research article rotational kinematics model based

Research ArticleRotational Kinematics Model Based Adaptive Particle Filter forRobust Human Tracking in Thermal Omnidirectional Vision

Yazhe Tang12 Jun Luo1 Y F Li2 and Xiaolong Zhou3

1Department of Precision Mechanical Engineering Shanghai University Shanghai 200072 China2Department of Mechanical and Biomedical Engineering City University of Hong Kong Kowloon Hong Kong3College of Computer Science and Technology Zhejiang University of Technology Hangzhou China

Correspondence should be addressed to Jun Luo luojunshueducn and Y F Li meyflicityueduhk

Received 16 June 2014 Accepted 3 September 2014

Academic Editor Shouming Zhong

Copyright copy 2015 Yazhe Tang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a novel surveillance system named thermal omnidirectional vision (TOV) system which can work in totaldarkness with a wild field of view Different to the conventional thermal vision sensor the proposed vision system exhibits seriousnonlinear distortion due to the effect of the quadratic mirror To effectively model the inherent distortion of omnidirectional visionan equivalent sphere projection is employed to adaptively calculate parameterized distorted neighborhood of an object in the imageplane With the equivalent projection based adaptive neighborhood calculation a distortion-invariant gradient coding feature isproposed for thermal catadioptric vision For robust tracking purpose a rotational kinematic modeled adaptive particle filter isproposed based on the characteristic of omnidirectional vision which can handle multiple movements effectively including therapid motions Finally the experiments are given to verify the performance of the proposed algorithm for human tracking in TOVsystem

1 Introduction

With the developing of computer vision and artificial intelli-gent automatic surveillance system becomes a hot researchtopic in this decade Conventionally most surveillance sys-tems [1 2] adopt the traditional visible spectrum camera forparticular monitor purpose However this kind of systemhas limited application as it relies on the proper illuminationand has a narrow field of view This paper proposes tointroduce a novel TOV surveillance system Compared to theconventional sensor the proposed system can work in totaldarkness with a global field of view

In computer vision community visual tracking [3ndash5]is an important research topic for automatic surveillancesystem [6] Many intelligent vision systems [5 7] have beendeveloped during this decade However most of them focuson the conventional imaging system In [8] the authorsadopted support vector machine (SVM) [9] for classificationand use Kaman filter to integrate with mean shift for trackingpedestrian in thermal imagery Yasuno et al presented a

system for pedestrian detection and tracking in far infraredimages They employed the P-tile method to detect thepedestrian firstly Then the detected pedestrian becomes thetemplate formatching to realize tracking purpose [10] In [11]the authors presented a two-stage template-based methodcombined with an Adaboosted classifier for pedestrian detec-tion in thermal image In [12] a generalized expectation-maximization (EM) algorithm is used to separate infraredimages into background and foreground layers first andthey incorporated with SVM for pedestrian classificationThen they presented a graph matching-based method forthe tracking purpose A vision based approach to track thehuman on a mobile robot using thermal images is presentedin [13] The approach combines a particle filter with twoalternative measurement models for tracking

To enable surveillance with a wide field of view acatadioptric omnidirectional sensor is adopted The omnidi-rectional camera as a novel imaging sensor has drawn lotsof concerns in computer vision community in these decadesCompared to the conventional vision sensor omnidirectional

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 347497 11 pageshttpdxdoiorg1011552015347497

2 Mathematical Problems in Engineering

Omni-image Distortion-invariant gradient feature Classifier Particle filter Tracked

targets

Rotational kinematic model

Figure 1 The schematic diagram of the proposed tracking system for TVO

camera can provide a 360∘ view of the environment in a singleimagewith a compact system configurationTherefore itmayhave a great promise for a wide range of applications [14]especially if in the situation requires a wide field of view In[15] a fisheye omnidirectional tracking system is presentedThey used the optical flow to detect the target and employcolor histogram integrating with kernel based particle filterto realize single target tracking in omnidirectional visionIn [16] the authors presented a catadioptric omnidirectionalsurveillance system which uses multibackground modelingand dynamic thresholding to make a target tracking in theclutter field to spot the sniper at the battlefield In additionsome algorithms utilize the color information to integratewith the particle filter for tracking in omnidirectional vision[15 17 18]

Thermal vision presents a temperature field distributionof the surrounding environment using single channel of graylevel intensity Color or texture information may be unstableto be used in thermal image However temperature fieldmakes the contour information become salient Thereforecontour information should be considered as an importantclue that can be used to distinguish the object from the otherin thermal vision However it is difficult to directly applythe most conventional contour features to the catadioptricomnidirectional vision due to its nonlinear distortion [19] Acommon solution is to unwarp the distorted omnidirectionalimage to a panoramic image or transform the coordinate oflocal area of omnidirectional image into a rectified imagefollowed by using of conventional algorithm [2] Howeverthe computational load of this method is extensive as theinterpolation is involved Furthermore it may introducenoise in the image which will degrade the performance ofthe algorithm Moreover underlying distortion still exist inthe rectified image Nowadays it is more and more con-sidered that the rectangular window and template matchingcommonly used in traditional images are not adapted forcatadioptric vision due to their serious nonlinear deforma-tion To solve the problem of distortion this paper adoptsthe equivalent theory proposed by Geyer and Daniilidisto model the single viewpoint catadioptric sensor with atwo-step projection via a unitary sphere centered on thefocus of the mirror (Geyer and Daniilidis 2001) [20] Wedefine a spatial gradient coding template on the equivalentsphere and achieve a distortion adaptive coding templatein the image plane through model back-projection Withthe modeled distortion-adaptive neighborhood a distortion-invariant gradient coding feature is developed for TOV Forrobust tracking we propose to develop a rotational kinematicmodel based particle filter based on the characteristic of

our system Compared with the zero-velocity model theproposed tracking algorithm should be able to handle morechallenging situations including rapid movement Due tothe involvement of kinematic model the proposed trackeris able to predict the state of target more reasonably with asmall number of particles Althoughocclusion is an extremelychallenging situation in thermal vision the proposed track-ing algorithm is able to handle the short term occlusioneffectively based on the distinct kinematic state of a targetduring tracking process Finally a series of experiments aregiven to verify the effectiveness of the proposed algorithmThe schematic diagram of proposed tracking approach isshown in Figure 1

The remainder of this paper is organized as followsSection 2 introduces the principle of the equivalent sphereprojection and the proposed distortion-invariant neighbor-hood adaptive gradient feature Section 3 presents the pro-posed rotational kinematic model based adaptive particlefilter for omnidirectional vision A series of qualitative andquantitative analyses are given in Section 4 to verify the per-formance of proposed algorithm Finally Section 5 concludesthis paper

2 Equivalent Projection ModeledGradient Coding Feature

21 Equivalent Projection Based Adaptive Neighborhood Def-inition The adaption of the neighborhood is essential toguarantee the accuracy of visual tracking Conventionalneighborhood of a given point for the perspective imagesis usually simply defined as the square region centeredat this point Central catadioptric omnidirectional visionexhibits serious nonlinear distortion due to the involvementof a quadratic reflection mirror Therefore conventionalneighborhood definition is not appropriated for catadioptricimages because it does not take into account the distortion ofthe image

Catadioptric omnidirectional vision which can be mod-eled by a unified projection model was introduced by Geyerand Daniilidis [20] who have demonstrated the equivalencewith projection via a unitary sphere centered on the focusof the mirror This two-step projection consists first inprojecting a 3D point 119875

119908to sphere from the center of the

sphere 119874119888 The next step consists in projecting the point on

the sphere 119875119904to the image plane from a point 119874

119901placed

on the optical axis to obtain a pixel point 119875119894(Figure 2) The

equivalence is very interesting since it allows performingimage processing in a new space in which deformationsare taken into account In order to deal with distortions

Mathematical Problems in Engineering 3

Op

Oc

Ps

Pw

Pi

Figure 2 Equivalence projection of catadioptric system

we suggest working in the equivalent sphere space Thissphere surface can be represented using spherical angles theazimuth 120579 isin [minus120587 120587] and the elevation 120601 isin [minus1205872 1205872] Thelocalization of a point with spherical coordinates is definedby two parameters (120579 120601)

Let us define a point 119883119878on the sphere S2 at 119883

119878= (120579 120601)

and its corresponding point in the image plane is 119883119894 Then

the spherical neighborhood of 119883119878 noted 119873

119878(119883119878) is defined

as

119873119878(119883119878)

= (1205791015840

1206011015840

) isin 1198782

|100381610038161003816100381610038161205791015840

minus 12057910038161003816100381610038161003816le 120579thresh

100381610038161003816100381610038161206011015840

minus 12060110038161003816100381610038161003816le 120601thresh

(1)

where 119873119878(119883119878) is the set of spherical points contained in the

surface patch centered at 119883119878and whose ranges along 120579 and

120601 directions are 120579thresh and 120601thresh respectively Correspond-ingly the neighborhood 119873

119894(119883119894) of a point 119883

119894in the image

plane I2 is defined as the pixels that lie in the projection of thespherical neighborhood of its spherical point onto the imageplane

22 Equivalent Projection Modeled Gradient Coding FeatureTracking in the TOV is difficult as limited information canbe utilized in thermal image coupled with serious nonlineardistortion of catadioptric vision A thermographic camerais a device that forms an image using infrared radiationDifferent to the conventional visible image thermal imagereflects the temperature field distribution of the object orthe environment Therefore only one channel of gray levelpixel represents the intensity of the temperature range thatis to say fewer features can be employed in thermal imageHowever contour information is salient over the temperaturedistribution image and it is a stable clue which can beused to distinguish the object from the others in thermalimage Coupled with catadioptric sensor the contour featurepresented in the image is seriously deformed This paperpresents an adaptive neighborhoodmodeled gradient codingfeature for TOV based on the equivalent sphere theory torealize a distortion-invariant target representation for visualtracking Before applying the feature coding the algorithmshould calculate the gradient over the image samples as (2)to generate the gradient map With the equivalent projected

Figure 3 Adaptive neighborhood based feature coding template forgradient extraction

neighborhood model the distortion-adaptive coding tem-plate can be obtained To enable an even codingwe uniformlydefine a series of spatial conics in the spherical coordinatesystem with the specific angle interval in the azimuth andelevation directions respectively The interface between theunit sphere and spatial conic on the sphere is the definedspatial coding template which can be used to back-project inthe image plane for the distortion involved coding templategeneration (Figure 3) As shown in Figure 3 the area ofthe coding units varies due to the effect of distortion Toeliminate the effect of area difference between the codingunits the gradient information inside the coding units isaveraged for unit-normalization This step can transformthe distorted contour feature inside the units to a normalspace Through the distortion normalization the proposeddistortion-invariant gradient information can be obtainedThe normalized gradient features inside the coding unitsare concatenated to formulate the final contour codingdistortion-invariant feature and it will be classified by thesupport vector machine (SVM) For training purpose we candirectly extract the gradient feature from the conventionalrectangle images Then the trained classifier can be appliedover to the distortion-invariant gradient feature for classifi-cation Consider

119892 (119909 119910)

