Research Article Automatic Parking Based on a Bird's Eye ...

Research ArticleAutomatic Parking Based on a Birdrsquos Eye View Vision System

Chunxiang Wang1 Hengrun Zhang2 Ming Yang2 Xudong Wang1

Lei Ye3 and Chunzhao Guo4

1 Research Institute of Robotics Shanghai Jiao Tong University Shanghai 200240 China2Department of Automation Shanghai Jiao Tong University and Key Laboratory of System Control andInformation Processing Ministry of Education of China Shanghai 200240 China

3 College of Mechatronic Engineering and Automation National University of Defense Technology Changsha 410073 China4Toyota Central RampD Labs Inc Nagakute 4801192 Japan

Correspondence should be addressed to Ming Yang mingyangsjtueducn

Received 1 September 2013 Revised 12 December 2013 Accepted 27 December 2013 Published 31 March 2014

Academic Editor Heiner Bubb

Copyright copy 2014 Chunxiang Wang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper aims at realizing an automatic parking method through a birdrsquos eye view vision system With this method vehicles canmake robust and real-time detection and recognition of parking spaces During parking process the omnidirectional informationof the environment can be obtained by using four on-board fisheye cameras around the vehicle which are the main part of thebirdrsquos eye view vision system In order to achieve this purpose a polynomial fisheye distortion model is firstly used for cameracalibration An imagemosaickingmethod based on the Levenberg-Marquardt algorithm is used to combine four individual imagesfrom fisheye cameras into one omnidirectional birdrsquos eye view image Secondly features of the parking spaces are extracted with aRadon transform based method Finally double circular trajectory planning and a preview control strategy are utilized to realizeautonomous parking Through experimental analysis we can see that the proposed method can get effective and robust real-timeresults in both parking space recognition and automatic parking

1 Introduction

With the increase in population and economic developmentof modern society of world more and more people havecars of their own The result is that traffic jam is more oftenthan ever before What is worse in the increasingly crowdedcities the embarrassment in parking is one of the mostdifficult problems for drivers People often have to waste alot of time on searching for free parking spaces Sometimesit is a quite challenging task for drivers to park their carsin a limited space In this context the researches on PAS(Parking Assistance Systems) and automatic parking systemshave become one of the hotspots in the field of intelligentvehicles J D Powerrsquos 2001 EmergingTechnology Study showsthat over 66 of consumers are likely to purchase parkingassistance systems [1]

There are several categories of parking assistance systems[2] The most prevailing approach now is to use sensor-based techniques such as laser scanners ultrasonic radars

and vision sensors Laser scanners have high stability andaccuracy but they are of high cost and short life and easilyaffected by the rain and snow weather Ultrasonic and shortrange radars are of low cost long life and small size Howevertheir accuracy is low and the detection range is short andtherefore they cannot be applied in vertical parking modeVision sensors such as cameras are of low cost as well as longlife and their precision is also fairly high In addition they canprovide real-time vision assists and rich image informationto drivers [3] But vision sensors have poor performance indarkness conditions which have no additional light sources

As amain trend for parking assistance systems the vision-based systems are promising and many researchers andcompanies have developed their systems by using camerasHowever it is very difficult to maneuver vehicles by usingone single camera since the blind spots are inevitable insome complicated conditions such as narrow valleys andthe reverse parking In this paper a low-cost birdrsquos eye viewvision system is constructed by installing four fisheye cameras

Hindawi Publishing CorporationAdvances in Mechanical EngineeringVolume 2014 Article ID 847406 13 pageshttpdxdoiorg1011552014847406

2 Advances in Mechanical Engineering

(a) Front camera (b) Left camera

(c) Right camera (d) Back camera

Figure 1 The calibration images from different cameras

around the vehicle to provide the image covering all thevehicle surroundings

Generally an automatic parking system consists of threecomponents path planning including free parking spacedetection automatic steering and braking system used toimplement the planned trajectory and a HMI (HumanMachine Interface) which can provide information (such asvisual and audio) of the ongoing parking process [4]

To find free parking space various vision methods areproposed which can be classified into three categories Somerecognize adjacent vehicles by using the 3D structure of park-ing lots [5 6] Some detect the parking space markings [78] The others recognize both adjacent vehicles and parkingspace markings [4 9] For example Fintzel et al developeda stereovision-based method for parking lots [5] Xiu et aldeveloped a monocular vision-based parking lots markingrecognition using neural networks [7]The proposedmethodbelongs to the second category

Hough transform is often used for detecting the linemarking in the parking space [8 10ndash12] However the perfor-mance of Hough transform is not robust to challenges due tothe noise clutter and variation in illumination and weatherconditions in detecting parallel line pairs [13] Furthermorein the parking assistance system the wide-view images ofthe vehicle surroundings often covermultiple parking spacesAlmost all parking spaces are parallelograms Neverthelessunder the influence of the noise in image Hough transformis inefficient in detecting multiple parallelograms simultane-ously compared with the Radon Transform [14 15] In thispaper we employ theRadon transform rather than theHoughtransform to enhance the robustness and detection accuracyWe also introduce clustering and filtering [16] to improverobustness against the challenges such as shadows

The remainder of this paper is organized as followsSection 2 introduces the birdrsquos eye view vision system basedon four fisheye cameras Section 3 describes the details ofparking space detection based on the Radon transform In

