Dynamic Programming and Curve Fitting Based Road Boundary Detection

Transcription

1 Dyamic Programmig ad Curve Fittig Based Road Boudary Detectio SHYAM PRASAD ADHIKARI, HYONGSUK KIM, Divisio of Electroics ad Iformatio Egieerig Chobuk Natioal Uiversity Ga Deokji-Dog Jeoju-City Jeobuk SOUTH-KOREA Abstract: - This paper presets a visio based road boudary detectio based o the combiatio of dyamic programmig ad d order polyomial approximatio. The iitial estimate of the most likely road boudaries are obtaied by a modified dyamic programmig o a cost field defied o the edge image. A secod order polyomial is fit to the iitial coarse estimate of road boudaries to obtai a refied estimate of the road boudaries. The secod order approximatio of the road boudaries allows the estimatio of the curved segmets i additio to the straight segmets of the road boudaries. Experimet results for road images take uder various o-ideal scearios with shadow, umarked lae segmets ad curvatures are preseted. Key-Words: - lae detectio, dyamic programmig, curve fittig Itroductio Icreasig safety cocers o the road have led to the ivestigatio ad deploymet of may Itelliget Vehicle Assistat Systems (IVAS) i vehicles. Accurate road lae ad boudary lie detectio is oe of the key tasks of the IVAS. Visio based approaches have bee widely used i the literatures for road lae detectio [- 0]. The visio based techiques ca be broadly divided ito the feature based ad model based lae detectio. The feature based techiques [-5] extract the low level image features like color or edges to estimate the road lies. The model based techiques [6-0] employ a liear or quadratic lae model for lae represetatio ad are more robust agaist oise ad missig data. GOLD system [] uses edge based lae boudary detectio. LOIS system [3] uses edge magitude ad orietatio as features ad a parabolic approximatio for road laes. LANA algorithm [4] is based o a set of DCT coefficiets for diagoally domiat edges ad parabolic approximatio for the road model. A road boudary extractio based o dyamic programmig ad Radomized Hough trasform is preseted i [0] ad a system based o a hyperbola pair approximatio is preseted i [7][8]. I this paper we propose a combiatio of the feature based ad the model based method for robust performace. A similar approach for road boudary detectio is proposed i [0], but the curret work differs i that it accouts for the ear as well as the far field ad ulike [0] is suitable for curved road segmet estimatio. The rest of the paper is orgaized as follows: Sectio II presets the details of the proposed method; sectio III provides the experimetal results ad sectio IV cocludes the paper. Proposed Method The algorithm preseted i this paper is differet from others as it uses a combiatio of dyamic programmig [] ad secod order polyomial approximatio of the road lae. I additio to fidig the trivial straight lae segmets, the cost field ad eighborhood i the dyamic programmig is modified to accommodate for curved road lae.. Horizo Lie Detectio To limit the ROI for the search of the most likely road lae segmets, a horizo lie is separatig the road regio from the backgroud is foud iitially. The horizo lie is estimated by usig a horizotal itesity profile [9]. For a image of size MxN, The horizotal itesity profile (H profile ) is give as, N H ( i) = I( i, () profile i {,,.., M } j= The horizo lie is marked by a sigificat differece i itesity above ad below it, usually the sky regio beig brighter tha the road regio. The first miimum of H profile, Fig., assumig the top left corer of the image, Fig., as origi gives the positio of the horizo lie. ISBN:

2 { d + D( k,,( k, R( i, )} D( i, = mi, j () Fig.. Horizotal itesity profile with first miimum at x=64; The horizo lie superimposed i the origial image.. Edge Extractio The most distictive edge pixels appear alog the road boudaries due to sharp cotrast betwee the road surface ad paited lies or some type of o-pavemet surface. I additio edge pixels also provide directioal iformatio. The Sobel operator is used to extract the edge image. Sice the road boudaries are parallel o the groud plae ad ot parallel to the image plae, they appear to coverge i the image plae. So the edge pixels with ear vertical ad horizotal orietatio are filtered out from the edge image, Fig., as they are more likely to be related to other structures rather tha the road lae. Fig.. Edge image (threshold=0.3) with the ear horizotal ad ear vertical edges filtered out..3 Road boudary selectio by Dyamic Programmig Dyamic programmig is a global optimizatio algorithm to compute the optimal path by takig the local miimum at each ode. Let D( i, ad D ( k, be the shortest distace to the goal from ode ( i, ad ode ( k, respectively. Assumig d ij, kl is the shortest distace from ode ( i, to its eighborig ode ( k,, the D ( i, ca be expressed i terms of D ( k, ad d, by the followig equatio Here, R ( i, is the set of eighborig odes of ode ( i,. Eq. () is repeatedly applied locally util all the correspodig odes have their miimum distace to the goal obtaied. A optimal path is defied as the path that has the lowest cost from a startig poit to the goal poit. For each ode o the possible path, the ext ode amog R( i, is the oe with the miimum cost to the goal lie. This process is repeated util the goal poit is reached. To accommodate for the curves i the road lae the search eighborhood for dyamic programmig is modified as, ( k, R( i, k = i, l { j, j, j, j+, j+ } (3) The lik cost d, from ode ( i, to all eighborig odes ( k, is assumed to be ad a cost o the odes themselves is defied usig the itesity of the image pixels I( x, y ) coditioed o the edge image I (, ) edge x y as, ( I( i, ) if Iedge ( i, = odecost ( i, = (4) η ( I( i, ) if Iedge ( i, = 0 where η >. For the experimets η =0 is take. The horizo lie is set as the goal lie o the road image as the road lae is ot visible beyod the horizo lie. The distace iitializatio o the cost field is doe as, 0 if i= horizo lie pathcost( i, = (5) η elsewhere where η >>. =000 is take for the experimets. The road lae is the foud i two phases. I the first phase, the miimum cost from the goal lie to every ode is accumulated towards the startig lie usig Eq. (). Oce the cost field is computed, Fig 3, the secod phase is to trace alog the miimum cost path towards the goal lie, startig from the two start poits. For a image of size MxN, the two startig poits are set at the bottom left ad bottom right of the image as give by Eq. (6) Sl ( M, = mi{ pathcost( M, ; j {: N / 6} (6) Sr ( M, = mi{ pathcost( M, ; j {5 N / 6 : N} Fig. 3 shows the two lae boudaries traced by dyamic programmig..4 Secod Order Polyomial Approximatio (, ) ( x, y ) be the set of data poits for Let { x y } ad { } l r the left ad right lae retured by dyamic programmig. These data poits give a coarse estimate of the road boudaries which at times seem urealistic. ISBN:

3 colum Propagatio of the accumulated cost field row xi yi = a xi + b xi + c xi i= i= i= i= 3 xi yi = a xi + b xi + c xi i= i= i= i= yi = a xi + b xi + c i= i= i= i= The ukow coefficiets ca be obtaied by solvig the liear equatios of Eq. (9). Oce the coefficiets of the polyomial are estimated, we ca have a smooth ad realistic estimate for the road boudaries.fig.4 shows the refied estimate of road lae. (9) Fig.3. Optimal path fidig usig dyamic programmig;. Propagatio of the accumulated cost field. The optimal path geerated by backtrackig from the startig poits to the goal lie i the cost field. As road boudaries are simple curves which ca be safely approximated by a secod order polyomial, we fit these data poits to a polyomial of the form y= ax + bx+ c. The data poits are fit to the curve by miimizig the sum of the squares of the offsets of the poits from the curve. The best fittig curve f ( x ) has the least square error, i.e., [ yi f ( xi )] [ yi ( axi bxi c)] mi i= i= (7) Π= = + + = where a, b ad c are ukow coefficiets ad x i are the kow row positios ad y i the correspodig colum positios. To obtai the least square error, the ukow coefficiets a, b ad c must yield zero first derivatives. Π = xi [ yi ( axi + bxi a i= Π = xi[ yi ( axi + bxi (8) b i= Π = [ yi ( axi + bxi c i= Expadig the above equatios, we have Fig.4. Smooth road boudaries extracted after fittig a secod order polyomial to the data of Fig 3. 3 Experimetal Results The proposed method is evaluated o differet road images cotaiig the ear ad far field. Typical cases, Fig.5 (a-e), with shadow, umarked laes, o-ideal road textures ad curved roads are cosidered to test the robustess of the proposed method. Fig 5 shows a typical road with o-ideal texture ad missig lae markigs. The lae detectio problem becomes challegig due to may oisy edge segmets ad the missig lae markigs. Fig 5(a p ) shows the propagatio of the cost field ad Fig. 5(a ) shows the detected road lie boudaries after a secod order polyomial is fit to the lae data poits foud by dyamic programmig. The coefficiets of the approximated polyomials for the left ad right boudary are give i Table. Fig. 5 shows a road with discotiuous lae markigs. The propagated cost field ad the detected road boudaries are show i Fig. 5(b p ) ad Fig. 5(b ) respectively. Fig. 5(c) shows a road with oil stais ad shadow ad the cost field ad detected road boudaries are preseted i Fig. 5(c p ) ad 5(c ) respectively. Fig. 5(d) shows a curved road segmet with cotiuous lae markigs ad the propagated cost field ad the detected road boudaries are preseted i Fig. 5 (d p ) ad Fig. 5 (d ). Further evaluatio o a curved road with ISBN:

4 discotiuous lae markigs is preseted i Fig.5 (e), Fig.5 (e p ) ad Fig. 5(e ). The simulatio results preseted i Fig.5 show that road boudaries uder varyig coditios ca be detected usig the proposed algorithm. (e) (e ) (a p ) (b p ) (e p ) Fig. 5 Road lae detectio uder various road coditios. Road with o-ideal texture ad missig lae pait. Road with discotiuous lae markigs. (c) Road with oil marks ad shadow. (d) curved road segmet.(e) curved road segmet with discotiuous markigs.(ap-ep) Propagatio of the accumulated cost field of the correspodig images. (a -e ) The detected road boudaries of the correspodig road images. (a ) (c) (b ) (d) Table. The coefficiets of the polyomials fit to the data from dyamic programmig for the left ad right lae i each image. Coefficiets-> a b c left Image right Image left right Image left (c) right Image left (d) right Image left (e) right (c p ) (d p ) (c ) (d ) 4 Coclusio I this paper a robust method for road boudary detectio is proposed. The horizo lie is extracted to limit the search space for the road boudary. Edge cadidates are extracted ad dyamic programmig is employed to obtai the optimal road boudaries. The search eighborhood i dyamic programmig is modified so as to accommodate the curved segmets of the road lae alog with the straight segmets. At the fial stage a secod order polyomial is fit to the road lies extracted from dyamic programmig to have ISBN:

5 more realistic ad refied road boudaries. The experimets carried out show that the proposed method has good performace ad is robust uder o-ideal road coditios also. Refereces: [] R.,Bellma, Dyamic programmig, Priceto, NJ: Priceto Uiv. Press, 957 [] B. M, Broggi, GOLD: A parallel real-time stereo Visio system for geeric obstacle ad lae detectio, IEEE Trasactios o Image Processig, 998, pp [3] C. Kreucher, S. K. Lakshmaa, A Driver warig System based o the LOIS Lae detectio Algorithm, Proceedig of IEEE Iteratioal Coferece O Itelliget Vehicles, 998, pp. 7 - [4] C. Kreucher ad S. Lakshmaa, LANA: a lae Extractio algorithm that uses frequecy domai features, IEEE Trasactios o Robotics ad automatio, 999, pp [5] D. J., Kag ad M. H., Jug, Road lae segmetatio usig dyamic programmig for active safety vehicles, Patter Recogitio Letters Vol.4, 003, pp [6] Q. Che, H. Wag, A Real-Time Lae Detectio Algorithm Based o a Hyperbola-Pair, Proceedigs of IV006. IEEE Itelliget Vehicles Symposium, 006, pp. -6 [7] O.O. Khalifa et. al, A Hyperbola-pair based lae detectio system for vehicle guidace, Proceedigs of the World Cogress o Egieerig ad Computer Sciece, Vol., 00 [8] Wag Y., She D., ad Teoh E, Lae detectio usig splie model, Patter Recogitio letters, Vol., 000, pp [9] W. Lu, H. F. Wag, Q. Z. Wag, A Sychroous Detectio of the Road Boudary ad Lae Markig for Itelliget Vehicles, Eighth ACIS Iteratioal Coferece o Software Egieerig, Artificial Itelligece, Networkig, ad Parallel/Distributed Computig, 007,pp [0] H. Li, H. Kim, C. Li, L.O. Chua, Road Boudary Detectio based o the Dyamic Programmig ad the Radomized Hough trasform, Iteratioal symposium o Iformatio Techology covergece,007, pp ISBN: