the context of the ARTag

square marker system (Fiala, 2004): It should pro-

vide low false positive/ negative detection rates as

well as not confuse the markers with each other. It

was pointed out that correlation based marker track-

ing systems like the popular ARToolkit (Kato and Bil-

inghurst, 2000) will not perform well in these areas,

therefore ARTag made use of digital codes. Correla-

tion based trackers are also not able to handle occlu-

sions robustly, because the “ﬁducialness” of an ob-

served ellipse is a threshold decision and the correla-

tion measure cannot be used to identify and correct

read errors. While ARTag performs well concern-

ing the detection- and confusion rates, the used dig-

ital code however is only capable of correcting two

bit errors out of 36 bits, which prohibits robust detec-

tion under larger occlusions. Other tracking systems

also do not address the problem properly. The precise

error correction capabilities of CyberCode where not

mentioned in (Rekimoto and Ayatsuka, 2000), so we

assume they are negligible. The tracker developed by

(Naimark and Foxlin, 2002) has no read error protec-

tion. In (Sattar et al., 2007) possible protection meth-

ods are suggested but the developed system does not

attempt to handle occlusions as well.

Our ellipse ﬁtting technique is composed of 3

other methods. (Cai et al., 2004) use a RANSAC

based approach which computes a test model from

5 random contour points. They introduced the ﬁt-

ting factor for deciding if the model ﬁts the data well.

(Song and Wang, 2007) reduced the amount of con-

tour points to 3 which decreases the amount of needed

iterations. Both approaches however did not make use

of an error tolerance as it is common in RANSAC. We

found out that the ﬁtting factor is occasionally high

for a poor ﬁt when the points are chosen randomly

and solved this problem using a separation idea found

in (Zhang and Liu, 2005). Other ellipse ﬁtting tech-

niques are either too slow (genetic algorithms, e.g.

(Yao et al., 2004)) or can not cope with defects to a

desired extend (optimization based approaches, e.g.

(Fitzgibbon et al., 1999)).

3 ELLIPSE DETECTION

Ellipses found in an image are the ﬁrst indicator for

the presence of a circular marker. We ﬁrst detect

closed contours in the thresholded, binary input im-

age, which serve as a region of interest (ROI) and

narrow the search scope (remark: These ROIs do not

necessarily need to be closed, in fact we delete cer-

tain parts from them). Our ellipse detection method

applied to each of the found contours is based on the

method of (Song and Wang, 2007). Their algorithm

roughly performs the following steps:

For each input contour do:

1. Select 3 contour points P

, P

2. Compute a tangent T

at P

using a least squares

ﬁt of a line to the contour points found within a

5x5-raster around P

3. Compute the potential ellipse center C from the

tangents.

4. Compute an ellipse E using C and P

5. Accept E if its ﬁtting factor F is adequate.

We found several problems in this approach. First,

no error tolerance was used during the point hit test

which slows down the computation. We use a cross-

shaped mask allowing an error of 2 pixels in each pos-

itive and negative x/y direction.

Second, a 5x5 raster for tangent computation can

cause tangent distortions when outliers are captured

by the raster. Since our input contours are sequenced,

connected pixels, we can use the previous and suc-

ceeding pixels with respect to an index for tangent

computation for higher robustness.

Third, Ellipses ﬁtting the contour poorly can nev-

ertheless score a high ﬁtting factor. This results from

the fact, that the model (test ellipse) is compared

against the data (input contour) (refer to (Cai et al.,

2004) for details) and not vice versa as it is usually

done in a RANSAC algorithm. While sparing the

costly computation of the geometric distance of ev-

ery contour pixel to the test ellipse (see (Forsyth and

Ponce, 2003), p.338), this enforces only local ﬁtting

in the area covered by the test ellipse. When the ran-

domly chosen tangent indices are close to each other,

the resulting test ellipses are often stretched and small

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

388

Figure 2: Green: part of the correct ellipse, blue: P

, red:

derived model evaluated in a RANSAC-iteration. It scores

a high ﬁtting factor but does not ﬁt the contour well.

and therefore can produce a high ﬁtting factor (Figure

To resolve this problem, we use the tangent sepa-

ration idea mentioned in (Zhang and Liu, 2005). We

enforce it in our approach with the evenly distributed

tangent (EDT)-constraint:

= P

i−1

+ ((

+ x) · cs) mod cs (1)

Where x ∈ [−0.1..0.1] is chosen randomly, cs is the

size of the input contour and P

, i ∈ {2, 3} are point

indices referring to the input pixel array. P

Is chosen

randomly. This assures an appropriate size of the test

ellipse.

