A Markerless Joint Detection through a Hand Geometric Representation

Aline de Faria Lemos

and Nagy Bal

azs Vince

Department of Mechatronics, Optics and Mechanical Engineering Informatics,

Budapest University of Technology and Economics, M

uegyetem rakpart 3. Bldg D, Budapest, Hungary

Keywords:

Joint Position Estimation, Human Hand, Particle Swarm Optimization, Genetic Algorithm, Image Processing,

Optimization.

Abstract:

In several ﬁelds, such as man-machine interface and occupational therapy, the human hand-joint position is

required. Traditional methods usually rely on image processing allied with marker placement, e.g. reﬂexive

marker, which can be time-consuming and uncomfortable for the subject. For these reasons, scientiﬁc efforts

are being made to create reliable and convenient joint tracking. This paper proposes a methodology that

generates geometric ﬁgures to mimic the hand conﬁguration. This process is made possible by an optimization

algorithm, which ﬁnds the most suitable placement of these geometric shapes. One time the real hand and the

created representation share similar features, the joints position can be estimated. Two optimization algorithms

were employed: particle swarm optimization and genetic algorithm. In both cases, satisfactory results were

obtained. Although, particle swarm optimization marginally outperformed the latter method.

1 INTRODUCTION

The human hand and its ability to manipulate objects

with dexterity are hallmarks of human evolution. It

is through the hand that much of the mechanical hu-

man iterations with the world take place. The hand

performs mechanical tasks ranging from the use of

high force to functions that require delicacy and pre-

cision (Leon et al., 2013; Barroso, 2010). The ver-

satility of the hand is possible due to the complexity

of its structure and its reﬁned control, which enable

the execution of multi-digital prehension and pinch

movements (Hagert et al., 2012; Souza et al., 2015).

The study of the human hand and the characteriza-

tion of pinch function have an important role in mul-

tiple ﬁelds (Gruji

c and Bonkovi

c, 2015), such as the

study of pathologies (Kingsbury et al., 2014; Bar-

roso et al., 2011; Coimbra, 2011), rehabilitation of

upper limbs (Musiolik, 2008; Barroso et al., 2011;

Neves, 2011), development of man-machine interface

(Matsubara and Morimoto, 2013; Adams et al., 2015;

Endo and Kawasaki, 2015), design of robotic arms

and biomechanical models (Leon et al., 2013; Saikia,

2014; Quigley et al., 2014; Deimel and Brock, 2016).

The analysis of hand articular movement can be

performed by different equipment or procedures. Tra-

https://orcid.org/0000-0001-9898-6370

https://orcid.org/0000-0002-8489-7200

ditional methods usually rely on manual measure-

ments, e.g. manual goniometry, or marker-based tech-

niques, e.g. stereophotogrammetry (Barroso et al.,

2007). Although the manual goniometer is the most

frequently used technique, its inter-rater reliability is

criticized (Crasto et al., 2015). On the other hand,

marker-based techniques can be time-consuming and

uncomfortable for the subject. Nowadays, the litera-

ture contains promising markless solutions for hand

tracking and pose estimation (Zhou et al., 2016; Su-

pancic et al., 2015; Sridhar et al., 2015; Mueller et al.,

2017; Mueller et al., 2018). However, no benchmark

was established. For this reason, hand joint estima-

tion is still an open research challenge. This work

presents a methodology to generate a geometric hu-

man hand model. The underlying concept of genera-

tion process leverages image processing allied to op-

timization methods. From this model, joint positions

are estimated, which composes in the main goal of the

paper: a markerless hand joint detection method.

2 METHODOLOGY

The present study consists of a human hand joints de-

tection algorithm, which is composed of digital im-

age processing allied to optimization techniques. The

method is based on reconstructing the pose present

626

Lemos, A. and Vince, N.

A Markerless Joint Detection through a Hand Geometric Representation.

DOI: 10.5220/0008971706260633

In Proceedings of the 12th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2020) - Volume 2, pages 626-633

ISBN: 978-989-758-395-7; ISSN: 2184-433X

in certain hand image by placing polygons over the

hand dorsal surface and hand segments, creating a

low-resolution representation of the hand based on

geometric shapes where all the geometric properties

are known. For instance, hand segments can be ap-

proximated by rectangles, information about the ac-

tual shape of the segment is lost. However, informa-

tion about the position and dimension is preserved.

Conceptually, it is easy to grasp the feasibility of

the task in hand. The human mind can trivially draw

a geometric representation of the hand which cap-

tures relevant information about joints’ position, Fig.1

shows such representation. The procedure to auto-

matically create this representation can be interpreted

as a search algorithm, where the parameter space is

composed of shape’s deﬁnitions. Particle Swarm Op-

timization (PSO) and Genetic Algorithm (GA) were

proposed to ﬁnd the most suitable conﬁguration ac-

cording to the divergence from the hand and the ge-

ometric representation. The remainder of the section

explains in detail each step of the procedure.

Figure 1: Illustration of a possible arrangement of the drawn

polygons, in contrast to a hand picture.

2.1 Cost Function

The cost function is summarized in the Fig. 2. It re-

ceives a series of geometric ﬁgures parameters as in-

put and is composed of two modules, ”Draw poly-

gons” and ”Pattern recognition”. The ﬁrst creates an

illustration of the human hand by using geometric ﬁg-

ures, which are drawn by using the parameters con-

tained in the particle values. The second uses a pat-

tern recognition technique, based on XOR logical op-

eration, to compare the polygons image to a picture

of the human hand. The function outputs the area per-

centage of the resulting image in relation to the hand

picture. The mentioned modules are detailed in the

following subsections.

Input(polygons

parameters)

Drawabinaryimage

containingthepolygons

Binaryimageofthe

humanhand

Patternrecognition

(pixeltopixelXOR

betweenbothfigures)

Output(percentageof

blackpixelsfromthe

previousstepresulting

imageinrelationto

blackpixelspresentin

thebinarypictureofthe

humanhand)

CostFunction

Figure 2: Cost function block diagram.

2.1.1 Draw Polygons Module

”Draw polygon” is the module responsible for cre-

ating a new binary image containing six geometric

ﬁgures: one trapezium and ﬁve rectangles. These

polygons are meant to compose an illustration that

imitates the posture of a human hand in a superior

view. Fig. 1 illustrates a possible arrangement of the

geometric ﬁgures in contrast to a hand picture. The

polygons are mandatorily connected to each other by

their extremities. The advantage of this constraint is

twofold, it ensures physiology soundness (since it is

known the linkage between segments), and reduces

the complexity of the task (since it lowers the number

of parameters to be deﬁned). These connections are

also the estimated joint positions and are illustrated by

the red dots present in Fig. 1. For the purpose of fa-

cilitating joint referencing, they were enumerated in

the following sequence: index ﬁnger metacarpopha-

langeal, proximal and distal interphalangeal joints

and thumb metacarpophalangeal and interphalangeal

joints, as illustrated in Fig. 3a

The polygons are drawn considering that the hand

is executing a cylindrical pinch movement. In this

case, the ﬁrst polygon to be drawn is a trapezium,

which represents the dorsal surface of the hand. Rect-

angles 2, 3 and 4 correspond to proximal, medial and

distal phalanges of the index ﬁnger. Similarly, rectan-

gles 5 and 6 stand for proximal and distal phalanges

of the thumb.

The geometric ﬁgures are created from their ver-

tex points, which are calculated from the parameters

A Markerless Joint Detection through a Hand Geometric Representation

627

shown in Fig. 3b. They are the input of the cost func-

tion and, consequently, the particle value, which in-

cludes 23 variables. In this ﬁgure, D indicates a di-

mension, θ are the rectangles angular positions and

P is a Cartesian point. The particle includes only

the y coordinate of the points PR2, PR5, P1 and P2

and both y and x coordinates of the points P3 and P4.

The ﬁrst number of this nomenclature correlates to the

polygon index. On the other hand, the second number

classiﬁes the variable into height (1) or width (2). Ta-

ble 1 contains all cost function input variables, along

with their description.

