Optik 125 (2014) 289 295

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Optik

jou rn al homepage: www.elsev ie

Vehicle speed measurement based on gray constalgorith

Jinhui La a

a Department o , Unive100083, Chinab Department o Madis

a r t i c l

Article history:Received 3 FebAccepted 20 Ju

Keywords:Vehicle speed Gray constrainImproved threMoving detect

sed oportas the . By ttly. Te, whity (knding

redu, sinc

value. Experimental comparisons between the method and other VSM methods show that the proposedapproach has a satisfactory estimate of vehicle speed.

2013 Elsevier GmbH. All rights reserved.

1. Introdu

Vehicle sc informain ITS. At prbe categori(2) softwareof inductionment, radaris vehicle sp

An indudetector emthe loop, thcalculate thdirectly emit is installefreezing, fomeasureme[2,3]. For las

Corresponversity of ScieTel.: +86 010 6

E-mail add(J. Lan), gordon

0030-4026/$ http://dx.doi.oction

peed measurement plays an important role in the traf-tion collection, and it is also a hot and difcult issueesent, the vehicle speed measurement methods couldzed into two types: (1) hardware-based methods and-based methods. The hardware-based methods consist-coil loop speed measurement, laser speed measure-

speed measurement, etc. The software-based methodeed measurement by video images [1].ction-coil loop speed measurement method is a loopbedded into the ground. When the vehicles go acrosse loops magnetic eld changes, and the detector cane vehicle speed. Since the induction-coil loop must bebedded in the lane, it will easily disrupt the road whend or maintained. And the loop is also affected by theundation subsidence and other factors. Moreover, thent accuracy will be greatly reduced when trafc slowser speed measurement, a laser detector is located above

ding authors at: School of Automation & Electrical Engineering, Uni-nce and Technology Beijing, Beijing 100083, China.2334961.resses: ustblanjinhui@gmail.com, lanjh@ustb.edu.cnlj@163.com (J. Li).

the roadway, it detects the moving objects distance and time formany times and then uses them to calculate the moving objectsspeed, which is based on the light waves speed measurement [4].The laser detector can work day and night under different weatherconditions, but extreme temperatures could yield performance lossin their functionalities [2,5]. Radar speed measurement adopts theDoppler radar effect. When the emission source or the receiver hasrelative motion, the received signal frequency will change. Radarspeed measurements have a high demand on the angle of installa-tion, which have limitations in the application [6].

For the vehicle speed measurement by video images, camerasare installed on the top of lane or placed alongside a roadway toshoot moving vehicles. The images captured by camera are ana-lyzed by the image processing and pattern recognition algorithm,which are used to calculate the vehicle speed. The common meth-ods used in the vehicle speed measurement by video images arecorner detection, texture analysis, video tracking, and so on [712].These methods can well nd the matching location of the vehi-cle in the two consecutive image frames, but the large amountof computation cannot meet the requirements of real-time speedmeasurement. The method of virtual line can replace the real loop,but it is likely to create vehicle speed miscalculation because of theimage frame acquisition period [13,14]. In addition, matching thedifferent parts of vehicle in two consecutive images can affect theactual moving distance of the vehicle because of the size change ofthe bodies in the consecutive images [12,15,19].

see front matter 2013 Elsevier GmbH. All rights reserved.rg/10.1016/j.ijleo.2013.06.036m

na,, Jian Lia,, Guangda Hua, Bin Ranb, Ling Wangf Instrument Science and Technology, School of Automation and Electrical Engineering

f Civil and Environmental Engineering, School of Engineering, University of Wisconsin-

e i n f o

ruary 2013ne 2013

measurementt optical ow algorithme-frame difference algorithmion

a b s t r a c t

Vehicle speed measurement (VSM) bameasurement in the intelligent transmeasurement method, which containgray constraint optical ow algorithmmoving vehicles can be detected exacthe vehicle contours optical ow valucomputed accurately. Then, the velocthe vehicles contour and the correspocan yield a better optical ow eld byit can reduce computation obviouslyr .de / i j leo

raint optical ow

rsity of Science and Technology Beijing, Beijing

on, Madison, WI 53706, USA

n video images represents the development direction of speedtion systems (ITS). This paper presents a novel vehicle speedimproved three-frame difference algorithm and the proposedhe improved three-frame difference algorithm, the contour ofhrough the proposed gray constraint optical ow algorithm,ich is the speed (pixels/s) of the vehicle in the image, can be

m/h) of the vehicles is calculated by the optical ow value of ratio of the image pixels to the width of the road. The methodcing the inuence of changing lighting and shadow. Besides,e it only calculates the moving target contours optical ow