Our goal is to detect occluded markers. In this

scenario the ellipse-shaped contour resulting from the

marker border will be broken. When applying a con-

trast enhancement to the input image, the occlusions

cause outlier parts in the form of convexity defects

in most cases (Figure 3). To prevent the choice of

Figure 3: Broken contour caused by occlusion.

tangent indices from outlier parts we remove these

defects from the contours. The direct least squares

method of (Fitzgibbon et al., 1999) is used to obtain

the ﬁnal ellipses from from the consensus sets.

4 MARKER IDENTIFICATION

Those Ellipses observed in an image that did not orig-

inate from a marker must be excluded according to

the data found in their interior. To uniformly access

this data we hypothesize 2 possible camera poses, fol-

lowing (Chen et al., 2004). The distinction of the 2

poses is described later in this section. We chose a

marker identiﬁcation based upon a digital code, since

this provides higher robustness compared to a cor-

relation based identiﬁcation (Fiala, 2004). Read er-

rors can also be corrected, which is desired in case

of occlusions. Our markers carry 32 bits on 3 rings,

12 bits on the 2 outer- and 8 bits on the inner ring.

The reasoning for this layout is described at the end

of this section. To uniformly access these bins the

marker must ﬁrst be properly oriented, respectively

the unknown camera rotation around the normal vec-

tor at the marker’s center must be computed. While a

square naturally induces 4 possible orientations, a cir-

cular marker needs special features for this. We there-

fore placed 4 spots on the outer marker border to ob-

tain 4 possible orientations(Figure 4). The symmetry

of these points guarantees that the rotation can be de-

termined even when other bright spots where found,

which is the case under occlusion. The correct among

the 4 possible rotations is determined by the decoding

properties of the bit sequence read at the respective

rotation. Only a single sequence must be allowed to

correctly decode. This idea originates from ARTag

(Fiala, 2004).

Figure 4: One of our new, digital markers.

Thus our processing steps are similar to ARTag:

Read 4 permutations, correct errors (RS stage), accept

the code word which passes the CRC check (CRC

stage). Because our goal is to ﬁnd markers under

occlusion, the error correction abilities of the code

must be signiﬁcantly higher. To achieve this we use a

long FEC- (a Reed Solomon (RS) in our case) and a

short CRC code, inversely to ARTag. This is possible

since we found that about 55% of all permutations

scramble the code word such that the RS code can

not recover it. It is discarded after the RS-stage. The

CRC-code distinguishes only between the remaining

ambiguities and is variable with respect to this objec-

tive. Since it cannot be computed analytically (Rice

et al., 2004), testing revealed that using the genera-

tor polynomial 0x8D (CRC-8-CCITT, (Moon, 2005)),

no other than the 0-codeword must be excluded for

ambiguities. We moreover assume a marker will not

carry more than 60 bits and thus construct primitive

RS codes over GF(16) = GF(2

) = GF(q

). The

RS code words then have a maximal symbol length of

n = q

− 1 = 15 with 4 bits per symbol. Our FEC-

redundancy length is 16 bits = 4 symbols. With stan-

dard decoding 2 symbols = 8 bits can be corrected.

In order to obtain valid permutations of the code

and therewith predictable decoding results, a bin

count divisible by 4 is necessary for each ring as il-

lustrated in Figure 5. When this is not the case, in-

valid bins are sampled and we can not be sure of the

ROBUST DETECTION AND IDENTIFICATION OF PARTIALLY OCCLUDED CIRCULAR MARKERS

389

obtained value. For these reasons the ﬁnal code used

on our markers is 32 bits long, composed of an 8 bit

non-redundant ID, an 8 bit CRC code and a 16 bit RS

code, stored in 3 rings with 12 bits (outer rings) and 8

bits (innermost ring) (Figure 4). ARTag markers use

a 36 bit code with 10 bit ID, 16 bit CRC code and 10

bit FEC code.

