Editors Laszlo T. K6czy Janusz Kacprzyk Department of Autom ation Systems Research Institute Szechenyi Istvan University Poli sh Acade my of Science... Gyor 'Warsaw

Hungary Poland

Claud iu R. Pozn a Department of Inform ation Technology Szcchcnyi Istvan Unive rsity Gy{)r Hungary

lSSN J l\()(J -')49X ISSN IR60-9-03 (electronic) ISBN ~r;~ - 3 -3 J9-03205-4 ISBN 978-3-319-03206-1 (elloo k) DOl IO . I 007/9n - ~-:' 19-03206- 1

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c Springer lntcm ational Publishing Switzerland 2014 This work is subjec t to copyri ght. All rights arc reserved by the Publi sher, whet her the who le or pan of the rna reriul i ~ concer n ed . 'p -c ifically the rights of translation. reprinting. reus" of illus tration v, rcciuuion. broadcusting, reprod uction on microfilms or ill any other physical way. and transmi ssion or lntonnation storage and retrieval, elec tronic adaptation, computer software , or by similar or dis . imilar methodology now known or hereafter developed . Exempted from this legal reservat ion arc brief excerpts in co nnection with review s or scholarly analys is or material supplied specifically for the purpose of being en tered and executed on 3 computer system , ior exc lusive usc by the purch aser of the work . Du plication of this publication or pM S thereof is permitted only under the provisions of the Copyr ight Law of rhc Publisher' s local ion. in its current version. and permission for usc must always be obtained from Springer. Permissions for usc may be obtained through Rightsl.ink at the Copynghr Clearance Center. Vio lnrions are liable to p rosecut ion under the respective Copyright Law. The usc of ge neral de scripti ve nam es. regis tered names, trademarks. service marks. e tc. in this publication docs not im ply, even in the absence of a specific statem ent, lim such names arc exempt rrom rh.: r" k~ \': ! 11 1 protect ive laws and regulations and therefo re free lor general use. Wh ile the advice nnd informatio n in this boo k are believed to he true and accurate at the dale of publi cation . neit her the Hl11hors nor the: "ditors nor the publisher can accept any legal responsibility for uny err ors or omi ssions Ilwl m"y he made. The publi sher makes no warranty. cxpresx or implied. wi th resp".cl to llll! IIJ:ltl!naJ contained herein.

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reface

dly perceived area of . ( of inteu..ive researc

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Contents

Part I Fuzzy Systems: Theory

Prospects for Truth Valuation in Fuzzy Extended Logic. . . . . . . . . . . 3 'esa A. Niskanen

Coherence and Convexity of Euclidean Radial Implicative Fuzzy Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I5 David Coufal

Pa r i II Fuzzy Systems: Application

Catastr ophe Bond Pricing with Fuzzy Volatility Parameters. . . . . . . . 27 Piotr Nowak and Maciej Romaniuk

Evaluating Condition 01" Bulldings by Applying Fuzzy Signatures nd R-Fuzzy Operations ... , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

.Adam Bukovics and Laszl» T. K6czy

T he Deterrninatiun or the Bitratc on Twisted Pairs by Mamdani Inference Method .... , , , . . . . . . . . . . . 59 Ferenc Lilik and Uiszl6 T. Koczy

Constru ction Site Layout and Building Material Dlsrrlbution Plann ing Using Hybrid Algorithms , 75 Bence Kalmar. Andras Kalmar, Krisztian Balazs and Laszlo T. Koczy

Part ill Neural Network

Accuracy of Surrogate Solutions of Integral Equations by Feedforward Networks . 91 'era Kurkova

SJ)J

xiv Contents

Vehicle Classification Using Neural Networks with a Single Magnetic Detector " 103 Peter Sarcevic

Part IV Clustering and Image Processing

Exemplary Applications of the Complete Gradient Clustering Algorithm in Blointorrnatics, Management and Engineering. . . . . . .. 119 Piotr Kulczycki, Malgorzata Charytanowicz, Piotr A. Kowalski and Szyrnon Lukasik

A Hierarchical Approach for Handwritten Digit Recognition Using Sparse Autoencoder _ . . . . . . . . . . . . . . .. 133 An T. Duong. Hai T. Phan, Nam Do-Hoang Le and Son T. Tran

Fuzzy Single-Stroke Character Recognizer with Various Rectangle Fuzzy Grids _ J45 Alex Tormasi and Uiszl6 T. KOC7.y

Part V Robotic Systems

Delay and Stittncss Dependent Poly topic LPV Modelling of Impedance Controlled Robut Interaction . . . . . . . . . . . . . . . . . . .. 163 Jozsef Kuri, Peter Galambos and Peter Baranyi

Local Center of Gravity Based Gathering Algorithm for Fat Robots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Kalman Bolla, Zsolt Csaba Johanyak, Tamas Kovacs and Gabor Fazekas

Intelligent Robot Cooperation with Fuzzy Communication , 185 A. Ballilgi, L. T. K6ay and C P O/II; l

Indoor Pose Estimation Using 3D Scene Landmarks for Service Robotics _ , 19tJ Tiberiu T. Cocias, Sorin M, Grigorescu and Florin Moldovcanu

Part VI Data Manipulation

A Novel View of Bipolarity in Linguistic Data Summaries 215 Janusz Kacprzyk, Slawomir Zadrozny and Mateusz Dziedzic

sion and -­__ . _

z_ L

_.~... of Dime ed An nealing

1J ontro l

ra tion for Short­

- '~------.~

Indoor Pose Estimation Using 3D Scene Landmarks for Service Robotics

Tiberiu T. Cocias, Sarin M. Grigarescu and Florin Moldoveanu

Abstra ct In this paper, a markerlcss approach for esti mating the pose of a robot using only 3 D visual information is presented. As oppos ite to traditional methods ,our approach makes use of 3D features solely for deterrnining a relat ive position bet ween

e imaged scene (e.g, landmarks present on site) and the robot. Such a landmark is .alculated from stored 10 map of the environment. The recogn ition of the landmark is performed via a 3D Object Retrieval (3DOR) search engine. The prese nted pose estimation technique produces a reliable and accurate pose information whi ch can be - rther used for complex scene understand ing and/or na vigat ion . The pe rformance of

e proposed approach has been evaluated against a traditional marker-based position stirnation library.

Keywor ds 3DOR· Shape matching : Convexity . 3D dcscriptors : Indoor robot avigation . Service robotics

1 Introduction

n the las! few years, cost attracti ve and affordable 3D scanning technol ogy has . awned a large number of algorithms developed for the purpose of analyzing 3D isual information. As a co nsequence. the amoum of 3D models and shapes avail -le for benchmarking, both on the internet and in dom ain-specifi c databases, has .reascd significantly [I]. For the common case of robotic navigation, the precise

- T. Cocins (0 ) . S. M. Grigorescu . F Moldo vcanu :r-pallamenl of Automation, Transilvania University 01" 13r,1 ' c1I'. Brasov. Romania . ail: tiberiu.cociaswunitbv.ro

• ~ I. Grigoresco e-mail: s,grigorcscueiunirbv.ro

:- loldovcanu e-mail: lIIoldof@Ullitbv.T(J

_ T.Koczy cl aJ. (ed s.), Issues and Chall enges ofIn telligent Syst ems Coniputational Intelligence, Studies in Computational Intelligence 530,

-' ")1: IO.J007/97S-3--'19-03206-L15. © Springer International Publishing Switzerland 2014

199

2UO TT C ­

pose of the robot is mandatory for achieving different imposed goals. Thus. {ion. grasping or obstacle avoidance rely exclusively all the estimated poses __ Starting fr orn the presumption {hat the robot uses only machine vision as a pe mechanism. its pose can be estimated using either 20 features [4]. 30 land or a combination of both IS]. Considering strictly the image domain, the Pas Video (PrY) approach tries to determine the robot's pose by observing the in image features from subsequent frames. From another point of view, in the image domain. using a special marker placed in the scene, the pose of the ro be determine..xl relative to the observed marker (6]. The dimension and the pan the marker needs to be a priori established. Further, multiple markers can be for complex scene understanding or for different robotic tasks. Nevertheles... a system has lillie chance to cope with new situations since it is based on a visual markers.

In our approach. the issue of pose estimation addresses only 30 features ex (rom the imaged scene. In this sense. the problem can be spliuco in two main p Firstly, the perceived scene is sea rched fur similaruies against a series of pre­scenes scans. Further, in the second phase, using the previously determined si ities. the posi tion and perspective of the robot is estimated. The search Pf' tackled from the 3D Object Retrieval (3DOR) point of view. Tasks like 3D recognition, complex model segmentation or scene reconstruction are invcstig from the 3DOR perspective [7. S). The main issue related to the 3D object rc engines is reduced to the problem of determining the similarity 01' two given xh or surfaces. In literature, there are several methods thai deals with 20 contours... _ surfaces and volumes or shape statistics 19. 10]. To produce correct correspondc the object retrievalprocess must followa validationstep. In [II]. the validation DC.

based 011a ratio belween Iwo distance samples. whereas in r12J. a fast and sirnple idation algorithm based Oil the slope of the line connecting the corresponding is presented. For a more accurate correspondence validation approaches, met such as the one presented in [13Jmust be used. The main contribution of our pa is the usage of a 3DOR search engine for retrieving the pose of a robot relative 3D landmarks.

The rest of the paper is organized as follows. In Sect. 2. the overall machine vis apparatus is presented. In Sect. 3, the proposed pose estimation approach is describe followed by the performance evaluation results given in Sect. 4.

2 Machine VISionApparatus

The need for robotic pose estimation is mandatory for complex scene undersr andins

or for any other further interaction with the environment The presented approach makes use of previous detected landmarks and their known locations fordetermining a relative position of the robot with respect to the environment. The block diagrarn i Fig. 1 depicts the main components of a robotic pose estimation and object modelling

201 Indoor Pose Estimation Using 3D Scene Landmarks for Sen-ice Robotics

,../ -..,,-- I i'-: g~ f----~:~:------!~~,' ~ ·~t~~Qf' I I

: Information :

l Acquisition: f 3D Scene : , Robotic Volumetric 1 Stereo vision ~ Pose ~ Reconstruction I..... Object

1- ToF cameras ! EsUmation and Modelling , , Segm entation1- Structured light,!(MS Kinect) ! l- Laser scanners: ,1 J'

Fig. 1 Processing flow for robotic 3D pose recon strucn on am] object volumetric modelling in mobile manipulation

fl ow used in mobile manipulation. The pose of The robot is essentia l for achieving an easy and secure robotic grasp configuration.

2.1 Shape Recognition Framework

The main objective of Ihe approach is to find the viewed perspective of the scene inside ~ l large scan representation of the location in which the robot navigates. One reliable search method. with the main aim of finding the similarity between two ;ivcn surfaces, is represented by the 3D Object Retrieval - 3DOR mechanism f141. Conceptually, the 3D Object Retrieval method (~CC Fig. 2) tries to identify a template model (quN y) nrnong a large number of shapes (targets). The origin of the technique ies in the abundance oravailable 3D object representations on the internet. It is used n ainly for object recognition and surface reconstruction.

For a large objects database. the algorithm cannot off er real-time model extrac­11 , hut it compensates with precision and reliability. As depicted in Fig.2, the 'crall structure is coarse divided into two sections: on-line and off- line. TIle first

ub-structure is used 10 process only variable information, such as templates dcscrip­extraction, or correspondence identification and validation. whereas the second

-stru cture deals with static data such as database models or database descriptors omputation. necause a scene is represented by large models, the on-line cornpura­

n of the scene' s descriptors is not feasible . Thus , in pur work. we have calculated

202 T. T. Coc ias e t a; Indoor Pose Est imation Using 3D . ce

.- - --- - ---- -_ -- _ _..- -_ .. ---- ----_. -. - -- -_ .. -- .._ -------_..---- - - - ~ ~

(3)

Estimate Robot Pose

I I Online : ~ :::~ :~ ::::::::::::::::::::::::: ::L:: ~:: : : ~ : :::::: :::::: :::: : :::::::: _ ---..­: I :

: :, ,: :. ,. . : : c l, ., ., ,, ,, . l ~~ 11 ... .. .. • • _ .. .. .. _ .. _ ...... .. .. ..... _ .... _ .. .. .. ...

Fig. 2 Generic 3D object retrieva l sea rch engine fram ework

the descriptors off-line. The similarity between the 3D shape models can occ ur or in the direction of partial matching becau se the robot canno t perceive the entire bac ­bone struc ture of the scene's landmarks. Finally , the database target shape with .. highest confi dence (similarity) is used to estimate the relati ve pose of the robot . Ig. 3 Encod ing a pan icutar local surf

ace. I> S ig nature structure, c Output h'

2.2 Surface Description - res, one or more geometric rneas

subset of the support. Th e . econThe main obj ecti ve nf the 3DOR search engine is to establish valid corresponde unt, mesh trian gles etc.) is uccurnbet ween surfaces. Si mple and di rect point 10 point surface co mparison, ba. ed

uan tized domain (e .g. point coo rdiEuclidean points coord inates, is impossible because of the variable sam pling rat cr a Reference Axis (RA) or a Ipreci sion of different depth se nsors, To overcome this, a descriptor can be use

thod makes usc of both approacrepresent the complex surface of each model involved in the process . The descri re liable local surface descriptor. G ' ha-, as ma in purposc the embedment of the urfuces geometry in a unique repre

- prope r comb ination of signaturation r IO]. The output description is u histogram which maps a cert ain su rface the best choice for rep resen ting inhigh-di mensional, yet finite . vecto r space prese rving in the same time as much in" d the SHOT descriptor for rep~eIllation as possible. In the end, a low -dimension vecto r (his togram) is con stru ct

finition of the RF and histogram 2Shape descriptors can be roughly divi ded in three main categories: (1) fe based; (2) gra ph based and (3) other descriptors types. Because of lhe large occl reg ions 01" the perceived scene, the rob ot can make use only of feature based des c~

tors . Further, the feature based descriptors can be divided in the following su :.3 Shape Simi/mily by Partial gories: ( I) global fe atures; (2) local fea tures; (3) distribution based and (4) . map s, For a reliable similarity estimatio n, only the local features can be used. ;.

robotic platform can perceivein some scen arios, the global structure of the land mark can not be fully observe . a particular landmark can contaithe robotic platform (12). Tn this sense, the specific l iterature po ints out sevcral l

Ie the ex trac tion of any global .descriptors such as: Signature of His tograms of Orien'Iations (SHOT ) [ I I ]. descriptors presented in 2.2.Images (15). Fast Points Features Histogram [161.Spherical harm onics [17]. ~. _

n ': 'ode l.~ (PDM ). that is a tempi teTIle descriptor can describe a sur face thro ugh signatures and/or histogram . ching.firs category represent s the 3D surface nei ghborhood of a given point by deni

mvariant local Ref erence Frame ( R I~) and encoding, accor ding to [he local c

indo or Pose Estimation Using 3D Scene Landmarks for Service Roboti cs 203

(a)

(b) (c)

255o

Fig. 3 Encoding a particul ar local surface using compact refe rence fram e and histograms, a Input surface. b Signature structure. c Output histogram

nates, one or more. geometric measurements compu ted individually on each point of J subset of the support. The second category, the local geometry or topology (point ,:oUI1 I , mesh triangles etc.) is accumu lated into a histogram according to a specific quantized domain (e.g. point coordinates. curvatures) which requires the definition of either a Reference Axis (RA) or a local RF. For the case of SHOT descriptor [ I I I, the method makes usc of hath approaches, that is signatures and histograms , for creating J reliable local surface descriptor. Given the robust RF proposed by the authors and the proper combination or signatures and histograms, the SHOT descriptor is one f the best' choice lor representing incom plete surface models. In our work we have sed the SHOT descr iptor for representing both template and ta rgets. In Fig. 3, the d inition of the RF and histogram generation for a parti cular surface is presented.

1.3 Shape Similarity by Partial Matching

The robotic platform CB Il perceive the scene from only one perspective, Because of is, a particular landmark can contain large occluded region s, thus making impos­

ible the extraction of any global structural information . By using the local feature -ascd descriptors presented in 2.2, the similarity between two given point distrib ­ion models (PDM), that is a templale and" target, can be evaluated using partial tching.

------------

204 T. T. Cocias t:l al. Indoor Pose Es timation Us ing 3D Sceoe

Table 1 Quality measurements fo r hislognlm matchi ng

Distance Mathematical form ulation EXec: match Half ma tch Total mis s-match

measure

d (H[ . H 2)

L: H j'(i) . H2' (i )

CUITeMiOIJ d = /':i :7"T<== =;;;== 1.0 0.7 - 1.0 JH I '2 (i ) . H2' 2(i ) cocff.

Hi.' = f(, (i) - ~ r'I;,H!:(j )

a = L ( !i IU ) - H2U))2 t: ..-::;-ChiSqr 0.0 2.0 j HI U) + H 2(i )

Histogram d = L min(H J (i ). H2(i» 0.5 0.0 intersecnon

Ll-Nonn 0.0 1.0

L2-N orm 0.0 1.0

d = I-I: 0.55 1.0

For each point of the model M = {PO. PI . .. . Pi }, where i = 0 ... nr Points , : histogram H (i ) describing the neighbor point distribution information is genera; By comparing two given histograms. a similarity measure between the region. ca be determined. Further, 10 compute an overall shape simila rity measure, a brute/orr. matching technique can be used. The approach searches for each histogram of I temp/me model. namely the target. which is the most similar histogram inside t second model. T he amount of similarity is given by a similarity quality mea. tire described in the next paragraphs.

Different types of similarity measures can be found in literature, From those \\ mention the correlation coefficient. CliiSqr distance, histosram intersection. the L;­and L2-NOl711 and the Battachurvya distance [18J. Table J centralizes the mathcmat­ical formulation of each measurement technique.

In Table 1, d is the measured distance, HI i. a histogram from the template shape while J-h is the histogram of the target shape. .

Considering the mathematical complexity and the computation lime. the L2-No is one of the most computati onal efficient. If the computational lime is not an imp ' iment , the Hartacharyya distance can be chosen for best precision. The result of t .

matching process is represented by a vector C iu which the template points. repre­sented through histograms. are linked by correspondences (in terms of indexes) wiir

Fig.4 Correspondences matching e. ones the template surface . whereas the (best viewed in col or )

the points from the target model. 11>

where N is the number of points Depending on the size of th

in Sect. 2.2, the number of corre Lof correspondences is low, Thi

Figure 4 illustrates the established ccne, where large flat surface, ar A~ depicted in Fig.4. not al

pointing to wrong surfaces. Thi . cene. In order 10 reject all the ones described in the next sub. ec i

2.4 Correspondence Validation

The aim of the validation procc..

ase o

paper.

- =~

.

L t connections between local reaion . to have only discrimin ative ; urfac size of the RF, which . for the is high. whereas for a larze RF the n the similarity measure. 1;1(hi this issues: ( I) neighbour distanc

The fi rst filter aims at keeping onI deuce c(i ) is considered to be di.produces a ratio factor below 0.7 in Eg.2, is formed using the measured Since all histogram s are norrnaliz

205 Indoor Pose Estimation Using 3D Scene Landmarks for Service Robotics

Fig. 4 Correspondences matching example. The red points highlight the Target surface. the blue ones the template surface. whereas the lines dep icting the computed corresponde nces arc green (best viewed in color)

the points from the target model. Thus. a correspondence c is defined as follows :

where N is the Humber of points defining each shape (target and template). Depending on the size of the reference frame. defined by the descriptors given

In Sect. 2.2 , the number of correspondences varies. For regular surfaces the number of correspondences is low. This is because of the am biguity of the linking process. Figure 4 illustrates the esiabli shed correspondences for the case of an un iversity lobby " ene, where large 11aL surfaces arc present

As depicted in Fig.4 , noL al correspondences are correct. Many of them arc pointing 10 wrong surfaces. This hap pens because of the flat walls present in the scene. In order \0 reject all these bad corres pondences, special filters, such as the nes described in the next subsection . need to be used.

2.4 Correspondence Validation

The aim of the validation process is to filter Ollt the correspondences pointing to wro ng connections between local regions. For a given sce ne clou d M , it is almost impossible . have only discriminative surfaces. The amount of am biguity is con trolled by the ize of the RF, which, for the case of a small RF. the number of bad correspondences ~ igh , whereas for a large RF' the number is milch lower but with the cost of altering

similar ity measure. In this paper, two sequen tial filters are addressed for so lving is issues: ( I) neigh/JOur distance validation and (2) probabilistic slope fi ller. The first filter aims at keeping only discriminative correspondences. A correspon­

..Lnce c(i) is considered to be di scrim inative (c.g. unique) if, its description HI (i) ucc s a ratio factor below 0.7 in the target description. This ratio, described by

;::.y. 2, is formed using the measured similarities with respec t to the target model. Smce all histograms are normalized, the ratio is defined within the interval [0 . 1].

206 .T. T. Coc ias e t _

Fig. 5 Different ratio factors for a se rie s or corres ponde nt regions

disiNNratio = - - - - ­

di .H~' (' ('oltd N N

The two distances involved in the ratio computation arc determined as folio Considering a given template description HI(i ), the question is: which is the m similar correspondent description H2(j) within all target descriptions. This CUi'.

spondence c(i) is considered to have the smallest distance (the highest similari dis/ A' N. Next, biding the previous correspondentdescription /-12(j) . the di S lm 'orr

is computed by determi ning which is the next most similar correspondent /-I: within all targets. where j. k = 0 . .. si re Of ttarget ), Fig.5 shows the compu., target ratio:'> lor different regions of the model.

Using this approach, if a given template description, /-II (i ) , can be found in di ffercnt regions. H2(j) and /-12(k ) of the target model. the resulted corresponde will be rejected fro m the correspondence vector C because the surface is co nside ­

ambiguous, Again, not all remaining correspondences can be considered trustful. Further,

probabilistic slope filte r, tries 10 eliminate all cross correspondences. The princi uses the slope auribun- to filler OUl any bad corre: pondcncc. . The slopes arc computed using tile following equations:

[P I (x ) - P2(X)] [P I C::) - P2(Z) ] 1111 = , TIl') = - --- - ­

[PI (x ) - P2(X)] - [PI (x ) - P2(X»

where, 1/1 1 and 111 2 Me the 211 slopes of the c (i ) that respects 111). 1n2 E M . P

a point in the template model and P2 is a point belonging to the target model Fig.6). The slope is computed from tWO 20 perspectives, namely x Oy and :: as presented ill Eq,3. Using this slopes, a pro babilistic density fun ction (PD F . described in Eq .4 and used 10 estimate a pattern of the slope correspondences. T

core of the PD.... is actually a maximum likelihood estimator (!\rILE) as the one Uti. 5

:!door Pose Estimat ion Usin g 3D Scene ,­

Ig. 6 Co rres ponde nce matchinp exa mple

(a) 1

? Vi

i-:. 0.6

0.4

0.8

(b) 0.25r-- ..--- - ­

0,2 1

_. 7 Probubi l lsric density function ba Is

() = oro

Any correspondence slope exceedinz the determined Gaussian di. tri ­

filter the two input shapes. tempi rdinate system. In Fig.7. the extra c slope distributions can be oh en

The combinat ion of the presented fi . ~ ndences which can be trustworthv

207 Indoor Pose Estimation Using 3D Scene Landmarks for Service Robotics

m

Fig.6 Correspondence matching example

..~ . _ ,; __.•....._._ .

· · · · · · · · · · · r · · · · · · · · · · · · ~ · · · · · · · · · · ·

r ::::::::-~ . _ ~ ...

g,. 0.6 ., Vi 0.4

0.8

(b) 0.25r--~-~-~--~-~----,

0.2

5.0.15 c Vi 0.1

0.05

302010·10·20~3(:::0~*=::::=i:====!=~::3;=*==?

Fig. 7 Probabilistic den sity function based filtering. a Slope dara examples, b Est imated slop e cis

(4)

8 = arg wax L (OIM) (5) OE6!

Any correspondence slope exceeding a certain threshold of the standard deviation rom the determined Gaussian distribution will be rejected . In order to be ab le to use is filter the two input shapes , templ me and target. must be registered in the same

.oordinate system. In Fig. 7, the extraction of the slope panerus for 3 given series of cree slope distributions can be observed.

The combination of the presented filters produces in the end, only reliable corrc­-ondences which can be trustworthy use for further robot P()~C estimation.

208 1. 1. Cocias e __

- _- _

­r,

­

seer

3 Pose Estimation Using 3D Landmarks

The position and orientation or the view point focusing the landmark provides the inform at ion needed to estimate the robot '~ pose. Thus, by relating the pose of ' camera sensor to the scene object, an estimated robot position ins.ce a large sc environment can be determined (e.g , the robot is situated at the first room of tz;

3'rd floor. The goal is to determine the camera pose C using a sci ofcorrespondez

points Pi and the camera' s intrinsic and extrinsic parameters. Firstly, the tran sforrnation matrix thomographv) H R- L between the camera sen

(robot) and the perceived scene (containing the landmark) is used to estimate rotation RR-C and the translation T R-L. A transformation H L-S (see Eq, 6) rcla the perceived scene and the global scene is determined from set of minimum 4 poi HL-S l19].

H = (s~ I)Of 1

where s is the scale factor, R is the matrix rotation and t is the translation rna

For reducing the search space dime nsionality the No rmal Aligned Radial F lure (NARF) key point extractor is used [20] . TIle correspondences between input clouds are computed using the measures from Table l . Once the pairs of c spondent key points are determined using the Pcrspect ive-NiPoint (PNP) algori the homography HL - S between the visible part of the scene and the scene itse obtained , This is actually a rough transformation used to align the robot's perspec to the overall scene. An Iterat ive Closest Point (f CP) determines next a fine c1 alignment. Thus, the robot' s pose is obtained from three hornography rnatrice Eq. 7). namely, the homography between the robot and the imaged surface. the between the seen surface and the overall scene and. in the end . the hornography H generated by the ICP alignment.

4 Experimental Results

4.1 Scene Set-up

For evaluation purposes, different indoor robot navigation scenarios have considered. For imaging the scene, the robot was equipped with a Kinect'" RG sensor. To create the target model s, e.g virtual scans or different chamber a srCK LMS500 laser scaner was used. Two target models were used in this xe a chamher from the Machu Piccliu temple (see Fig. 8) and a lobby from a building, e.g. university building (see Fig. 9).

Indoor Pose Estimation Using 3D SCCI1e'Lar.- -

Ig. 8 Idemifying a spcci fie region inside a • ad the target arc marked with red. wh < •

l a o 9 Idemifyi ng a specific region in .id orcas the lobby target model is biue. The entcd models (best viewed in color)

The similarity between the seen

rmed using the L2-Norm, while the ring distance quality measure and p s represented by a SHOT descript sed marker detection approach \\ a t' s pose with respect to an ificial AR~

A particular region was cropped for pie chamber. Next, using the propo

d to be the template) was searched in . red in a database), III terms of corr

- ry, was represented by 12.72 1 pain -.685 points . Figurc9 illustrate the

209 Indoor Pose Estimation Using 3D Scene Landmarks for Serv ice Robotics

Fig. 8 Identi fy ing a spec ifie region inside a target . The corresponding po ints between the temp late and the target are marked wi th red , whereas the large! points are blue

Fii,:. ':) Ident ifying a sped lie region inside a target. The temp late model (ai r-vents) i shown in red whereas the lobb y l<Irgel model is blue, The 1$"" <:/1 lines depict the cor respondences between the presented models (be st viewed in co lor)

The similarity belween the scene per spectiv e and the dat abase targe ts was per­formed using the L2-Norm, while the correspondences were validated via the neigh­boring disraucequaliIy measure and probabilistic slope fiIter, were used . Each surface was represented by a SHOT descriptor. For evaluation purposes, an ARTool Kr-rC1IJ

based marker det ection approach was used for obtaining a parall el estimate of the robot' s pose with respect to artific ial ARToolKIT landmarks.

A particulur region was croppe d for fl known posit jon ins ide the Machu Picchu temple chamber. Next, using the proposed approach, the cropped region (now consid ­creel to be the templates was searched inside all defined targets (monum ent chambel's stored in a database). In terms of correspondences dimensionality, the template . or :juery, was represented by 12.72] point s, whereas the target model was defined by ~ 4 5 . ()85 points. Figure 9 illustrates the result of the first matching scenario.

210 T. T. Cod as ct al. Indoor Pose Estimation Using 3D Scene

Table 2 Me asured er rors for different robo t pose estima tion scene 3. Gri goresou, S.M.: On robust 3D

_

~

Scene Method Pose errors ~--'------'--------:C--'--------'-------'----'---'---~""'-----:7"-X (mm) y(mm) z(mm) pitch (0) y3W(0)

Machu Picchu Our approach 8.89 33.58 15.11 2.54 1.39 s.is ARTl'oiK it

Lobby Our approach I 1.25 32.79 21.35 3.98 2.69 3 .35 ARToolKil 10.64 18 ,56 15.25 2.25 1.97 2.7S

The highest density of valid correspondences defined the visible pan of the land­mark, which was used for estimating robot's pose. Numerical error results are given in Tabie2 .

Considering the case of a real robotic scenario, a pani cular region , depicting two distinctive ai r-vents, were perceive inside an university lobby. Th e algori thm' configuration was identical to one used in the Machu Pice/III test scenario. From :3

to tal of4l)Y7 sea rched points, describing the templ ate mod e l, 8 valid correspondences and 2 outliers were found inside of 2.798.245 scene points. as shown in Fig. 9.

As seen in Table Z, the presented approach outputs an overall erro r below 5 % f(V' any measured parameter. Because the Ma clut Pice/iii dataset is a standard evaluation scene 1211 . no ARToolKiI grou nd truth information co uld be provided. T he pos ition of the robot was deter mined rela tive to the closest landmark sensed by the sensor.

5 Conclusions

In this paper, a 3DOR engine based robot ic pose estimation technique has bee» proposed. The uonl of the approach is to enable accurate pose estimation using onl; 3D visual informntion ex tracted directly from the imaged scene. Alon g with thi approach, tWO correspondence filter s ' vere integrated with in the 3POR method. Th filters produce dense and accurate correspondences which can he further used f 3D shape recognaion or pose estimation. As future work the authors co nsider ~

enhancement of the computation time thro ugh parallel computational devices (e.g Graphic Pro cessors), as well as the application of the method to other co mput ~

vision arcnx , such as 3D medical imaging.

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