BUILDING LOCAL K-D TREE FOR FLEXIBLY LABELING

ARTICULATED POINT SETS

Wu Huang and Shihong Xia

Institute of Computing Technology of the Chinese Academy of Science, Graduate University of Chinese Academy of Science

#6 Academy South Road, Beijing, China

Keywords:

Optical motion capture, Label markers, Local k-d tree, Clinical gait analysis.

Abstract:

Optical motion capture system is widely used to acquire human motions by capturing the trajectories of mark-

ers that are attached to the body. Identifying the marker trajectories is challenging but indispensable in most of

real applications. Conventional methods rely on either labor-intensive manually labeling or auto-labeling with

assumption of pose similarity to the topological model. This paper presents a novel method to ﬂexibly label

markers from human motion capture sequences. The point sets in a rigid segment deﬁned in the topological

model are ﬁrstly clustered by using the spectral clustering algorithm. For each rigid segment, a local k-d tree

is constructed to robustly match two point sets without pose similarity assumption. To match all rigid bodies

with those in topological model for efﬁciently and correctly labeling, the labeling process is carefully designed

using the articulated structure of acquired data. Experiments show that our method outperforms conventional

methods in accuracy and is robust when labeling markers in motion capture sequences from different subjects.

1 INTRODUCTION

Marker-based motion capture (MOCAP) system has

become one of the most popular methods for ac-

quiring human motions in clinical gait analysis,

sports training and computer games(Guerra-Filho,

2005)(Gleicher, 1999).It can reconstruct the motions

of moving subjects by measuring the 3D trajectories

of passive reﬂective markers attached to the subjects.

To use the recorded data, information such as joint an-

gles, skeletal parameters and the topology of the cap-

tured subjects should be extracted. Most commercial

tools (e.g. Vicon(OMG, 2009)) provide an additional

process called labeling to identify each marker based

on the predeﬁned topological model to get the geo-

metric information. Unfortunately, this work is of-

ten accomplished manually which is labor-intensive,

highly non-productive and error prone. Every time a

new subject is to be captured, the manual identiﬁca-

tion is needed.

Generally speaking, different captured subjects

will have different geometric information. Essen-

tially, the labeling work is to generate geometric mod-

els for different captured subjects. Currently, most ap-

proaches assume that the geometric model has been

identiﬁed in the ﬁrst frame of motion sequences as

most commercial tools do. Some approaches provide

a topological model as a point set template and use

the method of Point Pattern Matching (PPM) with ar-

ticulated sparse feature points to generate geometric

models for different captured subjects automatically.

The topological model only contains marker set and

the topology of the captured subjects without speciﬁc

geometric information. However, this automatically

labeling process requires the captured subjects to per-

form the same initial pose as the topological model.

In situations such as clinical gait analysis for disabled

people, it is difﬁcult for them to perform special pose.

It is still an open problem to label captured markers

automatically using topological model without the re-

quirement of special initial pose.

This paper describes a new method to automati-

cally label points or generate geometric models in ac-

quired motion data, which only requires that the ac-

quired data has the same spatial distribution of points

in each rigid body and does not need the identical

scale and pose with the topological model. To serve

this purpose, we assume non-interrupted marker tra-

jectories can be obtained. To construct a local k-d tree

for each rigid body (Here, ”local” means that the k-d

tree is built within a local rigid body.), we ﬁrst clus-

ter these marker into different rigid groups. The la-

beling process is implemented using constructed local

k-d tree articulately to obtain robust labeling results.

288

Huang W. and Xia S..

BUILDING LOCAL K-D TREE FOR FLEXIBLY LABELING ARTICULATED POINT SETS.

DOI: 10.5220/0003299802880294

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2011), pages 288-294

ISBN: 978-989-8425-37-9

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Input and output of our approach. Left are 3D

marker trajectories acquired from MOCAP system. Right

are the results of marker labeling that are also the geometric

models.

Fig. 1 shows the input and output of our approach.

2 RELATED WORK

The task of labeling markers or identifying acquired

data based on the topological model can be consid-

ered as the problem of Point Pattern Matching (PPM)

with articulated sparse feature points.

Many researchers have efforts on the area of

PPM(Cox and de Jager, 1992)(Li et al., 2003).

Their work mainly focuses on geometric invariant

or constrained satisfaction in afﬁne transformation.

The methods frequently used include graphics, in-

terpretation trees(Gaede and Gnther, 1998), Haus-

daorff distance(Mount et al., 1999), geometric hash-

ing(Wolfson and Rigoutsos, 1997). The human is

a high-dimensional nonrigid object that can perform

various complicated motion. The geometric invariant

or constrained satisfaction employed in these methods

can not be easily met during human’s performances.

As a result, these approaches can hardly adapted for

the situation of high-dimensional articulated motion.

Baihua Li et al.(Li et al., 2004)(Li et al., 2008)

introduced a segment-based method for PPM and

employed it to solve the problem of labeling mark-

ers. The used topological model is obtained manually

from the same acquired subject at different poses. The

labeling process is carried out within each rigid seg-

ment. Their method can identify acquired data that

is obviously visually different from the topological

model. Unfortunately, the computation cost is high,

and the topological model for different subjects needs

to be re-built manually. Qian Yu et al.(Yu et al., 2007)

proposed a method to label markers for multiple inter-

acting articulated targets. They learnt a motion model

and a structure model for each target from calibration

sequences, and used them to identify markers. Us-

ing learned models, their method can label markers

for different interacting targets. In order to start the

marker tracking, the markers in the ﬁrst frame of cali-

bration sequences for each target must be correctly la-

beled by hand. In fact, this manually process is estab-

lishing a correspondence from the topological model

to the acquired motion data.

To label different subjects with a generic topolog-

ical model that has similar topology to the acquired

subjects, Baihua Li et al.(Li et al., 2005) designed a

new similarity k-d tree and used this data structure to

identify markers in only one frame. The method can

identify acquired data that have non-identical scales

with the topological model. It can be processed very

fast, but the method requires that the pose of acquired

data and topological model must be similar. Bent-

ley(Bentley, 1975) ﬁrst introduced the binary k-d tree

in 1975, in which he used axis-orthogonal cutting

hyper-planes through data points to partition recur-

sively a point-set at each interior node into two sub-

sets. Then Bentley(Bentley, 1990) introduced an opti-

mized semi-dynamic k-d tree taking the data distribu-

tion into account, to construct this kind of k-d tree,

one should ﬁrst ﬁnd out the dimension of the data

that has the largest spread to determine the orthogonal

hyper-plane axis, and then the mean-partition of data

extension in that dimension is calculated to locate the

hyper-plane.

Other researchers tried to extract the informa-

tion such as skeletal parameters, joint angles and the

topology from marker trajectories without the step

of labeling. Adam G.Kirk et al.(Kirk et al., 2005)

used spectral clustering algorithm(Ng et al., 2001) to

identify rigid bodies from motion capture sequences

and estimated the skeletal parameters. Edilson de

Aguiar et al.(Aguiar et al., 2006) adopted a method

that was very similar to that was proposed by Adam

G.Kirk et al.(Kirk et al., 2005) to automatically ex-

tract the articulated skeletons from 3D marker tra-

jectories. Alexander Hornung et al.(Hornung et al.,

2005) also proposed a method to extracted articulated

skeletons from motion sequences. They introduced a

self-calibrating process to get the topology of the cap-

tured objects. The methods mentioned above can es-

timate skeletal parameters and topology without iden-

tifying each marker which is convenient for computer

animations.

However, to get precise locations of joints in clin-

ical analysis, the experience formulas provided by

biomechanics are always used and the step of label-

ing is always required so these methods can not be

easily applied to our problem. Inspired from their

method of identifying rigid bodies, we also apply the

spectral clustering algorithm(Ng et al., 2001) to get

marker groups representing different rigid bodies and

the details will be given in Section 3.1.

BUILDING LOCAL K-D TREE FOR FLEXIBLY LABELING ARTICULATED POINT SETS

289

Figure 2: Pipeline overview of our algorithm.

3 OUR APPROACH

The topological model used in our method is an artic-

ulated structure composed of rigid bodies, in which

the neighbor rigid bodies are linked with the shared

markers. In order to label the acquired motion data

with a generic topological model, we use the intrin-

sic rigid segment constraint of 3D marker trajectories

to cluster the markers into rigid body sets. Inspired

by the fact that k-d tree is a state-of-the-art method

for matching point pattern with similar distributions,

we build local k-d tree structure for each marker set

in the topological model and the acquired data. Since

the obtained rigid segment has the property of geo-

metric invariance during afﬁne transformation, so the

proposed method can also label markers in the case of

distinct pose difference.

Given the 3D marker trajectories acquired from

commercial optical MOCAP system, our approach

can give name for each trajectory without manual ef-

fort. There are three steps to accomplish this task.

The ﬁrst step is to divide markers into different

groups. Each one of them represents a rigid body part.

We call this process Clustering Rigid Point Sets(See

Section 3.1).

Give a list of body segments and their associated

markers, we can build a local k-d tree according to the

topological model for each marker group(See Section

3.2). The topological model has similar topology but

non-identical scales to acquired data and a local k-d

tree is also constructed for each rigid body in the topo-

logical model. Our labeling process is based on these

local k-d trees to build a correspondence between the

topological model to acquired data.

Finally, in order to match each rigid body with

the one in topological model, we make the labeling

process articulately execute for each marker group

based on the topology provided by the topological

model. We call this process matching articulated

point sets(See Section 3.3). Fig. 2 illustrates the

pipeline of our approach.

Figure 3: Rigid body clustering. Left shows the input

points. Right is the result of rigid body clustering. Different

color groups represent different rigid bodies.

3.1 Clustering Rigid Point Sets

In this section, we illustrate our clustering procedure,

which is used to identify individual rigid bodies from

the marker’s 3D trajectories.

In a rigid body, the distance between any two

markers keeps almost constant over time. However

it varies if the markers belong to different parts. To

choose markers of each rigid body, we employ spec-

tral clustering algorithm(Ng et al., 2001) on the stan-

dard deviation of the mutual marker distances over

time. To avoid manually effort we get the afﬁnity ma-

trix A as(Zelnik-manor and Perona, 2004) did:

i, j

(

exp(−d

i, j

/(2δ

)), i 6= j

0, i = j

(1)

where d

i, j

is the standard deviation of distance be-

tween marker i and j δ

= d

k,i

is the K-th neighbor

of marker i in the standard deviation space. In our ex-

periments, we use a single value of K = 5 because the

number of markers in each group is no more than 5

and it gives good results.

We apply spectral clustering algorithm(Ng et al.,

2001) hierarchically to get robust clustering result

based on the topological model. First, the cluster-

ing algorithm will divide the point set into two clus-

ters, C

and C

, which represent upper and lower part

of human respectively. Then the spectral clustering

is employed again within each cluster to get proper

marker groups that can be used to represent rigid bod-

ies. Fig. 3 demonstrates that our approach can ro-

bustly identify all individual segments of the human

body.

Because the common point shared with two seg-

ments can be clustered into any of the two segments,

compared with the topological model there will be

some segments having one point lost. This lost point

must be added into proper segment while labeling. To

solve this problem we design an articulated point set

matching procedure that will be discussed in detail

later.

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3.2 Building Local K-D Tree

In this section, we give introduction on how to build

local k-d trees for the point sets in topological model

and acquired one. As there is no identical scales be-

tween topological model and acquired data, the la-

beling work can not be accomplished by solving the

problem of absolute orientation(Arun et al., 1987) so

we make use of local k-d trees to label markers in dif-

ferent rigid bodies.

The local k-d tree is built for each rigid body,

which is identiﬁed by the procedure introduced in

Section 3.1. Since single rigid will hold geometric

invariance during afﬁne transformation, constructing

local k-d tree for each rigid body and labeling their

associated points can be applied to acquired data that

are signiﬁcantly different from topological model.

As the topological model point set T = {t

∈

}

i=1

and the acquired point set O = {o

∈ R

}

i=1

are usually obtained in distinct coordinate systems

and performing different pose, they need to be aligned

to a consistent coordinate system by centering and ro-

tation before constructing local k-d tree. This process

can change two point set with different statues into a

same pose under a consistent coordinate. Firstly, the

centroids of T and Q is estimated as in Equ. 2. Sec-

ond, the orientation vectors can be calculated from the

weighted second distribution moments as Equ. 3 and

Equ. 4 in(Li et al., 2005)

−→

∑

i=1

−→

∑

i=1

(2)

−−→

∑

−

−→

)|t

−

−→

| (3)

−−→

∑

−

−→

)|o

−

−→

| (4)

where t

∈ T,o

∈ O and M is the number of points in

the point set.

Finally, each point in T and O should be trans-

formed with respect to their centroid and the orienta-

tion vectors by suitable translation vector t and rota-

tion matrix R as in Equ. 5.





′





= R(









+ t) (5)

where x, y,z denotes the original coordinates of each

point in the point set and x

′

represents the

aligned coordinates.

For the topology model, the rotation matrix R can

be set as identity matrix and the translation vector t is

the negative centroid vector of

−−→

. For the acquired

point set, R represents the rotation matrix of rotating

−−→

into

−−→

and t is also the negative centroid vec-

tor of

−−→

. In the former work of (Li et al., 2005), for

the acquired data the R was deﬁned as a rotation ma-

trix only around the z-axis because they assumed that

human objects were standing straight, parallelling to

the vertical z-axis and there are no rotations around

other two axis. To satisfy this assumption, the cap-

tured objects must perform the same pose with topo-

logical model and they can only change their orien-

tations around the z-axis. As we build k-d tree for

each rigid body rather than the whole body, the issue

caused by pose difference can be handled by label-

ing each local rigid segment. Because the rigid bod-

ies can maintain geometric invariance during afﬁne

transformation, we can deﬁne rotation matrix R for

acquired data around each axis to align local different

rigid bodies. This operation makes our method can

apply to acquired data, which has visually different

pose with the topological model.

Now, for a given aligned 3-dimension topological

model points set

T = {

∈ R

}, we can build local k-

d tree for it. Firstly, we sort the points respectively

along x-axis, y-axis and z-axis. Then the orthogonal-

axis OA

∗

will be determined as Equ. 6.

∗

max

ϕ∈{x,y,z}

∆ϕ (6)

where ∆ϕ = max

∈

((

k+1

)

− (

)

i+1

)

≥

(

)

),(i = 1, ..., M) is the maximum coordinate

interval in the direction ϕ,and i is a sorting index.

Next, we divide the point set into left subset P

and

right one P

. The points in the left subset are smaller

than OA

∗

in axis ϕ

∗

while the right are bigger. Then

an interior node containing the orthogonal-axis(e.g.

x,y or z) and the number of points n

split to the left

tree will be constructed. In the subset P

and P

, the

procedures of choosing orthogonal-axis and splitting

point set based on the axis will be implemented recur-

sively until they contain only one point. Then a leaf

node storing this point is built.

Finally, for the aligned acquired points set, we use

the informationstoring in each interior node of its cor-

responding local k-d tree in the topological model to

construct the acquired one. Starting from the root

node, we ﬁrst split the aligned acquired point set

based on the hyper-plane orthogonal-axis contained

in its corresponding local k-d tree’s root node in the

topological model. Then the n

smallest points along

this axis in the acquired point set are stored in the left

child node, and the rest are stored in the right child

node. In this way, the acquired point set will be split

into two parts at each interior node. In each subset,

this split procedure will be implemented recursively

BUILDING LOCAL K-D TREE FOR FLEXIBLY LABELING ARTICULATED POINT SETS

291

until the leaf node contains only one point. Up to now,

we have built a local k-d tree for acquired point set

that has the same structure with its topological model.

3.3 Matching Articulated Point Sets

Having built local k-d tree for each rigid body of ac-

quired data, the left-right traversal of the successive

leaf nodes in the two trees for point set in topologi-

cal model and acquired one serves to deﬁne the cor-

responding point-pair match. The label of each topo-

logical model point is assigned to its matching point

in the acquired data.

However, before labeling and building the trees,

there still exists a problem to be solved. Although

we have divided points into different groups and each

one of them represents the rigid body of human, we

still cannot tell the difference between these groups.

For example, which group represents the points at-

tached to the waist? Which one corresponds with

head? More importantly, the segments in the left

part and the right part can not be distinguished and

this left-right ambiguity will result in wrongly labeled

segments. A direct method maybe enumerating each

rigid body and found the right one. Employing this

violent method, the computation cost could be rather

high and the difference between left and right part

of acquired objects can not be told. Also the lost

point mentioned in Section 3.1 must be added into the

proper segment. To solve this problem, we make the

process of labeling carry out articulately based on the

topology provided by the topological model.

We begin to label markers from groups that are

classiﬁed as the lower part of human body. On gen-

eral, the points attached to the waist can be consid-

ered belong to either lower part or upper part, but

the experiments carried out by us suggest that if the

captured object exercises his joint in each degree of

freedom the points on the waist can be divided into

upper part. Then we can ﬁnd out one of the group

within the upper part that has minimal standard devi-

ation between the points pertained to the lower part

and consider them as waist. Then we can build a local

k-d tree for this rigid using the method mentioned in

Section 3.2 and labeling its associated points by the

left-right traversal of the successive leaf nodes in this

local k-d tree and its corresponding one in topological

model.

As the waist rigid has some common points with

other groups, we can use these points combined with

spectral clustering algorithm(Ng et al., 2001) to label

other groups. Here we take the left thigh as an exam-

ple. As shown in Fig. 4, left thigh rigid and waist rigid

share the same point named ”LFWT”. This point will

Figure 4: Example of same points. The blue ellipse rep-

resents the left thigh rigid and the green one is the waist.

The point that is surrounded by a red ellipse is the common

point named ”LFWT”.

be clustered into the rigid of waist because its stan-

dard deviations between other points attached to waist

rigid are closer to zero than the ones belonged to left

thigh rigid, which is the example of lost point men-

tioned in Section 3.1. After labeling the waist group

we can identify which point being ”LFWT”. Then we

add this point into the lower part group and use spec-

tral clustering algorithm(Ng et al., 2001) to identify

individual rigid bodies of the lower part. It is easy to

infer that the group containing point ”LFWT” is the

left thigh rigid and the matching process can be ex-

ecuted. Next, the points in the left calf rigid can be

labeled in the same way. This procedure will be car-

ried out articulately until all the points in each rigid

body have been labeled.

4 EXPERIMENTAL RESULTS

We tested our algorithm on motion capture sequences

from the CMU motion capture database(CMU, 2009),

in which 3D marker trajectories were acquired via Vi-

con system(OMG, 2009). The motion sequences we

used for testing are comprised of 200-1500 frames

and performing, for example, walking, simply exer-

cising his joints, jumping. The frame rate is of 120

frames/sec. Each marker has a non-interrupted trajec-

tory during the whole motion. The topological model

used in our experiments is taken from a subject that

have different scale and pose with the captured data.

It has 41 markers, and the marker set within each rigid

body of this topological model has the same spatial

distribution with acquired data.

For comparison, we use some frames from each

motion sequence and label them by our method and

the method in(Li et al., 2005). Fig. 5 shows labeling

results when these two methods applied to the same

sequences of exercising, jumping and walking. As

the acquired data are quite different from the topo-

logical model, our method performs much better than

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292

Figure 5: Labeling results for different motion sequence. a)

Shows the labeling results of exercising sequences. b) Illus-

trates the labeling results for jumping sequences. c) Shows

the labeling results of walking sequences. The topological

model used in the process of labeling is shown in the left.