Table 1 The calibration result of camera intrinsic parameters

120572 120573 120574 1199060

V0

2826672609 2873687659 234369402 3101461146 2424059147

Table 2 The calibration result of camera distortion coefficients

1198961

1198962

minus03111923795 005594397398

Section 4 the methods of path planning and path trackingfor automatic parking are introducedThe experiment resultsimplemented in the real scenes are given in Section 5 whichsubstantiated the effectiveness and robustness of the pro-posed method Finally the conclusion is drawn in Section 6

2 Birdrsquos Eye View Vision System

The Birdrsquos eye view vision used in the proposed system isbased on four fisheye cameras with 180-degree field of viewaround vehicleThe system consists of two phases calibrationand image mosaicking

21 Calibration The camera imaging model is geometricmapping from three-dimensional space to two-dimensionalpixel space Camera calibration is to find out the parametersof this mapping relation that is camera parameters whichcan be divided into intrinsic parameters and extrinsic param-eters

In the real calibration process we took the flat calibra-tion method proposed by Zhang [17] The original imagescaptured from the fisheye cameras are distorted see Figure 1In order to get high accuracy performance the followingsteps are performed Firstly the four fisheye cameras arecalibrated by using a chess board to obtain their intrinsicparameters and extrinsic parameters respectively Secondlya polynomial distortion model [18] based method is usedto correct each camerarsquos distortion Lastly according to theinverse perspective mapping (IPM) [19] from the imagecoordinate to the world coordinate the undistorted imagesare transformed to the IPM images in the same ground planeby using the extrinsic parameters Furthermore nonlinearLevenberg-Marquardt optimization algorithm [20] is alsoused to optimize camera parameters

From experiments we find that the above procedures canobtain comparatively ideal results the more control pointsare selected the more accurate intrinsic parameters and thebetter results after calibration can be obtained In this paper20 control points are selected on each image and the finalresults including calibration effects as well as intrinsic andextrinsic parameters are respectively shown in Figure 2 andTables 1 and 2

22 Image Mosaicking In order to obtain the omnidirec-tional information the four perspective images are combinedinto the one synthesized image We firstly apply vehiclecoordinate system-camera coordinate system joint calibra-tion to decide inverse perspective transformation parameters

Advances in Mechanical Engineering 3



Figure 2 The distortion removed images in different cameras

Then the Levenberg-Marquardt algorithm [20] is applied tooptimize inverse perspective parameters by minimizing theerror of feature points Besides in order to improve imagequality after inverse perspective transformation the bilinearinterpolation algorithm and the white balance procedure areintroduced An example after inverse perspective transfor-mation and an example of the final bird view image arerespectively shown in Figures 3 and 4

3 Parking Space Detection

31 Overview Generally the parking space is often locatedon one side of the moving vehicle Therefore in order toimprove the real-time performance of the automatic parkingonly the fisheye cameras on the parking space side willbe used to detect the free parking space while all of thecameras are used when the parking spaces are around the carSubsequently the IPM (inverse perspective mapping) imagesare used as the input for the free parking space detectionFurthermore in this paper we suppose that roads are flatSince visual field of fisheye cameras is small usually within2 meters of the vehicle such assumption is generally tenable

32 Radon Transform The Radon transform is named afterthe Austrian mathematician Johann Karl August Radon(December 16 1887ndashMay 25 1956) Applying the Radontransform in an image 119868(119909 119910) for a given set of angles canbe regarded as computing the projection of the image alongthe given angles The resultant projection 119877(120579 120588) is a lineintegral which is the sum of the intensities of the pixels ineach direction In other words the liner integral value 119877(120579 120588)is the projection of the geometry image along the direction 120579as shown in Figure 5



Figure 3 The calibration result between the cameras and car

Figure 4 Birdrsquos eye view vision system Images 119865119891 119865119897 119865119903 119865119887

are captured from the front left right and back fisheye camerasmounted on theCyberC3 vehicleThe image in the center is the birdrsquoseye view image synthesized from the four fisheye images

The formulation of the Radon transform is as follows

120588 = 119909 sdot cos 120579 + 119910 sdot sin 120579

119877 (120579 120588) = int

+infin

minusinfin

int

+infin

minusinfin

119868 (119909 119910)

sdot 120575 (120588 minus 119909 sdot cos 120579 minus 119910 sdot sin 120579) 119889119909 119889119910(1)

where 120575 is the Dirac Delta function (120579 120588) is the parameterspace about the Radon space 119877(120579 120588) is the value of Radonspace at (120579 120588) points

Radon transform and Hough transform both transformthe two-dimensional image plane (119906 V) to the parameterspace defined by (120579 120588) Therefore for both of these two


R120579(x998400)

y

x998400

x998400

120579

I(x y)

x

Figure 5 Radon transform

transforms any line in the image plane has correspondingpoints in the parameter space

However Hough transform quantifies the parameterspace to a lot of small lattices each ofwhich is an accumulatorPoints in the image plane will be accumulated in the cor-responding small lattices through the parameter transformAfter the transform all the small lattices will be detected andvalues in accumulators reflect the condition of the detectedline Therefore the detection result is easily influenced bynoise such as illumination and shadows and the detectionaccuracy and robustness are not very high

Radon transform is a mapping from the image plane tothe parameter space instead of discrete quantified latticesIn Radon space the corresponding mapping value of thedetected line in the image plane is the linear integral valuethat is the projection value of the pixelsrsquo intensities in theimage along every single direction 120579 The projection value isclosely related to the pixelsrsquo intensities of the detected lineTherefore Radon transform has better noise-tolerance abilityand robustness as well as accuracy in detecting lines withgray information which is the reason why Radon transformis employed to detect the free parking space