(a)

(b)

Figure 3: Illustrations containing the adopted nomencla-

ture. a) Joint enumeration for the purpose of facilitating

joint referencing. b) Cost function input data used to create

the polygons.

2.1.2 Pattern Recognition Module

The polygons image, generated on the ”draw poly-

gons” module, is compared to a human hand picture

to achieve the polygons’ best positions and dimen-

sions. To proceed with this comparison is crucial to

segment the hand picture by extracting the hand re-

gion from the image background. Thresholding was

the elected segmentation approach for this purpose.

In this method, the hand image, acquired in RGB, is

Table 1: Description of the cost function input data used to

create the polygons.

Variable

Polygon

Description

y coordinate of vertex 1

y coordinate of vertex 2

x coordinate of vertex 3

y coordinate of vertex 3

x coordinate of vertex 4

y coordinate of vertex 4

D21

Polygon height

D22 Polygon width

PR2

y coordinate of PR2 point

Polygon angular position

D31

Polygon height

D32 Polygon width

Polygon angular position

D41

Polygon height

D42 Polygon width

Polygon angular position

D51

Polygon height

D52 Polygon width

PR5

y coordinate of PR5 point

Polygon angular position

D61

Polygon height

D62 Polygon width

Polygon inclination angle

converted to grayscale. Then, the foreground is ex-

tracted from the image by applying thresholding to

the grayscale image, which results in a binary image

of the hand.

A pixel to pixel XOR logical operator is applied

to perform the comparison between the polygons im-

age and the binary human hand image. It consists of

an XOR operation between each pixel of the poly-

gons image and its correspondent pixel in the hand

image, similarly to methods present in the available

literature (Bovik and Desai, 2000; Koukounis et al.,

2011; Mookdarsanit et al., 2015; de Faria Lemos

et al., 2017). An analogous procedure is illustrated

in Fig. 4. In this ﬁgure, I1 represents a setpoint im-

age to which image I2 will be compared. The pixel to

pixel XOR operation is applied to these images (sec-

ond line of the illustration), resulting in the last ﬁgure

of the illustration.

The output of the ”pattern recognition” module is

the percentage between the number of black pixels

in the resulting image of the XOR operation and the

number of black pixels in the binary hand picture.

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

628

Figure 4: Illustration of a pattern recognition procedure by

using a pixel to pixel XOR operation. Source: (Bovik and

Desai, 2000), modiﬁed.

2.2 Optimization

Evolutionary algorithm is a set of algorithms applied

in complex search and optimization tasks, which re-

semble natural evolution. Based on Darwinian evolu-

tionary theory, genetic algorithms are the most pop-

ular techniques among them (Mirjalili and Lewis,

2016; Rashedi et al., 2009). In these algorithms,

a population of candidate solutions is, usually, ran-

domly generated and evaluated to select population

members who survive to reproduce. A recombination

process builds new individuals by application of the

crossing operator on the selected individuals and mu-

tation is applied to the descendants (Holland, 1992;

Holland et al., 1992; Sastry et al., 2005).

Proposed by Eberhart and Kennedy (Eberhart and

Kennedy, 1995), particle swarm is an optimization

algorithm based on social–psychological principles.

In this algorithm, all particles survive, contrary to

the selection method, used in evolutionary algorithms

(Kennedy, 2010). The method simulates birds’ preda-

tory behavior and uses the input parameters to deﬁne

a particle in the high dimension search space. The

searching direction of each particle is updated by its

best solution and also by a global best solution, which

is the best solution among all the particles that com-

pose the swarm (Rashedi et al., 2009; Feng et al.,

2018).

To optimize the cost function, described in the

previous subsection, the MatLab modules ”ga” and

”particleswarm” were elected to perform genetic al-

gorithm and particle swarm optimization, respec-

tively. The ﬁrst used gaussian mutation with a migra-

tion fraction of 0.2. Similarly, crossover rate, pareto

fraction and population size were selected as 0.8, 0.35

and 200. As for the latter, the optimization parame-

ters chosen for PSO were adaptive inertia with a range

of 0.1 to 1.1, swarm size, learning factor of cognitive

component and social component were respectively

set to 100, 1.49 and 1.49. The parameter sets for

both optimization methods were chosen by an itera-

tive approach, in which the best parameter combina-

tions were selected from the several tested groups.

Both methods shared the same input images and

search spaces for comparison purposes. However, ﬁve

different scenarios were created to provide sensitivity

analysis. The range of rectangles angular positions

were ﬁxed as 45 degrees in all simulated scenarios. In

contrast, the range of point positions and dimensions

started with the amount of 10 pixels and increased

to 20, 30, 40 and 50 pixels on subsequent scenarios.

These range values were chosen to vary around the

smallest hand segment dimension, which corresponds

to the width of the index ﬁnger distal phalanx, approx-

imately 40 pixels.

2.3 Images Acquisition

The human hand pictures used as comparison images

of the pattern recognition module are presented in

Fig. 5. These images were captured from a single sub-

ject while performing cylindrical pinch movements in

a controlled environment. They were acquired by a

Basler acA640 − 750um USB 3.0 camera with reso-

lution (HxV ), pixel size (HxV ) and frame rate of 640

px x 480 px, 4.8 µm x 4.8 µm and 751 fps equipped

with Basler lens C23 − 1216 − 2M with ﬁxed focal

length of 12 mm, aperture range from F1.6 - F16 and

a resolution of 2 megapixels.

Figure 5: Pose images used in the experiment. These im-

ages were acquired from a single subject while performing

a cylindrical pinch movement.

A Markerless Joint Detection through a Hand Geometric Representation

629

3 RESULTS AND DISCUSSION

This work aims to estimate ﬁve human hand joint po-

sitions, which are enumerated in Fig. 3a, from hand

images. These images were acquired from a single

subject while performing a cylindrical pinch move-

ment. In total, 4 different pose images were used in

the experiment, as presented in Fig. 5. For each pose,

5 distinct ranges of search space were selected, as dis-

cussed in section 2.2, and all tests were performed

using both optimization methods: PSO and GA. In

summary, 40 particular experiments were performed,

totalizing in 200 estimated joint positions.

In order to quantify the estimated joint positions’

performance, the positions of the joints were com-

pared with the human-annotated position. Naturally,

the actual location of the joint is not a single point,

rather a region. These regions were deﬁned as cir-

cumferences of 20 pixels radius for joints 1, 4 and 5

and 15 pixels radius for joints 2 and 3. The center

of each region was chosen as a physiologically suit-

able point for the joint position. The interpretation of

the positive result is here deﬁned as a point that falls

inside these regions, Table 2 synthesizes the results

achieved according to each scenario. Table 2 also

shows the maximum, minimum and average perfor-

mance of the scenarios in terms of the cost function

values described in section 2.1.2.

Considering all 20 experiments performed by each

optimization method, PSO outperforms GA in the

overall accuracy of positive results, with an assertive

rate of 82% of estimated joints placed inside the ﬁt-

ting regions, in contrast to 80% correctly estimated

by GA. PSO also achieved greater performance, with

8.8% on average in terms of the cost function values,

while GA obtained 10.1%.

The performance of the methods can also be esti-

mated by the distance between the output and the cen-

ter of the ﬁtting regions. These differences are labeled

from this point of the text as position errors. Fig. 6

shows the behavior of the distance from the center of

the joint over the adopted ranges. Even though a clear

relationship between the performance and adopted

range does not arise in either method, PSO showed

less variance in performance. It is worth to mention,

that the adoption of greater pixel range translates to a

more generalist method, allowing a wider gamma of

hand sizes.

The performance of the method can also be vi-

sualized grouped by joint individually, as shown in

Fig. 7. This ﬁgure displays the dispersion of the po-

sition errors for each optimization method in contrast

to the ﬁtting regions. At ﬁrst glance, it can be noticed

that for the majority of the joints present a component

Table 2: Results achieved by both optimization methods ac-

cording to each range of search space. Maximum, mini-

mum and mean percentage refers to the performance of the

scenarios in terms of the cost function values and positive

results indicate the total of assertive estimated joints.