The middle is the labeling result obtained by our methods.

The labeling result employed the method proposed in(Li

et al., 2005) can be found in the right.

the method proposed in(Li et al., 2005). We also la-

bel the acquired data which has different levels of dif-

ferences from the topological model using these two

methods. The results are given in Fig. 6. From the re-

sults, we can see that even slightly pose dissimilarity

can lead wrong identiﬁcation using the method in(Li

et al., 2005), but our method works fairly well. The

comparison suggests that our approach is well-suited

for automatically labeling markers from 3D marker

trajectories without the requirement of pose similar-

ity.

To evaluate the accuracy of the method proposed

in this paper, we also applied our method and the

method proposed in(Li et al., 2005) to each frame

of different kinds of motion sequences and the re-

sults are shown in Table 1. From the table, we can

see that our approach performs much better than the

method mentioned in(Li et al., 2005) for all the tested

motions. Using the method proposed by us, all mo-

tion sequences are correctly labeled while the method

in(Li et al., 2005) can only label some or even no

frame. Experiment results show that the method pro-

posed in(Li et al., 2005) is very sensitive to pose sim-

ilarity while our method can work correctly even with

visually obviously different pose.

Figure 6: Different topological model and labeling results.

a) Shows the labeling results using the topological model

that are almost the same as the acquired data. b) Shows

the labeling results using the acquired data that are different

from the topological model with the upper body. The topo-

logical models, labeling results obtained by our method and

the results produced by the method of(Li et al., 2005) are

shown from left to right.

Table 1: Labeling results on different motion sequences.

BHL represents the method proposed by Baihua Li(Li et al.,

2005).

Subject ID Motion Frames

Labeled Frames

Ours BHL

14 20 Exercise 1500 1500 0

06 01 Walking 493 493 0

16 03 High Jumping 409 409 226

16 05 Long Jumping 294 294 116

14 02 Boxing 1000 1000 0

16 44 Running 215 215 0

5 CONCLUSIONS

We have proposed a fully-automatic method for la-

beling markers from their 3D trajectories using local

k-d trees in this paper. Our approach can work prop-

erly even when the captured subject is different from

topological model in pose and scale. The experiment

results show that our approach performs better than

the most closely related methods.

The method proposed in this paper is also very

suitable for the application of clinical gait analysis for

patients. First, the special pose that may be imprac-

tical for disabled people performing is not required

during capturing. Second, it is convenient by remov-

ing the step of motion calibration because patients es-

pecially disabled patients always have difﬁcult in per-

forming motion calibration. Employing the method

proposed here, the only requirement for patients is

walking.

Our labeling method is based on the clustered

rigid bodies, but some rigid bodies are not strictly

BUILDING LOCAL K-D TREE FOR FLEXIBLY LABELING ARTICULATED POINT SETS

293

rigid, for example, the torso of human, especially

when the captured subjects perform vigorous exer-

cises like bending their body too low. In this situation,

our method may wrongly labeled markers attached to

these lax rigid bodies. However, the wrongly labeled

markers can be corrected using the constraint of tra-

jectories’ smoothness or solving the problem of abso-

lute orientation(Arun et al., 1987).

Our approach relies on the assumption that each

marker trajectory must be non-interrupted during the

whole motion. To accomplish the clustering task, we

also have to ask captured objects to exercise his joint

through the full range of motion. Although these

limitations are a little strict, but they can be satis-

ﬁed in practice to ask the captured subject to perform

calibration motion in the middle of capturing area.

This requirementcan effectively reduce the number of

invisible markers and obtain almost non-interrupted

marker trajectories. For the task of clinical gait anal-

ysis, we should let the number of invisible markers

be as less as possible. In future work, we plan to re-

duce the limitations mentioned above in order to label

markers with noisy marker trajectories.

ACKNOWLEDGEMENTS

This work was supported by the Knowledge

Innovation Program of Chinese Academy of

Science(KGCX2-YW-610) and the National Key

Technology Research and Development Program of

China(2008BAI50B07).

REFERENCES

Aguiar, E. D., Theobalt, C., and Seidel, H.-P. (2006). Auto-

matic learning of articulated skeletons from 3d marker

trajectories. International Symposium on Visual Com-

puting, 1:485–494.

Arun, K., Huang, T., and Blostein, S. (1987). Least-squares

ﬁtting of two 3-d point sets. IEEE Transactions on

Pattern Analysis and Machine Intelligence, 9(5):698–

700.

Bentley, J. L. (1975). Multidimensional binary search trees

used for associative searching. Communications of the

ACM, 18:509–517.

Bentley, J. L. (1990). K-d trees for semidynamic point sets.

In Proc.6th Ann. ACM Symp. on Computational Ge-

ometry, pages 187–197.

CMU, G. L. (2009). Motion capture database.

http://mocap.cs.cmu.edu.

Cox, G. S. and de Jager, G. (1992). A survey of point pattern

matching techniques and a new approach to point pat-

tern recognition. In COSMIG’92, Proc. South African

Symposium on Communications and Signal Process-

ing.

Gaede, V. and Gnther, O. (1998). Multidimensional access

methods. J. of Computer Surveys, 30(2):170–231.

Gleicher, M. (1999). Animation from observation: Mo-

tion capture and modtion editing. Computer Graphics,

33(4):51–55.

Guerra-Filho, G. (2005). Optical motion capture: Theory

and implementation. J. of Theoretical and Applied In-

formatics, 12(2):61–90.

Hornung, A., Sar-Dessai, S., and Kobbelt, L. (2005). Skele-

tal parameter estimation from optical motion capture

data. In VR’05,In: Proceedings of the IEEE Virtual

Reality Conference, pages 75–82. IEEE.

Kirk, A. G., O’Brien, J. F., and Forsyth, D. A. (2005).

Skeletal parameter estimation from optical motion

capture data. In CVPR’05,In: Proceedings of the

18th IEEE Conference on Computer Vision and Pat-

tern Recognition. IEEE.

Li, B., Meng, Q., and Holstein, H. (2003). Point pattern

matching and applicationsła review. In SMC’03,In:

Proceedings of the IEEE International Conference on

Systems,Man and Cybernetics.

Li, B., Meng, Q., and Holstein, H. (2004). Articulated pose

identiﬁcation with sparse point features. IEEE Trans-

actions on Systems, Man, and Cybernetics PartB,

34(3):1412–1422.

Li, B., Meng, Q., and Holstein, H. (2005). Similarity

k-d tree method for sparse point pattern matching

with underlying non-rigidity. Pattern Recognition,

38(12):2391–2399.

Li, B., Meng, Q., and Holstein, H. (2008). Articulated

motion reconstruction from feature points. Pattern

Recognition, 41(1):418–431.

Mount, D., Netanyahu, N., and Moigne, J. (1999). Efﬁ-

cient algorithms for robust feature matching. Pattern

Recognition, 32:17–38.

Ng, A. Y., Jordan, M. I., and Y.Weiss (2001). On spectral

clustering: Analysis and an algorithm. In NIPS’01,In:

Proceedings of the 15th Advances in Neural Informa-

tion Processing Systems, pages 849–856. MIT Press.

OMG (2009). Motion capture systems from vicon.

http://www.vicon.com/.

Wolfson, H. and Rigoutsos, I. (1997). Geometric hashing:

an overview. IEEE Transactions on Computational

Science and Engineering, 4(4):10–21.

Yu, Q., Li, Q., and Deng, Z. (2007). Online motion cap-

ture marker labeling for multiple interacting articu-

lated targets. Computer Graphics Forum (Proceedings

of Eurographics 2007), 26(3):477–483.

Zelnik-manor, L. and Perona, P. (2004). Self-tuning spectral

clustering. In Advances in Neural Information Pro-

cessing Systems 17, pages 1601–1608. MIT Press.

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