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290 J. Lan et al. / Optik 125 (2014) 289 295

In order to overcome the shortcomings of various methodsabove, this paper states a novel vehicle speed measurement methodbased on improved three-frame difference algorithm and the grayconstraint optical ow algorithm. Through the improved method,the contourvalue of thethe proposeow value method cantarget contoof interest puted. By ththe width ocalculated b

The rest speed measwhere the iconstraint oexperimentin Section 4

2. Vehicle

The senstop of lane.obtained. Bthe proposemotion parabe compute

2.1. Improv

2.1.1. InterfInterfram

detection bformance igenerated bthree-frame

The prin(1)(3):

p1(x, y) ={

p2(x, y) ={

p(x, y) = p

={

In (1) anvalue of theimage framp(x,y) is the

Althougtargets conis comparemethod is sand the gra

Impr resud thep. Torove

the trougn thrrove

e diffond

x, y)

e diff thir

x, y)

e newon.

x, y)

e new the dilate

x, y) =

x, y) =

x, y) =0, else

(7)

e result image p is derived from p3 and p6 via the xor oper-on.

, y) = p3(x, y) p6(x, y) ={

255, if(p3(x, y)! = p6(x, y))0, else

(8)

known that global threshold T for image binarization couldin distortion in a real image whose intensities vary gradually of vehicles can be detected exactly. The optical ow moving target contour can be computed precisely byd gray constraint optical ow algorithm. The optical

is the speed (pixels/s) of the vehicle in the image. The reduce computation by only calculating the movingurs optical ow value. In the image, we draw the region(ROI) and the speed of the vehicle in the ROI is com-e corresponding relation between the image pixels andf the road, the speed (km/h) of the moving target isy the optical ow value.of this paper is organized as follows. In Section 2, vehicleurement method proposed in the paper is described,mproved three-frame difference method and the grayptical ow method are introduced. Section 3 presentsal results of our method and the results analysis. Finally,, the conclusion on the experimental results is drawn.

speed measurement method

or used in the paper is a video camera installed on the According to the camera, vehicles information can bey the improved three-frame difference algorithm andd gray constraint optical ow algorithm, the vehiclesmeters can be acquired. Then, the vehicles velocity cand by the method.

ed three-frame difference method

rame difference methode difference method is widely used in moving target

y low computational complexity. In most cases, the per-s good. When target moves fast, the targets contoury two-frame video images produces overlap. So, the

difference method is proposed [16].ciple of the three-frame difference method is shown in

255, if|Fm(x, y) Fm1(x, y)| > T0, if|Fm(x, y) Fm1(x, y)| T

(1)

255, if|Fm+1(x, y) Fm(x, y)| > T0, if|Fm+1(x, y) Fm(x, y)| T

(2)

1(x, y) p2(x, y)

255, if(p1(x, y) = 255&&p2(x, y) = 255)0, else

(3)

d (2), Fm1(x,y), Fm(x,y) and Fm+1(x,y) denote the gray m1 image frame, the m image frame and the m + 1e at the spatial pixel point (x,y). T is the threshold value.

gray value of spatial pixel point (x,y) of target image.h the three-frame difference method can get the movingtour, the detected contour is partly overlapped, whichd to the real targets contour. The performance of thehown in Fig. 1. The green contour is the target contour,y areas are overlap regions in the m frame contour.