Figure 6 shows the comparison between the image trans-formation results derived respectively from Hough trans-form and Radon transform From the comparison we canconclude that the features in Radon space that is light spotsin Figure 6(c) are apparently more notable than those inHough space and the number of light spots in Radon spaceis equal to that of lines in the edge image Therefore weproposed amethod for detecting the free parking space basedon this merit

In China the colored parking line markings are usuallyeither white lines or yellow lines which have high intensitiesin the G and B channels of the RGB (Red Green and Blue)color model In the paper the G channel is used as the grayimage for the edge detection The Canny kernel detector isused to obtain edge image from the gray image Meanwhile

the intensity values of the edge points in the edge imageare preserved This is very important to make good use ofthe feature of Radon transform mentioned previously whichensures the high accuracy and robustness of the proposedsystem to the noises shadows or obstacles compared with thesystem using the Hough transform

Furthermore the parking space orientations can beobtained by voting in the angle histogram based on the linerintegral value 119877 in Radon space along the 120579 in the range of[0 180

∘) see Figure 7 From the figure we can conclude that

since there exists a certain angle between the parking spacemarking lines the corresponding angle histogram has twomain peaks and the transverse angle between these two peaksjust meets the fixed angle relation Therefore we can obtainthe parking space orientations from the angle histogram

However with the influence of adjacent vehicle distur-bance or noise such as uneven light or shadows of treesthere will exist several main peaks in one angle histogramand in the condition with severe noise the real parkingspace marking lines may get submerged see the third row ofFigure 7Therefore themethod talked above should bemod-ified In this paper we propose to use the relation between theprincipal direction and secondary direction of the parkingspace to superimpose the angle histogram of 120579 isin [0 180

∘)

on that of 120579 isin [0 90∘) and mark the principal direction and

secondary direction The modified angle histogram is shownin Figure 8 From the figure we can see that the accuracy andreliability are very high with the modified angle histogram

However the real parking spacemarking lines do not nec-essarily follow strict vertical or fixed angle relation and errorsusually exist Therefore in order not to lose generality werespectively take the neighborhood with a certain range ofthe principal and secondary directions as regions of interest

33 Features Extraction Vehicle parking space markings areoften constructedwith several fixedwidths and colored paral-lel line segment pairs According to the Radon transform thelines are mapped to the bright spots (BS) in the Radon spaceAs shown in Figure 9 they are in one-to-one correspondence

It should be noted that the parallel line segment pairs inthe edge image will produce BS pairs in the Radon spaceThetwo BS points in one pair have the same value 120579 and a fixedwidth Based on this feature a method to detect the center ofthe BS pair in the Radon space is proposed Considering theinfluence of noises clutters and vehicles in the edge imageit is necessary to take the area around the BS as the region ofinterest The detector structure is shown in Figure 10

HBS is the high bright spot of the pair and LBS is the lowbright spot of the pair PD is the two BS pixel distances of thefixed width mapped from the line pair

119881 (120579 120588) = 119877HBS + 119877LBS minus 119870119904 sdot 119877 (120579 120588)

minus 119877 (120579 120588 + PD) minus 119877 (120579 120588 minus PD) (2)

where119881(120579 120588) is the temporary value of the designed detector119877(120579 120588) is the line integral value in the Radon space at (120579 120588)Correspondingly 119877HBS 119877LBS 119877(120579 120588 + PD) 119877(120579 120588 minus PD) arethe line integral values in the Radon space respectively119870

119904is


(a)

600

400

200

0

minus200

minus400

minus600

0 20 40 60 80 1001201401600

20

40

60

80

100

120

140

160

180

200

(b)

300

200

100

0

minus100

minus200

minus300

0 20 40 60 80 1001201401600

05

1

15

2

25

3

times104

(c)

Figure 6 The contrast between Hough and Radon transform (a) The edge image with gray information (b) Hough space (c) Radon space

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0010203040506070809

1

0010203040506070809

1

0010203040506070809

1

Figure 7 The angle histogram

a factor related by the extent of the difference between 119877HBSand 119877LBS The value is defined as follows

119870119904=

max (119877HBS 119877LBS)

min (119877HBS 119877LBS) (3)

However the real lines pair of the parking spacemarkingsis not strictly with a certain width In order to avoid theinfluence of the line width errors 119877HBS and 119877LBS are taken asthe local maximum of their neighborhood near the BS alongdirection 120588

Finally in order to extract the center of the brightspot pair we limited the temporary value 119881(120579 120588) to be


0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

Figure 8 The modified angle histogram

L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)

Figure 9 (a) Lines L1 L2 L3 and L4 are the parking space marking lines in inverse perspective image (b) P1 P2 P3 and P4 are the brightspot pairs of the lines corresponding in Radon space

PDPD

PD2

PD2

HBS

LBS

Center of BS pair

Figure 10 The structure for BS pairs detection The yellow color isthe BS pair in Radon space

in the range of [0 1] by using the transform as fol-lows

119875 (120579 120588) =

119881 (120579 120588)

119877HBS + 119877LBSsdot

min (119877HBS 119877LBS)

max (whole Radon space)

(4)