Figure 5: Exemplary innermost code ring, 2 bins. When

rotated by 90

◦

the result of the sampling is unclear - the

value might oscillate between black and white due to small

errors in the pose estimation.

The symbols must be placed on the marker such

that they ﬁt to occluding objects well (Figure 6). We

therefore distribute the ﬁrst 6 symbols of a code word

(= the ﬁrst 24 bits) to the outer rings as seen in Figure

6 (right) and the remaining 2 symbols (= 8 bit) on the

innermost code ring.

Figure 6: Left: bad layout (2 symbols), recovery not possi-

ble. Right: good layout (2 symbols), recovery possible.

After successful identiﬁcation we use the read er-

ror information to distinguish between the 2 pose es-

timations. We moreover use composites consisting of

2 coplanar markers or 3 markers in different planes.

The a priori information of the planes the markers lie

in can be used to recompute the camera pose after suc-

cessful marker identiﬁcation. For 2 markers we com-

plete the approach that yielded the initial estimation

(Chen et al., 2004). For 3 markers in different planes

we use the approach found in (Kannala et al., 2006).

5 RESULTS

5.1 Ellipse Detection

We examined a series of intact ellipses with axis sizes

from 150:150 to 10:150 pixels. Each ellipse was ﬁtted

with a pure random choice of points for tangent com-

putation and our EDT-constraint, 100 times each. The

ellipses were always successfully detected. Our EDT-

constrained algorithm needs an average of 1.2-1.7 it-

erations per ellipse compared to an average of 3.0-5.1

iterations of the unconstrained RANSAC algorithm.

Both algorithms handle intact ellipses well, the EDT-

constraint shows out to be slightly better. The graph

depicted in Figure 7 gives a ﬁrst insight in how the al-

gorithm performs in the presence of defects. A grow-

ing defect is added to an ellipse with axis sizes of 75

and 150 pixels. The defect is not removed from the

detected contour. The algorithm stops trying to detect

the ellipse after 100 iterations, so an amount of 100 it-

erations corresponds to a failed detection. The ﬁtting

factor is set to accept defects up to 40%.

Figure 7: Fitting of an ellipse (axis sizes: 75 and 150 pixel)

with a growing defect that is not removed.

We can see that neither the EDT-constrained nor a

pure random choice of tangent candidate points pro-

duces reliable ﬁts. If the defects are removed how-

ever, EDT-RANSAC performs as expected (Figure 8),

the ellipse is not detected anymore at a defect size of

40% and a fairly low amount of iterations was needed.

With a pure random choice however, RANSAC still

detects an ellipse after the defect grew bigger than

40% although the demanded ﬁtting factor can not be

scored anymore. This behavior results from the prob-

lem described in Section 3 and is not desired.

Figure 8: Fitting of an ellipse (axis sizes: 75 and 150 pixel)

with a growing defect that is removed, the ﬁtting factor al-

lows a defect of up to 40%. Note the predictable behavior

of the EDT-constrained RANSAC in contrast to the false ﬁts

detected by the previous RANSAC after the defect is larger

than 40%.

Figure 9 shows the maximal defect size that still

yields a successful detection with a feasible amount

of 15 iterations for a series of ellipses with axis sizes

from 150:150 to 20:150 pixels. The ﬁtting factor is

set to allow a total defect of 85% for this experi-

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

390

ment. When a consensus set was successfully com-

puted from a test ellipse whose axes differed by more

than 5% from the known correct ellipse the search is

considered as failed (in this case the estimated ellipse

would not ﬁt to the contour). When no consensus set

was found after 15 iterations the search is also con-

sidered as failed. The results are shown in Figure 9.

This result shows that using defect removal, our al-

Figure 9: Maximal defect that could not be detected any-

more using 15 iterations (blue); Average iterations until ﬁrst

failed detection (red).

gorithm can detect ellipses with large defects of 50%

and higher with a fairly low amount of iterations. As a

comparison the original P-RANSAC algorithm (Song

and Wang, 2007) was used with an amount of 35 itera-

tions to successfully recover ellipses in (Kaewapichai

and Kaewtrakulpong, 2008). Compared to this we re-

quire only 40% of iterations to obtain good ﬁts.

5.2 Marker Identiﬁcation

In this section we present the detection rate of our

marker tracker and the risk of a false positive marker

detection.

The graphs in Figure 10 illustrate the detection

rate of our marker tracker, which measures the min-

imal detectable pattern size. 9 different markers are

ﬁlmed by a webcam (Microsoft LiveCam VC-6000

1.0) in top view at various distances with a resolu-

tion of 640x480. For each distance, the number of

detected markers is recorded for a total amount of 20

frames. Division by the expected 180 markers then

yields the detection rate. The rate will be plotted as

function of minimal marker diameter inside the im-

age. This experiment was accomplished for 9 intact

as well as 9 partially covered markers (Figure 10).

With both intact and occluded markers we can score

a very good detection rate. In case of intact markers

the graph has a steep ascend from no to constant de-

tection between 12 and 17 pixels. When all of the 9

markers are partially occluded we obtain a ﬁrst initial

Figure 10: Detection rate for intact and covered markers.

detection at a tag size of 15 pixel and constant detec-

tion at a size of 32 pixel, this means damaged tags

need to be approximately twice as big. The detection

rates for intact markers of ARTag and ARToolkit are

taken from (Fiala, 2004), p.32-35 for several camera

types. The tag-size intervals from a ﬁrst initial- to

constant detection are found in Table 1. Although dif-

Table 1: Marker size intervals from initial to constant de-

tection for ARTag and ARToolkit. A: Greyscale PGR Drag-

onﬂy 640x480, B: Color PGR Dragonﬂy 640x480, C: In-

tel Pro 640x480 webcam. “+” in case of ARToolkit means

the value can be higher, depending on the conﬁdence factor

(c.f.) used. Refer to (Fiala, 2004) for more details.

- A B C

ARTag 11-16 15-20 13-25

ARToolkit 10-30+ 10-55+ 15-26+

ferent camera types were used, it is obvious that the

detection rate of our markers can compete with these

results well. In case of intact markers we can score

almost the same detection rate with our webcam as

ARTag with the high-quality PGR Dragonﬂy camera.

When the markers are occluded, our detection rate is

slightly worse but still close to non-occluded ARTag

markers and much better than ARToolkit, which is not

able to handle occlusions of any kind.

The risk for a false positive marker detection

is 0.0039% (Fiala, 2005) in case of ARTag. With

higher error correction capabilities this risk grows

since more false words are mapped to a correct code

word. The risk in case of our markers is computed

with equation 2.

(1 +





· n +





· n

) · (4 ·255)

= 0.153% (2)

where n =

∑

i=1





= 15 are the possibilities to cor-

rupt a 4 bit symbol. Although almost 40 times higher

than in ARTag, this risk is still fairly low. In fact even

a much higher risk does not yet pose a problem since

the actual probability for a marker pattern to appear

in a scene by chance is not involved in these consid-

erations.

ROBUST DETECTION AND IDENTIFICATION OF PARTIALLY OCCLUDED CIRCULAR MARKERS

391

6 CONCLUSIONS AND FUTURE

WORK

We presented a pipeline for the robust detection of

circular markers. To accomplish this we use an error

tolerant ellipse detection algorithm as well as error

correcting codes together with a robust design of the

marker. The RANSAC-based ellipse ﬁtting algorithm

is able to detect ellipses with defects > 50% with a

fairly low amount of iterations. This is accomplished

by pre ellipse ﬁt removal of convexity defects from

contour candidates and the use of the EDT-constraint.

In the future this algorithm can be extended to ro-

bustly handle outward errors of the ellipses and occlu-

sions that do not cause convexity defects, but lines.

The occlusion of the marker must also be handled

after the successful ﬁtting of an ellipse to its con-

tour. We therefore introduced a robust, occlusion-

tolerating rotation indicator. Error correcting Reed

Solomon codes are used together with error detecting

CRC codes to ﬁnd and correct read errors caused by

occlusions and to obtain the correct orientation and

pose. Other than in ARTag, our goal was to mini-

mize the code for a better readability, yet maintaining

a high error correction rate. For this reason we also

used the error detection features of the actual error

correcting Reed Solomon code to ﬁlter out bad marker

orientations. We found that more than half of all pos-

sible marker-rotation caused permutations of all pos-

sible codes can be ﬁltered out in this way, allowing the

use of a shorter CRC code. Compared to ARTag, our

code therefore can correct up to 8 bit errors instead

of 2 and the CRC generator polynomial has half the

size. Thus approximately 30% of it can be covered.