= radic(119868 (119909 119910) minus 119868 (119909 minus 1 119910))2

+ (119868 (119909 119910) minus 119868 (119909 119910 minus 1))2

(2)

3 The Adaptive Particle Filter

Particle filter [21ndash23] is also known as Sequential MonteCarlo method (SMC) which has been widely used innonlinearnon-Gaussian Bayesian estimation problems InBayesian framework the aim of particle filter is to recursivelyestimate the hidden state 120601

119896 given a noisy collection of obser-

vations 1199111119896= 1199111 1199112 119911

119896up to time 119896 (119896 = 0 1 2 3 sdot sdot sdot )

Suppose that posterior 119901(120601119896minus1| 1199111119896minus1

) at time 119896 minus 1 is avail-


able the posterior 119901(120601119896| 1199111119896) can be obtained recursively

by prediction and update The prediction stage makes useof the probabilistic state transition model 119901(120601

119896| 120601119896minus1) to

predict the posterior probability of time instant 119896 as 119901(120601119896|

1199111119896minus1

) = int 119901(120601119896| 120601119896minus1)119901(120601119896minus1| 1199111119896minus1

)119889120601119896minus1

When observa-tion 119911

119896is available the state posterior can be updated using

119901(120601119896| 1199111119896) = 119901(119911

119896| 120601119896)119901(120601119896

10038161003816100381610038161199111119896minus1 )119901(119911119896 | 1199111119896minus1)where 119901 (119911

119896| 120601119896) is characterized as the observation model

Therefore state transition model and observation model aretwo important components to enable the tracking perfor-mance of particle filter

31 ObservationModel Observationmodel characterizes theobservation likelihood of the particle filter It is an importantcomponent to measure the probability confidence of theobserved data for state updating In this paper we employ thepossibility confidence 119902 of the classifier to effectively calculatethe observation likelihood Accordingly a parameter 119889 isdefined tomeasure the similarity between a sample candidateand a standard positive sample (equation (3)) Then theobservation model 119901(119911

119896| 120601119894

119896

) can be obtained by (4) where120582 is the variance as follows

119889 = 1 minus 119902 (3)

119901 (119911119896| 120601119894

119896

) prop exp (minus120582 sdot 1198892) (4)

119908119894

119896

prop 119908119894

119896minus1

119901 (119911119896| 120601119894

119896

) (5)

With the given observation model the weight 119908119894of particles

(equation (5)) can be calculated to effectively guide theparticles for tracking purpose

32 Adaptive Rotational Kinematics Based State TransitionModel The state transitionmodel characterizes the kinemat-ics of target in tracking process With a fixed system noisevariance 120590

119905 zero-velocity Gaussian state transition model

could well handle the random work if the system variance120590119905can cover the unit translation of target However it may

have a limited performance when the system variance is lessthan the unit displacement of target such as rapidmovementAlthough its performance can be improved by increase ofvariance 120590

119905but it also may result in computational ineffi-

ciency as many more particles are needed to accommodatethe large noise variance Particularly in the thermal vision astate transition model with a high noise variance is very easyto involve much interference

Based on the characteristics of the omnidirectional imagethis paper proposes to apply the polar coordinate system inthe image plane For dynamic tracking application we importa rotational kinematic model [24] into the particle filterAccording to the rotational kinematics in polar coordinatewe decompose the kinematic model into angle and radialdirections With the proposed adaptive particle filter thesystem kinematic state in motion vector can be effectively

predicted based on the motion history of target The definedrotational kinematic model is shown as follows

V120601119905= 120575120601V (120601119905minus1 minus 120601119905minus2) (6)

119886120601119905= 120575120601119886(V120601119905minus1

minus V120601119905minus2) (7)

120601119905= 120601119905minus1+ V120601119905119905 +1

21198861206011199051199052

+ 120590120601119905 (8)

where 120601 is the estimated state (120601 = 119903 120579) 120590120601119905

is the noisevariance at time instant 119905 in state 120601 direction In fact it ishard to predict the motion status of target in advance at themost practical applications Therefore a manual presettingcontrol factor is difficult to achieve a satisfactory performancein a compound movement In this paper an adaptive controlfactor 120575

120601119906is proposed as shown in (6) and (7) which could

scale the kinematic model adaptively based on the motionhistory of target It is defined as follows

120575120601119906= 1 minus 119890

minus119906

2

119905minus12120590

2

120601119905 120575120601119906isin [0 1] (119906 = V 119886) (9)

where120590120601119905

is the noise variance in120601 component at time instant119905

Based on (9) the adaptive control factor will have aresponse in accordance with the changing of previous kine-matics parameters (119906 = V 119886) of target If the system tracksthe target with the rapid movement a higher value of 120575

120601Vwill be generated and its acceleration component also willrespond according to the motion trend of target In otherwords when the unit displacement of target is beyond therange of system noise variance proportionally scaling upthe kinematic model could effectively assist the tracker toestimate the state of target close to its true solutionThereforekinematic model will be activated significantly during therapid movement Oppositely when the unit displacementof target is less than the system noise variance kinematicmodel will be greatly suppressed by the control factor asthe excessively amplified kinematic model will cause theoverestimation which will lead to vibration of systemThere-fore we can employ the control factor 120575

120601119906to scale the

kinematic model properly based on the history motion statusof target With the adaptive control factor 120575

120601119906 the system

state transition model is able to estimate the state direct tothe true solution properly but avoid the overestimationWiththe restraint of inertia of object its motion state is impossibleto make a very sharp change in a short unit time Thereforethe proposed adaptive control factor 120575

120601119906should be able to

timely adjust the kinematic model for quick response of thechanging motion status of target