C1C2

C3

C4

(a) In Radon space (b) In image

Figure 11The center detection result of theBSpairs of parking spacelines (a)119862111986221198623 and1198624 are the candidate points detected by theproposedmethod in Radon space (b)The red lines are the detectionresult of the points in image space

where 119875(120579 120588) is probability set of the center about the BSpairs The higher probability of 119875(120579 120588) is the more likely theparking space exists With known parking space orientationthe set 119862 can be obtained by series candidate feature pointsabout the possible parking space line segment pairs Thedetection result is shown in Figure 11


Carrsquos body interference


Figure 12 The car body lines of the car interfere with the detectionin Radon space (a) The points marked in yellow area are theinterfering points in Radon space (b)The lines marked in blue areaare the interfering lines of the carrsquos body

It should be noted that a number of factors such as the carbody lines shadows and the wear of the line markings mayoften affect the detection accuracy as shown in Figure 12

In order to get accurate parking space marking linessome measures to remove the noise factors should be taken

34 Clustering and Filtering The line segment pairs of theparking space markings are not always strictly in parallel inthe real world To solve this problem the local maximumalong the direction of 120579 near the candidate points is per-formed Furthermore although almost candidate points ofthe set 119862 belong to the parking space line segments it cannotdeal with the challenges due to shadows or the body lines ofthe car parked see Figure 12 Therefore we perform the 119870-means cluster algorithm first and then filter the interveningpoints of the set119862 by using the parking space geometry shapefeatures Finally the center points of the BS about the parkinglines can be fixed in the set 119862

The final detection result is shown in Figure 13 whichshows that the proposed method of designed line detectorclustering and filtering can effectively and accurately detectthe parking spaces in various scenes Furthermore theproposed method demonstrates the high robustness againstthe challenges such as shadows

Figure 14 shows the proposed methods take good perfor-mance in different scenes for parking space detection

35 Empty Parking Space Extraction The method talkedabove detects both the empty parking spaces and occupiedparking spaces Since when parking cars we are usuallyconcerned with empty parking spaces empty parking spacesshould be extracted

After parking space detection the principal direction canbe used to have image rotation calibration and the effect aftercalibration is shown in Figure 15

After image angle calibration a certain parking space istaken as the research object Considering accuracy robust-ness and real-time performance a quarter of the parkingspace depth is taken as the region of interest see Figure 16and the image area of the region of interest is taken as the

feature to decide whether a certain parking space is empty oroccupiedThe rate of the image area (image pixel numbers) tothe area of regions of interest (total pixel numbers in regionof interest) P1 and P2 is respectively defined as 119878

1and 1198782 and

a high threshold 119879119867and average threshold 119879

119872are set Firstly

compare 1198781with 119879

119867 If 1198781⩾ 119879119867 consider this parking space

as occupied and go to the next parking space Otherwise goto the region of interest P2 Secondly compare 119878

2with 119879

119867 If

1198782⩾ 119879119867 consider this parking space as occupied and go to

the next parking space Otherwise calculate 119878119898

119878119898=

1198782+ 1198781

2

(5)

Finally compare 119878119898

with 119879119898 If 119878119898

gt 119879119898 consider this

parking space as occupied and go to the next parking spaceOtherwise consider this parking space as empty

4 Path Planning and Path Tracking

In this section the method of path planning and tracking forvertical automatic parking based on the detection results ofthe free parking space is described

41 Path Planning Given what has been talked about pre-viously it is able to get the position information of theparking space In this situation a path planning method isneeded for the automatic parking Up to now there are twopath planning methods which are usually used for parkingvehicles that is single circular trajectory based path planningmethod and double circular trajectory based path planningmethod

The traditional single circular trajectory based path plan-ningmethod can be divided into three parts that is a straightline for the first part a circular arc for the second partand another straight line for the third part However thismethod is always constrained by the size of parking spacesobstacles space for parking and so forth which will lead tofailure of automatic parking Considering all these defectsthe traditional double circular trajectory based path planningmethod has done a lot of improvement Yet this method doesnot take into account the initial position of cars relative tothe target parking space As a result this method cannot plana parking trajectory which can be easily controlled Underthis circumstance we proposed an improved double circulartrajectory based path planning method

Figure 17 shows the details of this method XOY coordi-nate is the world coordinate P1 and P2 are the entrance guid-ance points obtained from the parking space detection resultin the image coordinate by using the inverse perspectivemapping Correspondingly WD is the parking space depthThe planned path is based on a double circular trajectorywhich has three switch points A B and C

(a) Before point A drive the car along the straight pathtill it reaches point A

(b) In the circular arc AB drive the car with a certainsteering angle for the circular motion

(c) In arc BC reverse the car in another certain steeringangle for the circular motion till reaching point C


(a) (b) (c)

Figure 13 Result of parking space detection after clustering and filtering (a) The detected points are the center of the BS pairs about theparking space marking lines in Radon space (b)The red lines are the result of the detected points mapped to image coordinate (c)The greenrectangles are parking space

Figure 14 The proposed method detection experiments of theparking space in different scenes

(d) After point C drive the car along the straight path

In order to improve the parking performance in acontinuous operation it is very important to minimizethe turning radius to fit the parking space However thesmaller the turning radius is the more likely the car mayhit the neighboring vehicles Therefore the turning radiusis calculated with the constraint of the geometry relation asshown in Figure 18

1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)

Table 3 Comparing the parking space detection of the proposedmethod with Hough space