The risk of a false positive detection is nevertheless

very low. In the future the markers can be extended

with the more sophisticated erasure decoding method

for the Reed Solomon codes to double the amount of

corrected errors.

ACKNOWLEDGEMENTS

This work has been partially funded by the project

CAPTURE (01IW09001) and the German BMBF

project AVILUSplus (01M08002).

REFERENCES

Cai, W., Yu, Q., and Wang, H. (2004). A fast contour-

based approach to circle and ellipse detection. Intel-

ligent Control and Automation, Fifth World Congress

on, 5:4686–4690.

Chen, Q., Wu, H., and Wada, T. (2004). Camera calibra-

tion with two arbitrary coplanar circles. In ECCV (3),

pages 521–532.

Fiala, M. (2004). Artag revision 1. a ﬁducial marker system

using digital techniques. Technical report, National

Research Council of Canada.

Fiala, M. (2005). Artag, a ﬁducial marker system using dig-

ital techniques. In CVPR ’05: Proceedings of the 2005

IEEE Computer Society Conference on Computer Vi-

sion and Pattern Recognition (CVPR’05) - Volume 2,

pages 590–596. IEEE Computer Society.

Fitzgibbon, A. W., Pilu, M., and Fisher, R. B. (1999). Di-

rect least square ﬁtting of ellipses. IEEE Transac-

tions on Pattern Analysis and Machine Intelligence,

21(5):476–480.

Forsyth, D. A. and Ponce, J. (2003). Computer Vision - A

Modern Approach. Prentice Hall.

Kaewapichai, W. and Kaewtrakulpong, P. (2008). Robust

ellipse detection by ﬁtting randomly selected edge

patches. In Proceedings of World Academy of Science,

Engineering and Technology, volume 48.

Kannala, J., Salo, M., and Heikkila, J. (2006). Algorithms

for computing a planar homography from conics in

correspondence. In BMVC06, page I:77.

Kato, H. and Bilinghurst, M. (2000). ARToolkit User Man-

ual. Human Interface Technology Lab, University of

Washington.

Moon, T. K. (2005). Error Correction Coding. John Wiley

& Sons, Inc. Hoboken, New Jersey.

Naimark, L. and Foxlin, E. (2002). Circular data ma-

trix ﬁducial system and robust image processing for

a wearable vision-inertial self-tracker. In ISMAR ’02:

Proceedings of the 1st International Symposium on

Mixed and Augmented Reality, page 27. IEEE Com-

puter Society.

Rekimoto, J. and Ayatsuka, Y. (2000). Cybercode: design-

ing augmented reality environments with visual tags.

In Designing Augmented Reality Environments, pages

1–10.

Rice, A. C., Cain, C. B., and Fawcett, J. K. (2004). De-

pendable coding of ﬁducial tags. In Murakami, H.,

Nakashima, H., Tokuda, H., and Yasumura, M., edi-

tors, UCS, volume 3598 of Lecture Notes in Computer

Science, pages 259–274. Springer.

Sattar, J., Bourque, E., Giguere, P., and Dudek, G. (2007).

Fourier tags: Smoothly degradable ﬁducial markers

for use in human-robot interaction. Computer and

Robot Vision, Canadian Conference, 0:165–174.

Song, G. and Wang, H. (2007). A fast and robust ellipse

detection algorithm based on pseudo-random sample

consensus. In Computer Analysis of Images and Pat-

terns, volume 4673 of Lecture Notes in Computer Sci-

ence, pages 669–676. Springer.

Yao, J., Kharma, N., and Grogono, P. (2004). Fast robust

ga-based ellipse detection. Pattern Recognition, In-

ternational Conference on, 2:859–862.

Zhang, S.-C. and Liu, Z.-Q. (2005). A robust, real time

ellipse detector. Pattern Recognition, 38:273–287.

VISAPP 2010 - International Conference on Computer Vision Theory and Applications

392