With the adaptive adjustment of control factor 120575120601119906

theproposed rotational kinematic model based adaptive particlefilter should be able to robustly handle more comprehensivemovements including rapidmovements Also the embeddedrotational kinematic model will not affect the stability ofthe tracking system in the normal-speed movement (thesystem noise variance can cover the unit displacement oftarget) To verify the performance of adaptive particle filterin normal-speedmovement we present an experiment to testits tracking accuracy with the zero-velocity modeled particle


22

21

2

19

18

17

16

15

1450 100 200 300 400

RMSE

Particle number

A-PFS-PF

Figure 4 The average root mean square errors (RMSEs) of rota-tional kinematic model based adaptive particle filter (adaptive-PF)and zero velocity model based particle filter (standard-PF) with thedifferent number of particles

filter due to the good performance of zero-velocity tracker innormal movement For a fair comparison both trackers areimplemented with some identical parameter settings suchas particle number 119873 and noise variance 120590 Here the scalestate 119904 follows the random Gaussian distribution As shownin Figure 4 the adaptive particle filter has a comparableperformance with zero-velocity modeled particle filter in thisexperiment and their RMSEs are around 178 Therefore itcan be verified that the proposed adaptive kinematic modelbased tracker has a stable performance on the normal-speedmovement

4 Experiments

In this section we present a series of experiments to ver-ify the effectiveness of the proposed algorithm on humantracking in TOV Since there is no available TOV datasetin public we build a thermal omnidirectional sensor fordata collection which consists of a FLIR Therma CAM PM695 camera and a hyperboloid catadioptric omnidirectionalmirror (Figure 5) The established TCO database containsseveral image sequences with different ambient conditionsEach set of image sequences contains hundreds of TOVframes that are sampled with 20Hz in a resolution of 320 times240 To verify the performance of the proposed algorithm thedetailed experiments are shown as follows

41 AccuracyAnalysis of AdaptiveNeighborhoodModeledGra-dient Coding Feature Unlike the conventional vision ther-mal vision reflects the temperature distribution Due to thedifference of temperature distribution we can roughly distin-guish the object from the others based on the clue of contourinformation As the involvement of catadioptric sensor the

Figure 5 System platform of the proposed thermal omnidirectionalcamera system

contour distribution of object is seriously distorted in TOVTo effectively handle the nonlinear distortion an equivalentprojection based gradient coding feature is proposed for thissystem To ensure a satisfactory performance of the proposedfeature a suitable sampling density for coding template isnecessary If the sampling density is dense it may result indata redundancy Oppositely it may lead to undersamplingif the sampling is too sparse For that purpose this paperselects three groups of configuration for coding template ina reasonable range to test their performancesThis paper setsthe neighborhoodrsquos aspect ratio of a human target as 12 Wedefine three templates with 12 16 and 20 units in the heightdirection and they are represented as EP12 EP16 and EP20for short Correspondingly these templates have 6 8 and 10units in the width direction respectively In this experimentwe compare the performance of our algorithm with thelocal coordinate transform [2] based histogram of orientedgradient (HOG) [25] For a fundamental comparison of theirperformance we use the zeros-velocity standard particle filterwith the Gaussian random scale distribution for trackingtesting

Figure 6 shows that equivalent projection based trackersachieve better performance than the local coordinate trans-formed HOG based tracker The RMSEs of EPs-G are lessthan 35 but the RMSE of LCT-HOG is around 53Thereforeit can be concluded that the equivalent projection basedfeatures performmuchbetter than local coordinate transformbased feature Analyzing the performance of the algorithmsfrom the level of coding complexity HOG integrates thegradient information with its orientation into a whole frame-work which should perform better than the method withonly gradient feature integrated also a comparison to verifythis phenomenon has been presented in [26] HoweverEPx-Gs achieved more stable performance than LCT-HOGbecause equivalent projection could effectively model thenonlinear distortion of omnidirectional vision but localcoordinate transform just supplied a linear projection modelwhich is apparently not suitable to the catadioptric vision Inaddition the EP16-G obtains the best performance (RMSE =13962) when 300 particles are being applied Therefore thispaper employs the feature configuration of EP16 for adaptive


EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE

Figure 6 The performance of equivalent projection based gradientcoding features (EP12-G EP16-G and EP20-G) and local coordinatetransform basedHOG (LCT-HOG)with different particle numbers

particle filter in the following experiments to further discussthe human tracking in thermal catadioptric vision

42 Performance Analysis of Adaptive Particle Filter On thebasis of characteristics of the proposed system this paperpresented a rotational kinematic modeled adaptive particlefilter for tracking purpose To verify the effectiveness of theproposed algorithm a series of analysis and experiments aregiven in Figure 7

To analyze the performance of the proposed adaptiveparticle filter we compare it with the method proposed in[27] which presented a motion estimation based adaptiveparticle filter for face tracking In [27] the authors arerequired to manually preset the scaling factor of motionmodel in advance In practice a presetting motion model isdifficult to meet the requirement of the whole experimentespecially for the compoundmovement If the motion modelis being excessively used it very easily causes system vibrationthat must lead to the tracking accuracy decline Here wegive an experiment to compare the RMSE of the proposedalgorithm and the whole motion modeled method in [27]For a fair testing both trackers are implemented with thesame system parameters such as the number of particlesAs shown in Figure 7 the RMSEs of M-PF are around218 and they achieved the lowest RMSE equal to 20635that is still higher than all the RMSEs of P-PF Thereforethe tracking accuracy of M-PF is lower than that of P-PFobviously On the other hand if the half of motion modelis implemented the tracking accuracy of system should beimproved but it may be difficult to handle some challengingrapid movements For comparison we test the above trackerson a rapid movement experiment that depicts a target movewith a high speed which is 6 to 7 times higher than that