Metric The proposed method(Radon space) Based on Hough space

Precision 971 938Recall 815 787

where 119871 is the wheel base of the car 119908 is the width ofthe car and 120601max is the maximal steering wheel angle 119877

1

is turning radius in the first turn Here it is the minimumturning radius of the vehicle 119877

2is the turning radius of the

second turn 119889 is the distance from the car coordinate centerto the lines between parking space entrance guidance points119863 road indicates the whole space of the car used during theparking procedure According to the above formulations it isable to get the position of the switch points and steeringwheelangle 120572 by setting an appropriate119863 road

42 Path Tracking Path tracking is mainly to solve theproblem how to determine the steering wheel angle andspeed at each time for the vehicle to follow the planned pathGenerally the speed of the vehicle is often low during thewhole parking process Therefore we only consider trackingof the steering wheel angle of vehicle

We employ the preview follow based on the PID(proportional-integral-derivative) strategy since it is simpleand efficient for the vehicle control [21]

The principle is shown in Figure 19 The preview point istaken in front of the vehicle with a certain distance Subse-quently the distance between the preview point and the targetpath is taken as the input of the PID controller Howeversuch method often has slow response and difficulties tocontrol accurately when the curvature of the path is large Toovercome this problem we proposed an improvedmethod ofthe PD controller based on the feed forward for the vehiclecontrol


(a) (b)

Figure 15 Principal direction correction

Depth D

D4

P1 P2

Region of interest

Figure 16 The region of interest for recognizing the free space

Preview point A uses a typical preview with straight linemethod to get minimum distance 1198901 between point A andthe target circular path Subsequently the preview point B isestimated by DR (Dead Reckoning) in the current pose of thevehicle in circles Correspondingly 1198902 is the distance usingthe same method with 1198901

The feed forward parameter is the steering wheel angle 120601calculated by the previous formulation So the final steeringwheel angle is calculated as follows

120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)

where the 1198901119894is the 1198901 in themoment of 119894 and the 1198902

119894is the 1198902 in

the moment of 119894119870119901and119870

119889are parameters of PD controller

Start

L

X A

B

C

P1

P2

WD

O

End

Y

Figure 17 Parking path based on a double circular trajectory

5 Experiments and Results

51 Experimental Platform The proposed system was imple-mented in our experimental platform based on the CyberC3[22 23] which has four fisheye cameras mounted around thevehicle The angle encoder for measuring the steering wheelangle and the odometer encoder are also installed on theplatform Details are shown in Figure 20

52 Detection Accuracy Figure 21 shows the proposedmethod based on the Radon transform is more robustthan those based on the Hough transform in the noisyenvironment Figure 22 shows that the Radon transformscan obtain a good performance in detecting multiple parkingspaces simultaneously This was also verified in [14] fordetecting for rectangles and [13] for parallelograms


Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)

Figure 18 Geometry relation in path planning (a) Path planning (b) The minimum turning radius in 1198772

A

B

e1

e2

Target path

Figure 19 Improved method for circular motion

In the experiments there were totally 2626 frames usedto compare the performance of the proposed method againstthose based on the Hough space under the same conditionThe comparison results are shown in Table 3

The precision and recall used in Table 3 are computed asfollows

Precision = true Positivestrue Positives + false Positives

Recall = true Positivestrue Positives + false Negatives

(8)

where the true positive is the frequency of the correctdetections of the parking spaces The false positive is thefrequency of false detections and the false negative is thefrequency of the missing detections

From the experimental results we can see that the pro-posedmethod performs robustly and accurately despite of thechallenges due to shadows and other vehicles

Figure 20 The CyberC3 vehicle mounted four fisheye camerassystem images 119862

119891 119862119903 119862119897 and 119862

119887are the fisheye cameras mounted

in the front right side left side and back of the car

Cracks interference

LFalse point

(a) Based on Hough space

(b) Based on Radon space

Figure 21The robustness of Radon space in detecting parking spaceis better thanHough transform in the same conditions including thesame detector clustering and filtering (a) The ground cracks noisein the edge image affects detection points in Hough space (b) Thenoise has no influence on detecting space in Radon space


(a) Based on Hough space (b) Based on Radon space

Figure 22 The performance of Radon transform has more accuracy than Hough transform in the same conditions including the samedetector clustering and filtering (a) The detection of parking spaces in Hough space (b) The detection of parking space in Radon space

Figure 23 Experiment result of free parking space

Table 4 The statistical result of empty parking space extraction

Name Number ProportionSuccessful detection 325 9939Unsuccessful detection 2 061False positive detection 1 031

53 Empty Parking Space Extraction Figure 23 is the experi-ment result of empty parking space extraction In this figurethe red rectangles are occupied parking spaces while thegreen ones indicate empty parking spaces

In the experiment of empty parking space extractionwe took 327 images of different environments and thequantitative evaluation results are shown in Table 4 In thistable false positive detection number means the number ofwrongly indicated parking slots that are not empty

Based on the experiment results we can see that theempty parking space extraction method which is based onregions of interest has very high accuracy

54 Automatic Parking Simulation Experiment In order toevaluate the proposed path planning and path trackingmethod a simulation of the path planning is executedin MATLAB The scale size is determined by the inverseperspective image The coordinate is transformed to theinverse perspective image coordinates One pixel represents2 cm in the real world coordinate Furthermore the proposedpath tracking simulation is executed in TORCS (The OpenRacing Car Simulator)