2.1.2. The

lap, anoverlaan impdetecttion thxor i

Imp

(1) Thsec

p1(

(2) Ththe

p2(

(3) Thati

p3(

(4) Thviato

p4(

p5(

p6(

(5) Thati

p(x

It isresult Fig. 1. Effect of three-frame differences overlap.

oved three-frame difference methodlt of the two-frame difference method produces over-

three-frame difference algorithm also produces partly eliminate the partly overlapped, this paper presentsd three-frame difference algorithm. The algorithm canarget contour precisely, and can get contour informa-h the operation of the difference, dilate, and andee consecutive frames.d three-frame difference algorithm steps are as follows:

erence image p1 is obtained by the rst frame and theimage frames via the difference operation.

={

255, if|Fm(x, y) Fm1(x, y)| > T0, if|Fm(x, y) Fm1(x, y)| T

(4)

erence image p2 is obtained by the second frame andd image frames via the difference operation.

={

255, if|Fm+1(x, y) Fm(x, y)| > T0, if|Fm+1(x, y) Fm(x, y)| T

(5)

image p3 is derived from p1 and p2 via the and oper-

= p1(x, y) p2(x, y)

={

255, if(p1(x, y) = 255&&p2(x, y) = 255)0, else

(6)

image p6 is derived from the dilated images p4 and p5and operation. SE is the 3 3 squared template, used

the image.

p1(x, y) SE

p2(x, y) SE

p4(x, y) p5(x, y) ={

255, if(p4(x, y) = 255&&p5(x, y) = 255)

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J. Lan et al. / Optik 125 (2014) 289 295 291

Fig. 2. Effect of improved three-frame difference.

due to illumination. Therefore, we adopt the local adaptive thresh-old segmentation method to extract the target from background.The global adaptive threshold T is used to do the initial segmenta-tion. The thresholding value T for the whole image is determinedby the difference between the mean and standard deviations of thewhole image.

Thresholding value T = mean std.The effect of improved three-frame difference algorithm is

shown in Fig. 2. From the gure, the precision contour of targetcan be obtained by the method. So, the algorithm has a betterresult than three-frame difference algorithm. In particular, whenthe velocity of the moving target is faster, the effect is more obvious.

To illustrate the superior performance of the improved method,experiments are done by the three kinds of frame differencemethod. Fig. 3 shows the original image, and they are 640 480pixels. The Fig. 4(a) shoFig. 4(b) shoand Fig. 4(c)paper.

From Figframe differdifference mtour. The cois precise, wedge pointsrespectivelygood perfor

For multi-target motion detection, the proposed algorithm canbe used as the initial partition, and then use the gray constraintoptical ow method to compute the moving targets velocity.

2.2. Basic equation of optical ow and the improved algorithm

The change of the gray value expressed by optical ow eld canbe used to observe the information of moving target in the image. Itcontains the information of the image points instantaneous veloc-ity vector of the target. According to the velocity vector, the velocityof the target can be calculated.

2.2.1. Basic equation of optical owOptical ow is proposed by Gibson at rst, and it is the moving

velocity of target in the gray mode. The calculation of moving tar-gets optical ow eld is based on two assumptions: (1) the grayvalue of a moving object is unchanged in a very short time; (2) eachpixel of the target has the same speed because of the targets rigidproperties [17].

Suppose that the point P in the image coordinates at (x,y) movesto (x + dx, y + dy) after dt. The gray value is I(x,y,t) at (x,y) andI(x + dx, y + dy, t + dt) at (x + dx, y + dy). As dt is short, the gray valueis unchanged by the assumption, and it is shown in (9). Also, (9) iscalled the basic optical ow equation.

I(x + dx, y + dy, t + dt) = I(x, y, t) (9)

The left side of (9) is expanded using Taylors formula, and is as follows.

x, y +

r sim ow

+ Iy

dx/dtspati

0th im

Fig. 4. Effect oimage.computed threshold value T is 102 from the images.ws the performance of two-frame difference method,ws the performance of three-frame difference method

shows the performance of the method proposed in this

. 4, it is easy to make the conclusion as follows: Two-ence method produces overlap obviously. Three-frameethod produces overlap at the corners of the cars con-

ntour obtained by using this paper proposed algorithmhich is shown in Fig. 4(c). Also, the number of the white

is 4530 in Fig. 4(a), 2573 in Fig. 4(b) and 2061 in Fig. 4(c),. So, the improved three-frame difference method hasmance.

shown

I(x + d

Afteoptical

I

x

dx

dt

u = image

Fig. 3. The original image: (a) the 529th image, (b) the 53f difference methods: (a) two-frame difference method image, (b) three-frame differen dy, t + dt) = I(x, y, t) + Ix

dx

dt+ I

y

dy

dt+ I

t

dt

dt+ o(t2)

(10)

plication and ellipsis the quadratic term, the basic equation (9) is simplied to (11).

dy

dt+ I

dt

dt

dt= 0 (11)

and v = dy/dt are the moving speed of the pixel at theal pixel point (x, y) in horizontal and vertical directions.

age, and (c) the 531st image.

ce method image, and (c) improved three-frame difference method

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292 J. Lan et al. / Optik 125 (2014) 289 295

Also, (u, v) is called for the optical ow eld. The basic optical owequation (11) can be expressed as (12) [18,19]

(Ix, Iy)(u, v)T + It = 0 (12)

where Ix =

2.2.2. Gray In pract

unchangedmet for theAccording tvalue is notow (9) anoptical ow

I(r + r) =

where I(r) =cient. C(r) is

The gray(13):

I(r + r) =

If m(r)tion of the bpractical apis suited foow error i

I = I(r +

After de

I = g +

where g =In (16),

objects), Ican be usedI. If the raaccurate. Othe affectiomation of tTherefore, teld distribform well uso on.

Since LKow eld, Hof objects amethod for

2.2.3. MotioTo meet

same movinthe smooththe velocityis representthe purpose

Es = [

On the unchanged

reasons. So, it requires that the proposed gray constraint opticalow error (15) is as small as possible, and it is expressed as (18).

Ec =

(I)2dxdy =

(Ixu + Iyv + It)2 dx dy (18)

eethnestical

(E

[(

e pa(the

errte, anEc. Cle sm

corr

n+1) +n+1) +

O2 iation

the he lote de comn be

)u(n+

)v(n+

refored by

= u(n

= v(n

n denf thee bere teue of, and

u(n+

tan

rder alg

aint oare ced byt to I/x, Iy = I/y, It = I/t.

constraint optical ow algorithmical application, the assumption that the gray value is

in a very short time in the optical ow eld cannot be reasons of block, multi-source, transparency and so on.o the generalized dynamic image mode (GDIM), the gray

constant, but changed. So, the basic equation of opticald (11) does not hold, we propose the gray constraint

equation, and it can be expressed as follows:

M(r)I(r) + C(r) (13)

I(x,y,t), M(r) = 1 + m(r), m(r) is the deviation coef- interference.

constraint optical ow equation is shown as follows

I(r) + m(r)I(r) + C(r) (14)

= C(r) = 0, (14) meets the gray value unchanged assump-asic optical ow equation, and it is the same with (9). Inplication, the gray constraint optical ow equation (13)r the actual situation. Also, the gray constraint opticals shown as below:

r) I(r) = m(r)I(r) + C(r) = Ixu + Iyv + It (15)

formation, (15) is expressed as follows:

It (16)

(Ixu+Iyv).g is the geometric component (the speed of moving

is the illumination component, and the ratio Y = g/I as the parameter of relative strength between g andtio is large, the velocity component estimated is quiten the contrary, the estimated speed is not accurate, andn of light is large. The ratio is signicant for the esti-he motion parameters and the structural parameters.he value of Y can be used to constrain the optical owution, which can make the optical ow algorithm per-nder a variety of challenging light, trafc condition, and

(LucasKanade) method may not perform well in denseS (Horn and Schunck) method can detect minor motionnd provide a 100% ow eld. Thus, we focus on HS

optical ow eld computation in our research [19].

n constraint equations of Horn and Schunckthe assumptions that the optical ow eld caused by theg object should be smooth, Horn and Schunck propose

ness constraint condition, which varies by the integral of components square. The smoothness constraint errored by (17). It calls for (17) to be as small as possible for

of the smoothness [17,19].(u

x

)2+(

u

y

)2+(

vx

)2+(

vy

)2]dxdy (17)

other hand, the assumption that the gray value is in the optical ow eld cannot be met for many

To msmootthe op

E =

+

is therrors cal owaccurasis on desirab

Thelows:

Ix(Ixu(

Iy(Ixu(

whereof iterdenotefrom ttemplaonly th(20) ca

(I2x +

(I2y + The

obtain

u(n+1)

v(n+1)

wherevalue odistanctions athe valas (23)

fp =

= arc

In ocal owconstrrithm obtainY is se the proposed gray constraint optical ow error and thes constraint error, Eq. (19) is set to nd the solution ofow (u,v).

c + Es) dx dy = {

(Ixu + Iyv + It)2

u

x

)2+(

u

y

)2+(

vx

)2+(

vy

)2]}dx dy = min

(19)

rameter that determines the weight between the twoerror of deviation from the smoothness Es and the opti-or Ec). When the image gray value of the measurement isd the can be made larger, which gives greater empha-onversely, if the image contains a lot of noise, is aall (less than 1) value.

esponding Euler equation of (19) is expressed as fol-

Iyv(n+1) + It) = 2u Iyv(n+1) + It) = 2v

(20)

s the Laplacian operator and n denotes the number. Suppose 2u = u(n+1) u(n), 2v = v(n+1) v(n). u, vaverage optical ow value of u, v, what can be derivedcal smoothing template of the images. The size of theepends on the requirements of the image. Considering

putation, the size of the template is 3 3, the result in written as follows:

1) + IxIyv(n+1) = u(n) IxIt1) + IxIyu(n+1) = v(n) IyIt

(21)

e, a natural iteration method solution of optical ow is (21).

) Ix(Ixu(n) + Iyv(n) + It) + I2x + I2y

) Iy(Ixu(n) + Iyv(n) + It) + I2x + I2y

(22)

otes the number of iteration, u0 and v0 denote the initial optical ow, which take zero. When the results of thetween two iterations are less than the threshold, itera-rminated. The optical ow is (u(n+1), v(n+1)). According to

u(n+1) and v(n+1), the velocity in the pixel P is expressed also the pixel Ps direction is expresses as (24).

1)2 + v(n+1)2 (23)

v(n+1)

u(n+1)(24)

to show the effect of the proposed gray constraint opti-orithm, tests have been done by video image. The grayptical ow algorithm and the basic optical ow algo-ompared. In the tests, the moving targets contour is

the improved three-frame difference method. The ratio1, and the parameter is 1. The images are shown in

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J. Lan et al. / Optik 125 (2014) 289 295 293

Fig. 5. (a) The original image, (b) effect of the improved three-frame and the basic optical ow algorconstraint optical ow algorithm.

Fig. 5(b) and (c). In the gures, when the optical ow value fp isbigger than the threshold value, the optical ow eld is shown.

From the gures, it is shown that the gray constraint algo-rithm is well-distributed in the optical ow eld and can performwell under a variety of challenging lighting and shadow. So, theimproved algorithm can work better than the basic optical owalgorithm.

2.3. Vehicle

In the vmajority of era need tocan be classmodel [20,2[2225].

In the cvehicles areinstallationtion schema

This papward and mIn the imaglength, instdelineated Fig. 7, the avertical dirlines of thepoint of thethe car.

When thin the ROI ipose the imis the stand

els i

7.5 0 pi

the Red t

in evis comeed o

1n

np=1

fp (26)

n denotes the number of points in the moving targeted by the improved three-frame difference algorithm, fps the optical ow geometry value of the point of target. favrs the optical ow geometry value of the block. According tometric value fp of the moving block and the ratio k betweenage pixels and the width of the road, the vehicle velocity iss follows:

r k (27)

erimental results and analysis

s paper presents a vehicle speed measurement method based improved three-frame difference algorithm and the pro- speed measurement

ehicle speed measurement system, cameras are thevision devices used. According to that whether the cam-

calibrate by manual, the vision-based VSM systemsied into two main models: (1) the calibrated camera1] [our system] and (2) the uncalibrated camera model

alibrated camera model, the appropriate positions of estimated by the geometric parameters of focal length,

angle and installation height. Fig. 6 shows the installa-tic diagram [1].er considers the issue that the camera is tilted down-ounted at a xed location on a bridge crossing the street.e, not all image is regions of interest. Adjusting the focalallation angle and installation height of the camera, wea region of interest (ROI) from the image. As shown inrea enclosed by green line is the detection area. In theection, the intersection point between the two white

double-lane and the edge of the image is the middle ROI, and the region can contain the whole contour of

e perspective effect is not considered, the width of roads equal to the image width (horizontal direction). Sup-age extracted from video is 640 480 pixels, and 7.5 mard width of double-lane national road. So the ratio of

the pixbelow:

k =64

In improvpointstarget The sp

favr =

whereobtaindenotedenotethe geothe imgiven a

V = fav

3. Exp

Thion theFig. 6. Installed schematic diagram.

posed graycarried outenvironmenposed methprocessor afrom the cacamera tiltbridge crostest has 30 ithm, and (c) effect of the improved three-frame and the proposed

Fig. 7. Region of interest.

n the image and the width of the road are expressed as

mxels

= 7.5/640 (m/pixel) (25)

OI, all detected moving targets are marked by thehree-frame difference method, and the speed of allery moving block are calculated, then the speed of theputed by the average speed of all points in the target.

f the target is shown as (26). constraint optical ow algorithm. The method was by VC++6.0 with OpenCV, and ran in MS Windows XPt. Several tests were performed to validate the pro-od. All tests were done on a PC with 1.9 GHz Celeronnd 1024 MB RAM. The vehicles, move toward or awaymera in the two-lane, are shot by the SONY HDR-XR260Eed downward and mounted at a xed location on asing the target street at 6 m high. The video used in theframes rate and the resolution is 640 480 pixels.

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294 J. Lan et al. / Optik 125 (2014) 289 295

Fig. 8. A vehicle in the ROI of the two-lane: (a) a vehicle move toward the cameraand (b) a vehicle move away from the camera.

Fig. 9. Two vehicles in the ROI of the two-lane: (a) two vehicles move toward thecamera and (b

3.1. Vehicle

For evalcles are usea vehicles sdirections, Red arrowstwo differencompared wvehicles veby radar at Vradar Vois in the vel

Table 1Vehicle move

Velocity ran

020 2040 4060 6080 80100 100120 120140 Above 140

Table 2Vehicles move

Velocity ran

020 2040 4060 6080 80100 100120 120140 Above 140

Table 3Average errors in different velocity range by the methods (%).

Velocity range/km/h Method

020 204040606080 80100 100120 120140 Above 140

Experimspeed accuof the propthat the errBut when tof the resuperformanc

From thrate of errothat is becawidth of ro

ordinis 25d. Al

mpa

rderred tsult

papel-ande thates nage ) two vehicles move away from the camera.

speed measurement by the proposed method

uating the performance of the proposed method, vehi-d to do experiments. Fig. 8 shows the performance ofpeed measurement in the double-lane in two differentFig. 9 shows two vehicles speed measurement effect.

denote the velocity of vehicle. 1000 cars velocity fromt directions is measured. The experimental results areith the velocity measured by radar. We estimate the

locity Vopt by the method and measure the velocity Vradarthe same time. The error is computed by the equationpt

/Vradar . The average error is statistics when the Vradar

Accframe metho

3.2. Co

In ocompaVSM re

In verticapensatelimining imocity range, and results are expressed in Tables 1 and 2.

toward the camera.

ge/km/h The number of vehicle Average error (%)

85 2.5110 1.5139 0.9302 0.8272 1.076 1.112 1.34 1.5

away from the camera.

ge/km/h The number of vehicle Average error (%)

79 1.3123 1.1164 0.9295 0.8254 0.967 1.215 1.43 1.7

vibration. Ting the adjuare backgroused in the

In papermoving vehis proposed(IFD) and thoutputs arerithm. Thentheir speedground subalgorithm. [2].