P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE

Figure 7 The performance of the proposed adaptive particle filter(P-PF) and the whole motion modeled method [27] (M-PF)

of the normal situation As shown in Figure 8 method [27]fails to track the target at the early stage of the experimentdue to the shortage of motion model Therefore it canbe concluded that a fixed preset motion model is hard toflexibly accommodate the multiple movements In contrastour proposed adaptive tracker could achieve a satisfactoryperformance since the adaptive kinematic model of systemcan be adjusted automatically based on the motion status oftarget

To further analyze the effectiveness of the proposed kine-matic model we present a compound movement experimentwhich describes a rapid movement mixed in a normal speedwalk froma single target At the early stage of this experimenta person walks around the omnidirectional sensor slowlyand the system variance can just cover the unit displacementof the person During this process the kinematic model isadaptively suppressed by the control factors to ensure thestability of system As shown in Figure 9 the control factorskeep small in angle and radial directions Accordingly thepredicted kinematic parameters are suppressed (Figure 10)From Frame 42 the target suddenly accelerates in angulardirection and keeps the high speed movement with a fewframes Following the changing of motion status of targetthe system quickly responds that the velocity factor in angledirection 120575

120579V is stimulated to a peak near to the maximum(Figure 9(a)) Accordingly the predicted velocity in angledirection V

120579is scaled up close to the true value at that

moment (Figure 10(a)) For the acceleration the accelerationfactor 120575

120601119886is activated significantly (Figure 9(c)) and the

predicted acceleration 119886120579is also being amplified accordingly

(Figure 10(c)) With the involvement of velocity factor 120575120579V

the predicted velocity V120579could catch up the true value

effectively during the rapidmovement A few frames later thetarget decelerates sharply to recover the low speedmovement


Figure 8 The tracking experiment with a rapid movement on the proposed adaptive particle filter (the first row) and the half of motionmodeled method proposed in [27] (the second row)

0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)

Figure 9 The distribution of 120575120601119906

in the compound movement


20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)

Actual valuePredicated value

(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)

Figure 10 The distribution of velocities and accelerations in the compound movement

Therefore the predicted velocity V120579falls timely since the

velocity factor 120575120579V recovers to a small value Because of

the sharp changing of velocity in angular direction theacceleration factor 120575

120601119886and predicted acceleration 119886

120579have the

significant responsesThen the control factors and kinematicparameters in angular direction are suppressed in the low-speed movement Likewise the motion status of target inradial direction has little change during the rapid movementAccordingly the control factor and kinematic parameters inradial direction have the correct but not drastic responses(Figures 9(b) 9(d) 10(b) and 10(d)) at thatmomentThroughthis experiment the performance of our proposed algorithmhas been further verifiedwhich could robustly track the targetthroughout the entire compound movement

43 Occlusion Handling Occlusion is a challenging topicin computer vision Particularly for thermal vision multi-targets tracking is extremely challenging since very limitedfeatures are usable In this paper we propose to employthe kinematic characteristic of the object to decrease theinfluence of occlusion to a great extent in our systemTechnically occlusion may be caused by the obstacle or thetarget In our system the occlusion caused by obstacle maybe activated if themean weight of particles decays sharply buttheirmean radial state 119903 is still in a reasonable value range (119903 isin((119903max+119903min)2minus120576 (119903max+119903min)2+120576) 120576 isin (0 (119903maxminus119903min)2))In this case the whole kinematic model will be implementedand the motion states of particles will be kept with a fewframes until the target shows again


Figure 11 The occlusion handling of the proposed adaptive particle filter with the normal-speed movement

Figure 12 The occlusion handling of the adaptive particle filter with the rapid movement

In the meantime system sampling is maintained fortarget searching and the system noise variance and particlenumber will be magnified proportionally to broaden thesearching area For multitarget tracking in TOV we centrallymanage the states of target to handle the occlusion from thetargets If any of two targets getting are closed and the angle120579Δbetween them is less than a threshold 119879 (120579

Δ= 120579119894minus 120579119895

119894 119895 = 1 2 119873) it declares occlusion from targets is goingto happen For this situation the motion states of targets willbe kept with a few frames until their intersection angle 120579

Δ

is bigger than the predefined threshold again During thisprocess the sampling of particles will be closed in case ofthe interference of undistinguishable contour caused by theoverlapping Through the experiments it can be verified thatthe proposed adaptive particle filter can effectively handle theshort term occlusions in TOV (Figures 11 and 12)

This section presented a series of experiments to vali-date the effectiveness of the proposed algorithm for TOVWith the involvement of equivalent projection model

a distortion-adaptive gradient coding feature is proposedand its performance has been proved by a tracking accuracyexperiment Moreover the experiments verified that theproposed rotational kinematic model based adaptive particlefilter can achieve a satisfactory performance even in thecomplex movements Finally our system is implemented inMatlab on a PC of an Intel Pentium 27GHz with 2G RAMand we achieved around 065 seconds with 200 particles perframe without optimization Therefore the proposed algo-rithm should have a great potential for real-time applicationin surveillance if it is implemented in CC++ and takingadvantage of GPU processing