From the simulation results (see Figure 24) it can befound that the proposed path planning is a good trajectoryfor automatic parking Furthermore the improved method

0

100

200

300

400

500

600

300 200 100 0 100 200 300

(a) Path planning simulation

Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)

Pure PID methodImproved method

(b) Path tracking simulation

Figure 24 The simulation result of the proposed method for pathplanning and path tracking


of path tracking is more fast and accurate than traditionalmethod (Pure PID method)

6 Conclusion

In this paper a low-cost birdrsquos eye view vision assistancesystem with four fisheye cameras has been developed whichcan provide the surrounding view of the host vehicle Thesystem can rectify the images captured by the fisheye camerasand mosaic them into a birdrsquos eye view image in real-timeFurthermore a method for detecting the free parking spacehas been proposed based on the Radon transform Thedetector for the center of bright point pairs is completed inthe Radon space By using the clustering and filtering basedon the shape features of the parking space we can alleviatethe effects of noises effectively In particular we compared theperformance of the proposed system against those based onthe Hough transform in the experiments The experimentalresults show that the proposed method has more accuracyand robustness in detecting the free parking space Finally asimulation of the path planning and path tracking is executedto evaluate the proposed method for automatic parking

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 General Program of NationalNatural Science Foundation of China (6117417851178268)the Major Research Plan of National Natural Science Foun-dation of China (9112001891220301) and National MagneticConfinement Fusion Science Program (2012GB102002)

References

[1] R Frank ldquoSensing in the ultimately safe vehiclerdquo in Proceedingsof the Convergence Conference and Exhibition 2004

[2] H Ichihashi KMiyagishi and K Honda ldquoFuzzy c-means clus-tering with regularization by K-L informationrdquo in Proceedingsof the 10th IEEE International Conference on Fuzzy Systems pp924ndash927 December 2001

[3] R Zhang P Ge X Zhou T Jiang and R Wang ldquoAn methodfor vehicle-flow detection and tracking in real-time basedon Gaussian mixture distributionrdquo Advances in MechanicalEngineering vol 2013 Article ID 861321 8 pages 2013

[4] H G Jung D S Kim P J Yoon and J H Kim ldquo3Dvision system for the recognition of free parking site locationrdquoInternational Journal of Automotive Technology vol 7 no 3 pp361ndash367 2006

[5] K Fintzel R Bendahan C Vestri S Bougnoux and TKakinami ldquo3D parking assistant systemrdquo in Proceedings of theIEEE Intelligent Vehicles Symposium pp 881ndash886 June 2004

[6] J K Suhr and H G Jung ldquoSensor fusion-based vacant parkingslot detection and trackingrdquo IEEE Transactions on IntelligentTransportation Systems no 99 pp 1ndash16 2013

[7] J Xiu G Chen M Xie et al ldquoVision-guided automatic parkingfor smart carrdquo in Proceedings of the IEEE Intelligent VehiclesSymposium pp 725ndash730 2000

[8] G J Ho S K Dong J Y Pal and K Jaihie ldquoParking slotmarkings recognition for automatic parking assist systemrdquo inProceedings of the IEEE Intelligent Vehicles Symposium pp 106ndash113 June 2006

[9] C-C Huang and S-J Wang ldquoA hierarchical bayesian gen-eration framework for vacant parking space detectionrdquo IEEETransactions on Circuits and Systems for Video Technology vol20 no 12 pp 1770ndash1785 2010

[10] P Degerman J Pohl and M Sethson ldquoHough transform forparking space estimation using long range ultrasonic sensorsrdquoSAE Technical Paper 2006-01-0810 2006

[11] J K Suhr K Bae J Kim and H G Jung ldquoFree parking spacedetection using optical flow-based euclidean 3d reconstruc-tionrdquo in Proceedings of the International Conference on MachineVision Applications pp 563ndash566 2007

[12] C R Jung and R Schramm ldquoParallelogram detection using thetiled hough transformrdquo in Proceedings of the 13th InternationalConference on Systems Signals and Image Processing pp 177ndash180 2006

[13] H Bhaskar N Werghi and S Al Mansoori ldquoCombined spatialand transform domain analysis for rectangle detectionrdquo inProceedings of the 13th Conference on Information Fusion pp 1ndash7 July 2010

[14] Q Zhang and I Couloigner ldquoComparing different localizationapproaches of the radon transform for road centerline extrac-tion from classified satellite imageryrdquo in Proceedings of the 18thInternational Conference on Pattern Recognition (ICPR rsquo06) pp138ndash141 August 2006

[15] H Bhaskar and N Werghi ldquoComparing Hough and Radontransform based parallelogram detectionrdquo in Proceedings ofthe IEEE Conference and Exhibition (GCC rsquo11) pp 641ndash644February 2011

[16] Y Zheng C-W Yeh C-D Yang S-S Jang and I-M Chu ldquoOnthe local optimal solutions of metabolic regulatory networksusing information guided genetic algorithm approach andclustering analysisrdquo Journal of Biotechnology vol 131 no 2 pp159ndash167 2007

[17] Z Zhang ldquoA flexible new technique for camera calibrationrdquoIEEE Transactions on Pattern Analysis andMachine Intelligencevol 22 no 11 pp 1330ndash1334 2000

[18] C Ricolfe-Viala and A-J Sanchez-Salmeron ldquoLens distortionmodels evaluationrdquo Applied Optics vol 49 no 30 pp 5914ndash5928 2010

[19] M Yang C Wang F Chen B Wang and H Li ldquoA newapproach to high-accuracy road orthophoto mapping basedon wavelet transformrdquo International Journal of ComputationalIntelligence Systems vol 4 no 6 pp 1367ndash1374 2011

[20] J More ldquoLevenbergndashmarquardt algorithm Implementationand theoryrdquo in Proceedings of the Conference on NumericalAnalysis pp 1ndash28 Dundee UK 1977

[21] D Yu and Y-H Wu ldquoModeling of driver controlling at car-following based on preview follower theoryrdquo in Proceedings ofthe International Conference on Intelligent ComputationTechnol-ogy and Automation (ICICTA rsquo08) pp 636ndash641 October 2008

[22] T Xia M Yang R Yang and C Wang ldquoCyberC3 a prototypecybernetic transportation system for Urban applicationsrdquo IEEETransactions on Intelligent Transportation Systems vol 11 no 1pp 142ndash152 2010


[23] H Fang M Yang R Yang and C Wang ldquoGround-texture-based localization for intelligent vehiclesrdquo IEEE Transactions onIntelligent Transportation Systems vol 10 no 3 pp 463ndash4682009

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Advances inOptoElectronics


Volume 2014

RoboticsJournal of


Chemical EngineeringInternational Journal of


Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation





Figure 1 The calibration images from different cameras

around the vehicle to provide the image covering all thevehicle surroundings

Generally an automatic parking system consists of threecomponents path planning including free parking spacedetection automatic steering and braking system used toimplement the planned trajectory and a HMI (HumanMachine Interface) which can provide information (such asvisual and audio) of the ongoing parking process [4]

To find free parking space various vision methods areproposed which can be classified into three categories Somerecognize adjacent vehicles by using the 3D structure of park-ing lots [5 6] Some detect the parking space markings [78] The others recognize both adjacent vehicles and parkingspace markings [4 9] For example Fintzel et al developeda stereovision-based method for parking lots [5] Xiu et aldeveloped a monocular vision-based parking lots markingrecognition using neural networks [7]The proposedmethodbelongs to the second category

Hough transform is often used for detecting the linemarking in the parking space [8 10ndash12] However the perfor-mance of Hough transform is not robust to challenges due tothe noise clutter and variation in illumination and weatherconditions in detecting parallel line pairs [13] Furthermorein the parking assistance system the wide-view images ofthe vehicle surroundings often covermultiple parking spacesAlmost all parking spaces are parallelograms Neverthelessunder the influence of the noise in image Hough transformis inefficient in detecting multiple parallelograms simultane-ously compared with the Radon Transform [14 15] In thispaper we employ theRadon transform rather than theHoughtransform to enhance the robustness and detection accuracyWe also introduce clustering and filtering [16] to improverobustness against the challenges such as shadows

The remainder of this paper is organized as followsSection 2 introduces the birdrsquos eye view vision system basedon four fisheye cameras Section 3 describes the details ofparking space detection based on the Radon transform In

Table 1 The calibration result of camera intrinsic parameters

120572 120573 120574 1199060

V0

2826672609 2873687659 234369402 3101461146 2424059147

Table 2 The calibration result of camera distortion coefficients

1198961

1198962

minus03111923795 005594397398

Section 4 the methods of path planning and path trackingfor automatic parking are introducedThe experiment resultsimplemented in the real scenes are given in Section 5 whichsubstantiated the effectiveness and robustness of the pro-posed method Finally the conclusion is drawn in Section 6

2 Birdrsquos Eye View Vision System

The Birdrsquos eye view vision used in the proposed system isbased on four fisheye cameras with 180-degree field of viewaround vehicleThe system consists of two phases calibrationand image mosaicking

21 Calibration The camera imaging model is geometricmapping from three-dimensional space to two-dimensionalpixel space Camera calibration is to find out the parametersof this mapping relation that is camera parameters whichcan be divided into intrinsic parameters and extrinsic param-eters

In the real calibration process we took the flat calibra-tion method proposed by Zhang [17] The original imagescaptured from the fisheye cameras are distorted see Figure 1In order to get high accuracy performance the followingsteps are performed Firstly the four fisheye cameras arecalibrated by using a chess board to obtain their intrinsicparameters and extrinsic parameters respectively Secondlya polynomial distortion model [18] based method is usedto correct each camerarsquos distortion Lastly according to theinverse perspective mapping (IPM) [19] from the imagecoordinate to the world coordinate the undistorted imagesare transformed to the IPM images in the same ground planeby using the extrinsic parameters Furthermore nonlinearLevenberg-Marquardt optimization algorithm [20] is alsoused to optimize camera parameters

From experiments we find that the above procedures canobtain comparatively ideal results the more control pointsare selected the more accurate intrinsic parameters and thebetter results after calibration can be obtained In this paper20 control points are selected on each image and the finalresults including calibration effects as well as intrinsic andextrinsic parameters are respectively shown in Figure 2 andTables 1 and 2

22 Image Mosaicking In order to obtain the omnidirec-tional information the four perspective images are combinedinto the one synthesized image We firstly apply vehiclecoordinate system-camera coordinate system joint calibra-tion to decide inverse perspective transformation parameters















120588 = 119909 sdot cos 120579 + 119910 sdot sin 120579

119877 (120579 120588) = int

+infin

minusinfin

int

+infin

minusinfin

119868 (119909 119910)