Adopted

Range

Comparison

Parameter

PSO GA

50 px

Max. pct. [%] 7.1 9.3

Min. pct. [%] 6.3 7.4

Mean pct. [%] 6.9 8.1

Positive results 15/20 17/20

40 px

Max. pct. [%] 8.0 12.7

Min. pct. [%] 5.8 8.7

Mean pct. [%] 7.0 10.2

Positive results 19/20 14/20

30 px

Max. pct. [%] 10.7 10.6

Min. pct. [% 7.0 8.1

Mean pct. [%] 8.8 9.5

Positive results 15/20 18/20

20 px

Max. pct. [%] 9.9 10.6

Min. pct. [%] 8.0 8.7

Mean pct. [%] 8.9 9.6

Positive results 17/20 15/20

10 px

Max. pct. [%] 17.4 17.5

Min. pct. [%] 8.8 9.0

Mean pct. [%] 12.4 12.9

Positive results 16/20 16/20

Figure 6: Sensibility analysis: Distance from region center

versus range.

of systematic error. However, the number of exper-

iments executed at this point is not large enough for

drawing conclusions. Future possibilities regarding

this fact will be mention on 4. On the other hand, it

is clear that there is a predominance of position errors

within the ﬁtting position.

Fig. 8 exempliﬁes the joint tracking result for an

arbitrary position and range. The ﬁgure is referent to

the result of the Particle Swarm Optimization method.

Because of the consistency across simulations led the

ICAART 2020 - 12th International Conference on Agents and Artiﬁcial Intelligence

630

(a)

(b)

(c)

(d)

(e)

Figure 7: Dispersion of the position errors for each opti-

mization method in contrast to the ﬁtting regions (dashed

line). a) Joint 1 - metacarpophalangeal joint of index ﬁnger;

b) Joint 2 - proximal interphalangeal joint of index ﬁnger;

c) Joint 3 - distal interphalangeal joint of index ﬁnger; d)

Joint 4 - metacarpophalangeal joint of thumb; e) Joint 5 -

interphalangeal joint of the thumb.

authors to elect it as the standard method of optimiza-

tion. In the ﬁrst image, Fig.8a, it is shown the output

of the XOR operation between the binary image of

the hand and its geometric representation. While in

Fig.8b the overlapped image from the hand and the

estimated joints are exhibit.

(a)

(b)

Figure 8: Example of a joint tracking result for an arbitrary

position and range. a) Output of the XOR operation be-

tween the binary image of the hand and its geometric rep-

resentation. b) Overlapped image from the hand and the

estimated joints.

4 CONCLUSIONS AND FUTURE

WORK

The position tracking of the hand joints has a diverse

gamma of application. Even though the literature of-

fers some solution, there is no convergence or es-

tablished approach. This work presented a novel al-

gorithm which utilizes two metaheuristic search ap-

proach allied to a simple image processing technique

to build a geometric representation of the human hand

while performing cylindrical pinch. From this model

is possible to derive joint positions through marker-

less digital images, information which is crucial in

certain ﬁelds, such as occupational therapy.

A Markerless Joint Detection through a Hand Geometric Representation

631

Future works should be carried out addressing but

not limited to these shortcomings:

1. Data Collection: As pointed out previously, the

lack of standardized, open-sourced dataset still

limits research in the ﬁeld. Data collection should

be carried out to support more robust solutions.

2. Models Building: The search for the most suit-

able optimization method is far from exhausted,

different solutions should be tested (e.g. artiﬁcial

immune system).

3. Models Integration: Support models can be

applied to boost effectiveness (e.g. population

creation schemes, dynamic bounds, occlusion

solver).

4. Error Analysis: Patterns in the error distribution

might arise when considering a bigger dataset,

which can be leverage (e.g. Error regression mod-

els).

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