5 Conclusion

In this paper we introduced a novel thermal omnidirectionalsensor that can work in total darkness and can achievea global field of view in a single image With the effectof distortion conventional contour features are hard to be


applied over to the proposed omnidirectional surveillancesystem directly Based on the equivalent projection theory anadaptive neighborhood-modeled gradient coding feature isproposed to effectively represent distorted visual informationin the catadioptric image For tracking purpose a rotationalkinematic modeled adaptive particle filter is proposed toeffectively handle multiple movements even including therapid movement and the short term target occlusion How-ever since only limited information can be employed in ther-mal vision long term occlusion in thermal omnidirectionalsystem is still a challenging topic which should be solved inour future work Importing a visible sensor into the thermalomnidirectional system may compensate the drawbacks ofthe thermal sensor and enrich the features pool that we canadopted which may supply the supports to reduce the effectof occlusion with a great extent

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Project nos 61273286 61233010) andCity University of Hong Kong (Project no 9680067) Theauthors acknowledge Xiaolong Zhou as a coauthor of thepaper

References

[1] I Haritaoglu D Harwood and L S Davis ldquoW4 real-time sur-veillance of people and their activitiesrdquo IEEE Transactions onPatternAnalysis andMachine Intelligence vol 22 no 8 pp 809ndash830 2000

[2] H Liu ZHuo andG Yang ldquoOmnidirectional vision formobilerobot human body detection and localizationrdquo in Proceedingsof the IEEE International Conference on Systems Man andCybernetics (SMC rsquo10) pp 2186ndash2191 October 2010

[3] Z H Khan and I Y-H Gu ldquoJoint feature correspondences andappearance similarity for robust visual object trackingrdquo IEEETransactions on Information Forensics and Security vol 5 no 3pp 591ndash606 2010

[4] D A Klein D Schulz S Frintrop and A B Cremers ldquoAdaptivereal-time video-tracking for arbitrary objectsrdquo in Proceedings ofthe 23rd IEEERSJ International Conference on Intelligent Robotsand Systems (IROS 10) pp 772ndash777 Taipei Taiwan October2010

[5] Y Liu J Suo H R Karimi and X Liu ldquoA filtering algorithm formaneuvering target tracking based on smoothing spline fittingrdquoAbstract and Applied Analysis vol 2014 Article ID 127643 6pages 2014

[6] X Zhou Y F Li B He and T Bai ldquoGM-PHD-Based multi-target visual tracking using entropy distribution and gametheoryrdquo IEEE Transactions on Industrial Informatics vol 10 no2 pp 1064ndash1076 2014

[7] H Liu S Chen and N Kubota ldquoIntelligent video systems andanalytics a surveyrdquo IEEE Transactions on Industrial Informaticsvol 9 no 3 pp 1222ndash1233 2013

[8] F Xu X Liu and K Fujimura ldquoPedestrian detection and track-ing with night visionrdquo IEEE Transactions on Intelligent Trans-portation Systems vol 6 no 1 pp 63ndash71 2005

[9] C J C Burges ldquoA tutorial on support vector machines forpattern recognitionrdquo Data Mining and Knowledge Discoveryvol 2 no 2 pp 121ndash167 1998

[10] M Yasuno S Ryousuke N Yasuda and M Aoki ldquoPedestriandetection and tracking in far infrared imagesrdquo in Proceedings ofthe 8th International IEEE Conference on Intelligent Transporta-tion Systems pp 131ndash136 September 2005

[11] J W Davis and M A Keck ldquoA two-stage template approach toperson detection in thermal imageryrdquo in Proceedings of the 7thIEEEWorkshop onApplications of ComputerVision (WACV rsquo05)pp 364ndash369 January 2005

[12] C Dai Y Zheng and X Li ldquoPedestrian detection and trackingin infrared imagery using shape and appearancerdquo ComputerVision and Image Understanding vol 106 no 2-3 pp 288ndash2992007

[13] A Treptow G Cielniak and T Duckett ldquoReal-time peopletracking for mobile robots using thermal visionrdquo Robotics andAutonomous Systems vol 54 no 9 pp 729ndash739 2006

[14] J Gaspar N Winters and J Santos-Victor ldquoVision-based nav-igation and environmental representations with an omnidirec-tional camerardquo IEEE Transactions on Robotics and Automationvol 16 no 6 pp 890ndash898 2000

[15] Y Shu-Ying G WeiMin and Z Cheng ldquoTracking unknownmoving targets on omnidirectional visionrdquoVision Research vol49 no 3 pp 362ndash367 2009

[16] T E Boult X Gao R Micheals and M Eckmann ldquoOmni-directional visual surveillancerdquo Image and Vision Computingvol 22 no 7 pp 515ndash534 2004

[17] J-C Bazin K-J Yoon I Kweon C Demonceaux and PVasseur ldquoParticle filter approach adapted to catadioptric imagesfor target tracking applicationrdquo in Proceedings of the 20th BritishMachine Vision Conference (BMVC rsquo09) pp 1ndash15 September2009

[18] J Ortegon-Aguilar and E Bayro-Corrochano ldquoOmnidirec-tional vision tracking with particle filterrdquo in Proceedings of the18th International Conference on Pattern Recognition (ICPR rsquo06)vol 3 pp 1115ndash1118 Hong Kong August 2006

[19] J Cheng H Zhu S Zhong Y Zeng and X Dong ldquoFinite-time119867infin

control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionalsrdquoISA Transactions vol 52 no 6 pp 768ndash774 2013

[20] C Geyer and K Daniilidis ldquoCatadioptric projectile geometryrdquoInternational Journal of Computer Vision vol 45 no 3 pp 223ndash243 2001

[21] S K Zhou R Chellappa and B Moghaddam ldquoVisual trackingand recognition using appearance-adaptive models in particlefiltersrdquo IEEE Transactions on Image Processing vol 13 no 11 pp1491ndash1506 2004

[22] M S Arulampalam S Maskell N Gordon and T Clapp ldquoAtutorial on particle filters for online nonlinearnon-GaussianBayesian trackingrdquo IEEE Transactions on Signal Processing vol50 no 2 pp 174ndash188 2002

[23] M Isard and A Blake ldquoCondensation-conditional densitypropagation for visual trackingrdquo International Journal of Com-puter Vision vol 29 no 1 pp 5ndash28 1998

[24] R D Gregory ldquoVector angular velocity and rigid body kinemat-icsrdquo in Classical Mechanics pp 457ndash467 Cambridge UniversityNew York NY USA 2006


[25] N Dalal and B Triggs ldquoHistograms of oriented gradients forhuman detectionrdquo in Proceedings of the IEEE Computer SocietyConference on Computer Vision and Pattern Recognition (CVPRrsquo05) pp 886ndash893 June 2005

[26] Y Tang and Y F Li ldquoContour coding based rotating adaptivemodel for human detection and tracking in thermal catadiop-tric omnidirectional visionrdquo Applied Optics vol 51 no 27 pp6641ndash6652 2012

[27] S Choi and D Kim ldquoRobust face tracking using motionprediction in adaptive particle filtersrdquo in Proceedings of theInternational Conference on Image Analysis and Recognition pp546ndash557 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Omni-image Distortion-invariant gradient feature Classifier Particle filter Tracked

targets

Rotational kinematic model

Figure 1 The schematic diagram of the proposed tracking system for TVO

camera can provide a 360∘ view of the environment in a singleimagewith a compact system configurationTherefore itmayhave a great promise for a wide range of applications [14]especially if in the situation requires a wide field of view In[15] a fisheye omnidirectional tracking system is presentedThey used the optical flow to detect the target and employcolor histogram integrating with kernel based particle filterto realize single target tracking in omnidirectional visionIn [16] the authors presented a catadioptric omnidirectionalsurveillance system which uses multibackground modelingand dynamic thresholding to make a target tracking in theclutter field to spot the sniper at the battlefield In additionsome algorithms utilize the color information to integratewith the particle filter for tracking in omnidirectional vision[15 17 18]

Thermal vision presents a temperature field distributionof the surrounding environment using single channel of graylevel intensity Color or texture information may be unstableto be used in thermal image However temperature fieldmakes the contour information become salient Thereforecontour information should be considered as an importantclue that can be used to distinguish the object from the otherin thermal vision However it is difficult to directly applythe most conventional contour features to the catadioptricomnidirectional vision due to its nonlinear distortion [19] Acommon solution is to unwarp the distorted omnidirectionalimage to a panoramic image or transform the coordinate oflocal area of omnidirectional image into a rectified imagefollowed by using of conventional algorithm [2] Howeverthe computational load of this method is extensive as theinterpolation is involved Furthermore it may introducenoise in the image which will degrade the performance ofthe algorithm Moreover underlying distortion still exist inthe rectified image Nowadays it is more and more con-sidered that the rectangular window and template matchingcommonly used in traditional images are not adapted forcatadioptric vision due to their serious nonlinear deforma-tion To solve the problem of distortion this paper adoptsthe equivalent theory proposed by Geyer and Daniilidisto model the single viewpoint catadioptric sensor with atwo-step projection via a unitary sphere centered on thefocus of the mirror (Geyer and Daniilidis 2001) [20] Wedefine a spatial gradient coding template on the equivalentsphere and achieve a distortion adaptive coding templatein the image plane through model back-projection Withthe modeled distortion-adaptive neighborhood a distortion-invariant gradient coding feature is developed for TOV Forrobust tracking we propose to develop a rotational kinematicmodel based particle filter based on the characteristic of

our system Compared with the zero-velocity model theproposed tracking algorithm should be able to handle morechallenging situations including rapid movement Due tothe involvement of kinematic model the proposed trackeris able to predict the state of target more reasonably with asmall number of particles Althoughocclusion is an extremelychallenging situation in thermal vision the proposed track-ing algorithm is able to handle the short term occlusioneffectively based on the distinct kinematic state of a targetduring tracking process Finally a series of experiments aregiven to verify the effectiveness of the proposed algorithmThe schematic diagram of proposed tracking approach isshown in Figure 1

The remainder of this paper is organized as followsSection 2 introduces the principle of the equivalent sphereprojection and the proposed distortion-invariant neighbor-hood adaptive gradient feature Section 3 presents the pro-posed rotational kinematic model based adaptive particlefilter for omnidirectional vision A series of qualitative andquantitative analyses are given in Section 4 to verify the per-formance of proposed algorithm Finally Section 5 concludesthis paper

2 Equivalent Projection ModeledGradient Coding Feature

21 Equivalent Projection Based Adaptive Neighborhood Def-inition The adaption of the neighborhood is essential toguarantee the accuracy of visual tracking Conventionalneighborhood of a given point for the perspective imagesis usually simply defined as the square region centeredat this point Central catadioptric omnidirectional visionexhibits serious nonlinear distortion due to the involvementof a quadratic reflection mirror Therefore conventionalneighborhood definition is not appropriated for catadioptricimages because it does not take into account the distortion ofthe image

Catadioptric omnidirectional vision which can be mod-eled by a unified projection model was introduced by Geyerand Daniilidis [20] who have demonstrated the equivalencewith projection via a unitary sphere centered on the focusof the mirror This two-step projection consists first inprojecting a 3D point 119875

119908to sphere from the center of the

sphere 119874119888 The next step consists in projecting the point on

the sphere 119875119904to the image plane from a point 119874

119901placed

on the optical axis to obtain a pixel point 119875119894(Figure 2) The

equivalence is very interesting since it allows performingimage processing in a new space in which deformationsare taken into account In order to deal with distortions


Op

Oc

Ps

Pw

Pi




119878= (120579 120601)



119878(119883119878) is defined

as

119873119878(119883119878)

= (1205791015840

1206011015840

) isin 1198782

|100381610038161003816100381610038161205791015840

minus 12057910038161003816100381610038161003816le 120579thresh

100381610038161003816100381610038161206011015840

minus 12060110038161003816100381610038161003816le 120601thresh

(1)




119894(119883119894) of a point 119883

119894in the image





119892 (119909 119910)


+ (119868 (119909 119910) minus 119868 (119909 119910 minus 1))2

(2)




vations 1199111119896= 1199111 1199112 119911







119896| 120601119896minus1) to


1199111119896minus1


)119889120601119896minus1



119901(120601119896| 1199111119896) = 119901(119911

119896| 120601119896)119901(120601119896





119896| 120601119894

119896


119889 = 1 minus 119902 (3)

119901 (119911119896| 120601119894

119896


119908119894

119896

prop 119908119894

119896minus1

119901 (119911119896| 120601119894

119896

) (5)












119886120601119905= 120575120601119886(V120601119905minus1

minus V120601119905minus2) (7)

120601119905= 120601119905minus1+ V120601119905119905 +1

21198861206011199051199052

+ 120590120601119905 (8)





120575120601119906= 1 minus 119890

minus119906

2

119905minus12120590

2

120601119905 120575120601119906isin [0 1] (119906 = V 119886) (9)

where120590120601119905






120601119906 the system







22

21

2

19

18

17

16

15

1450 100 200 300 400

RMSE

Particle number

A-PFS-PF



4 Experiments







EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE





P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE














0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Op

Oc

Ps

Pw

Pi




119878= (120579 120601)



119878(119883119878) is defined

as

119873119878(119883119878)

= (1205791015840

1206011015840

) isin 1198782

|100381610038161003816100381610038161205791015840

minus 12057910038161003816100381610038161003816le 120579thresh

100381610038161003816100381610038161206011015840

minus 12060110038161003816100381610038161003816le 120601thresh

(1)




119894(119883119894) of a point 119883

119894in the image





119892 (119909 119910)


+ (119868 (119909 119910) minus 119868 (119909 119910 minus 1))2

(2)




vations 1199111119896= 1199111 1199112 119911







119896| 120601119896minus1) to


1199111119896minus1


)119889120601119896minus1



119901(120601119896| 1199111119896) = 119901(119911

119896| 120601119896)119901(120601119896





119896| 120601119894

119896


119889 = 1 minus 119902 (3)

119901 (119911119896| 120601119894

119896


119908119894

119896

prop 119908119894

119896minus1

119901 (119911119896| 120601119894

119896

) (5)












119886120601119905= 120575120601119886(V120601119905minus1

minus V120601119905minus2) (7)

120601119905= 120601119905minus1+ V120601119905119905 +1

21198861206011199051199052

+ 120590120601119905 (8)





120575120601119906= 1 minus 119890

minus119906

2

119905minus12120590

2

120601119905 120575120601119906isin [0 1] (119906 = V 119886) (9)

where120590120601119905






120601119906 the system







22

21

2

19

18

17

16

15

1450 100 200 300 400

RMSE

Particle number

A-PFS-PF



4 Experiments







EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE





P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE














0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119896| 120601119896minus1) to


1199111119896minus1


)119889120601119896minus1



119901(120601119896| 1199111119896) = 119901(119911

119896| 120601119896)119901(120601119896





119896| 120601119894

119896


119889 = 1 minus 119902 (3)

119901 (119911119896| 120601119894

119896


119908119894

119896

prop 119908119894

119896minus1

119901 (119911119896| 120601119894

119896

) (5)












119886120601119905= 120575120601119886(V120601119905minus1

minus V120601119905minus2) (7)

120601119905= 120601119905minus1+ V120601119905119905 +1

21198861206011199051199052

+ 120590120601119905 (8)





120575120601119906= 1 minus 119890

minus119906

2

119905minus12120590

2

120601119905 120575120601119906isin [0 1] (119906 = V 119886) (9)

where120590120601119905






120601119906 the system







22

21

2

19

18

17

16

15

1450 100 200 300 400

RMSE

Particle number

A-PFS-PF



4 Experiments







EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE





P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE














0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










22

21

2

19

18

17

16

15

1450 100 200 300 400

RMSE

Particle number

A-PFS-PF



4 Experiments







EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE





P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE














0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










EP12-GEP16-G

EP20-GLCT-HOG

50 100 200 300 400

Particle number

7

8

6

4

3

5

2

1

0

RMSE





P-PFM-PF

50 100 200 300 400

Particle number

24

26

28

22

2

3

18

16

14

12

RMSE














0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0 50 1000

02

04

06

08

1

Frames

120575120579v

(a)

0

02

04

06

08

1

0 50 100

Frames

120575rv

(b)

0

02

04

06

08

1

0 50 100Frames

120575120579120572

(c)

0

02

04

06

08

1

0 50 100Frames

120575r120572

(d)




20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










20 40 60 80 100 120

Frame

3

4

5

2

1

0

minus1

v120579

(deg

s)


(a)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

v r(p

ixel

s)


(b)

20 40 60 80 100 120

Frame

2

1

0

minus1

minus2

120572120579

(deg

S2)


(c)

20 40 60 80 100 120

Frame

3

2

1

0

minus1

minus2

minus3

120572r

(pix

els2)


(d)






120579have the







Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Δ= 120579119894minus 120579119895


Δ




5 Conclusion






Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Acknowledgments


References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article rotational kinematics model based

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