R120579(x998400)

y

x998400

x998400

120579

I(x y)

x












∘)










119904is


(a)

600

400

200

0

minus200

minus400

minus600

0 20 40 60 80 1001201401600

20

40

60

80

100

120

140

160

180

200

(b)

300

200

100

0

minus100

minus200

minus300

0 20 40 60 80 1001201401600

05

1

15

2

25

3

times104

(c)


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0010203040506070809

1

0010203040506070809

1

0010203040506070809

1



119870119904=

max (119877HBS 119877LBS)

min (119877HBS 119877LBS) (3)




0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90


L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)


PDPD

PD2

PD2

HBS

LBS

Center of BS pair



119875 (120579 120588) =

119881 (120579 120588)


min (119877HBS 119877LBS)


(4)

C1C2

C3

C4

















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of






















120588 = 119909 sdot cos 120579 + 119910 sdot sin 120579

119877 (120579 120588) = int

+infin

minusinfin

int

+infin

minusinfin

119868 (119909 119910)





R120579(x998400)

y

x998400

x998400

120579

I(x y)

x












∘)










119904is


(a)

600

400

200

0

minus200

minus400

minus600

0 20 40 60 80 1001201401600

20

40

60

80

100

120

140

160

180

200

(b)

300

200

100

0

minus100

minus200

minus300

0 20 40 60 80 1001201401600

05

1

15

2

25

3

times104

(c)


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0010203040506070809

1

0010203040506070809

1

0010203040506070809

1



119870119904=

max (119877HBS 119877LBS)

min (119877HBS 119877LBS) (3)




0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90


L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)


PDPD

PD2

PD2

HBS

LBS

Center of BS pair



119875 (120579 120588) =

119881 (120579 120588)


min (119877HBS 119877LBS)


(4)

C1C2

C3

C4

















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









R120579(x998400)

y

x998400

x998400

120579

I(x y)

x












∘)










119904is


(a)

600

400

200

0

minus200

minus400

minus600

0 20 40 60 80 1001201401600

20

40

60

80

100

120

140

160

180

200

(b)

300

200

100

0

minus100

minus200

minus300

0 20 40 60 80 1001201401600

05

1

15

2

25

3

times104

(c)


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0010203040506070809

1

0010203040506070809

1

0010203040506070809

1



119870119904=

max (119877HBS 119877LBS)

min (119877HBS 119877LBS) (3)




0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90


L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)


PDPD

PD2

PD2

HBS

LBS

Center of BS pair



119875 (120579 120588) =

119881 (120579 120588)


min (119877HBS 119877LBS)


(4)

C1C2

C3

C4

















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a)

600

400

200

0

minus200

minus400

minus600

0 20 40 60 80 1001201401600

20

40

60

80

100

120

140

160

180

200

(b)

300

200

100

0

minus100

minus200

minus300

0 20 40 60 80 1001201401600

05

1

15

2

25

3

times104

(c)


0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

0010203040506070809

1

0010203040506070809

1

0010203040506070809

1



119870119904=

max (119877HBS 119877LBS)

min (119877HBS 119877LBS) (3)




0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90


L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)


PDPD

PD2

PD2

HBS

LBS

Center of BS pair



119875 (120579 120588) =

119881 (120579 120588)


min (119877HBS 119877LBS)


(4)

C1C2

C3

C4

















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90

0

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 900

01

02

03

04

05

06

07

08

09

1

0 10 20 30 40 50 60 70 80 90


L2

L1

L3

L4

(a)

P1P2

P3

P4

(b)


PDPD

PD2

PD2

HBS

LBS

Center of BS pair



119875 (120579 120588) =

119881 (120579 120588)


min (119877HBS 119877LBS)


(4)

C1C2

C3

C4

















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of





















1and 1198782 and






2with 119879

119867 If



119878119898=

1198782+ 1198781

2

(5)


with 119879119898 If 119878119898












(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a) (b) (c)





1198771=

119871

tan120601max

1198772sin120572 + 119871 cos120572 + 119908

2

sin120572 = 119863 road + 119863

(1198771+ 1198772) sin120572 = 119877

1+ 1198891015840+ 119863

1198632+ (1198772minus 119889 minus

119908

2

)

2

le (1198772minus

119908

2

)

2

(6)





1








(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a) (b)


Depth D

D4

P1 P2

Region of interest




120572 = 120601 + 1198701199011198901

119894+ 119870119889(1198901

119894minus 21198901

119894minus1+ 1198902

119894) (7)


119894is the 1198902 in

the moment of 119894119870119901and119870


Start

L

X A

B

C

P1

P2

WD

O

End

Y






Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









Y

X

E

B

AC

D

L

d998400 S

w

01

02

120572

120572

P2

P1

D road

R2

R1

(a)

0

rD

L

dd

S

w

R2

(b)


A

B

e1

e2

Target path






(8)




119891 119862119903 119862119897 and 119862



Cracks interference

LFalse point















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of



















0

100

200

300

400

500

600

300 200 100 0 100 200 300


Erro

rs o

f PID

cont

rolle

r (m

)

minus02

minus015

minus01

minus005

0

005

01

015

02

0 2 4 6 8 10 12

Mlleage (m)






6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of










6 Conclusion




Acknowledgments


References


























VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of











VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of








Research Article Automatic Parking Based on a Bird's Eye ...

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