Table 3 pthe three mmethod prodifferent ve

In additAs the camhigh. Also, posed methbetween twthem, and tthe vehiclesPaper [1]smethod

Paper [2]smethod

Our method

IFD BS

4.2 5.6 1.90.68 4.1 5.3 1.39.7 3.5 3.0 0.95.6 2.2 1.1 0.96.6 1.5 1.5 1.03.7 0.7 2.3 1.2

1.9 1.2 1.41.6

ents show that the method can measure the vehiclerate and real-time. Figs. 8 and 9 show the performanceosed method. The test results (see Tables 1 and 2) showor range of the speed measurement is relatively small.he velocity of vehicles is too fast or too small, the errorlts is large. When the vehicle is completely in ROI, thee of the method is the best.e test results (see Tables 1 and 2), they show that ther increases when the velocity is relatively large or small,use the actual ratio of the pixels in the image and thead are deviated from the ratio K.g to the proposed method, the processing time of each

ms, which is less then 45 ms by the basic optical owso it can meet the requirement of the real-time.

red with other VSM methods

to show the performance of the described method, wehe result of our method with paper [1] and paper [2]ss.r [1], a novel VSM method is proposed. Firstly, the-horizontal-histogram-based method is used to com-e background of an incoming image. The methodoise coming from the displacement between an incom-and a background image that is caused by camerahen, the speed of the vehicles is measured by analyz-stment image. The principal algorithms of the methodund subtraction (BS) and Hough transform. The camera

method is uncalibrated-camera-based camera [1]. [2], a novel speed measurement method by tracking theicles is illustrated. A novel adaptive threshold method

to binaries the outputs from the interframe differencee background subtraction (BS) techniques. The binary

used to detect moving vehicles by the shrinking algo-, the detected moving vehicles are tracked to estimates. The principal algorithms of the method are back-traction (BS), interframe difference (IFD) and shrinkingThe camera used in the method is a calibrated cameraresents the average error in different velocity range byethods, respectively. From the table, it shows that theposed in the paper has a satisfactory performance inlocity range.ion, the stated method can be used to count vehicles.era is xed on a bridge, and the height of bridge is notthe processing time of each frame is 25 ms by the pro-od. So, when the vehicles pass the ROI, the time intervalo vehicles in the same lane is long enough to separatehe number of the interval can be used as the number of

passed the lane. Test results show that the detected rate

J. Lan et al. / Optik 125 (2014) 289 295 295

is up to 99% by the proposed method. But when a big vehicle and asmall vehicle pass the ROI at the same time at the double-lane, andthe distance between the two vehicles is short, the detected resultmay be fault.

4. Conclusion

The VSM method on the base of the improved three-frame dif-ference and the proposed gray constraint optical ow algorithm hasthe characteristics of low cost, low computation and accurate speedmeasurement. In the method, the contour of moving vehicles canbe detected accurate by the improved frame difference algorithm,and the vehicle contours optical ow value, which is the speed (pix-els/s) of the vehicle in the image, is calculated by the proposed grayconstraint optical ow algorithm. In the image, we draw the regionof interest and only compute the speed of moving targets contourin the region, which can reduce the computational further. By thecorresponding ratio between the image pixels and the width of theroad, the speed (km/h) of the moving target is calculated. Exper-iments show that the method is easy to implement and has goodrobustness. Also, the speed estimate is satised. For the three-lane,four-lane and multi-lanes speed measurements, we can improvethe detection method to reduce the computation to meet the real-time requirement, and establish the accurate model between thepixels in thnext study.

Acknowled

This wor(Grant No. No. 410203Fundament12-017A).

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Vehicle speed measurement based on gray constraint optical flow algorithm1 Introduction2 Vehicle speed measurement method2.1 Improved three-frame difference method2.1.1 Interframe difference method2.1.2 Improved three-frame difference method

2.2 Basic equation of optical flow and the improved algorithm2.2.1 Basic equation of optical flow2.2.2 Gray constraint optical flow algorithm2.2.3 Motion constraint equations of Horn and Schunck

2.3 Vehicle speed measurement

3 Experimental results and analysis3.1 Vehicle speed measurement by the proposed method3.2 Compared with other VSM methods

4 ConclusionAcknowledgmentsReferences