ADAPTIVE SNAKES FOR URBAN ROAD EXTRACTION

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1 ADAPTIVE SNAKES FOR URBAN ROAD EXTRACTION Junhee Youn * James S. Bethel Geomatcs Area, School of Cvl Engneerng, Purdue Unversty, West Lafayette, IN , USA (youn,bethel@ecn.purdue.edu Commsson III, WG III/4 Keywords: GIS, Photogrammetry, Urban, Feature, Extracton, Dgtal, Image Abstract: For quckly populatng GIS database, t s mportant to derve accurate and truly road nformaton from magery. In ths paper, we descrbe the problem of urban road extracton from dgtal magery usng adaptve actve contour models (Snakes. Our road extracton processng has three steps. Frst, we segment the mage based on the domnant road drectons. Second, we detect the road lnes wth the so called acupuncture method. Fnally, we refne the road edges by applyng adaptve snakes to the corner desred approxmaton to extract the cty block. Durng the proces we assume that the road network and block pattern n the cty have a sem-regular grd pattern. For detectng the road lne we explot the dstrbuton of edges n an urban area. Lnear assocated wth roads are detected and these become the bass for ntal approxmatons to road grd pattern for snakes based refnement. In order to accommodate varable lne characterstc we have developed an adaptve algorthm whch locally modfes the weght of the energy terms. These deas are appled to same actual urban magery and the results are dsplayed and evaluated.. Introducton Rapd and accurate generaton of road data from magery s an mportant ssue n modern dgtal photogrammetry. Besdes normal method there are two categores for road extracton. One s sem-automatc extracton and the other s fully automatc extracton. In sem-automatc extracton, approxmatons are gven manually and an automatc algorthm extracts the road. In Vosselman and de Knecht (995, the operator provdes the ntal nformaton (startng pont and drecton and the subsequent road segments postons are determned after profle matchng n aeral magery. Manually gven data can be used as ntal nformaton for snake approaches; Gruen and L (997 proposed the method that the human operator select a few seed ponts and the lnear feature s automatcally extracted based on dynamc programmng and least squares B-splne snakes. For the fully automatc approach, ntal nformaton can be gven by other sources. Agours et al.(00 extended the tradtonal snakes to functon n a dfferental mode and propose a framework to dfferentate change detecton from the older record of GIS. There are several approaches to use mult resoluton aeral magery for automatc methodologes. That approach usually extracts the lnes n a reduced resoluton mage, and edges are extracted wth the orgnal hgh-resoluton mage. Both outputs are merged by usng a rule based system (Hepke et al And Baumgartner et al.(999 composed road segment by usng both resoluton level wth explct knowledge about the road and grouped these segments teratvely, consderng the local context. So far, not so many research groups concentrate on road extracton n urban areas. For rural case, the geometry, radometry and topology characterstcs of roads are smple to descrbe, compared to urban areas. The most dffcultes for urban road extracton are comng from the fact that materal and shape (lnear pattern for non-road structures are very smlar to the road. However, the road network n an urban area s usually sem-grd pattern. Prce (999 assumed that road network model s a regular grd form and the road has vsble edges. He used two manually gven ntersectng road segment whch gave nomnal nformaton for the sze and orentaton of the grd. These segments are expanded wth feature-based hypothess and verfcaton, and local context and a dgtal elevaton model s used for refnement and verfcaton of road segment. The grd characterstc for urban road networks s mportant assumpton for our approach. Hnz et al. (003 proposed a context-based decson makng model for urban road detecton, usng complex relatonshps among roads buldngs and vehcles. Here, context nformaton about the urban road s manly obtaned from hgh-resoluton magery and a dgtal surface model. In ths paper, we present automatc road extracton n urban areas wth adaptve snake for whch ntal seed ponts are calculated from a new approach for detectng road ways and ntersectons. Assumng urban networks to be a sem-grd pattern, there wll be evdent roads has several domnant drectons. Domnant drectons for roads can be determned based on the fact that road edges and buldng edges are usually parallel n the urban area. Wth domnant road drecton prelmnary road lnes are extracted for the snake refnement. These road lnes are used an ntal approxmatons. An adoptve strategy s derved wheren weghtng factor vary wth context of the road grd. Results are presented for some actual urban magery.. Regon-Based Image Segmentaton The Basc concept of ths approach s to splt the mage nto regons based on domnant road drectons. In urban area most of the roads are straght and the road network often has a grd form, so the roads wll exhbt domnant drectons. Meanwhle, havng the same grd pattern for the whole area s an deal case. Certan parts of the area may have north-south drecton roads and another part may be northeast-southwest drecton roads. Consderng such varous grd pattern a parttonng scheme s proposed. In our approach, the parent mage s subdvded nto four chld mage blocks (regons when the parent mage whch covers an area wth more than two domnant road drectons.

2 The process has three steps; lne segment extracton, domnant drecton detecton and mage splttng wth quadtree data structure.. Lne Segment Extracton Calculatng a road s domnant road drecton starts from extractng the lne segments from the edge mage snce most of the roads n the urban area are lne-shaped and edge detecton s the most common method for extractng meanngful dscontnutes magery. We can t say extracted lne segments from edges are all belongng to road because so many features n urban areas have also lne shape edges. In addton, buldng edges and road edges are often parallel. So we can use most of the lne shaped edges for calculatng road drectons even though they correspond for non-road features. To extract the lne segment the Canny operator s appled to track all edges. Snce the fle sze of modern magery are qute large, we downsampled the magery to work at reduced resoluton. By reducng the resoluton, much nformaton s lost but to determne only the regon s domnant drecton, usng a reduced resoluton mage s suffcent. The mage for our study area and ts detected edges are shown n Fgure. The bnary mage for the canny detected edges s shown n Fgure b, wth black pxels represents the edges. Those edge pxels are for buldng road tree car and other features. (a Fgure : Image for study area and ts edges. (a Aeral mage over Purdue Campus (b Detected edges wth reduced resoluton mage by canny algorthm (b and each group s pxel elements ρ-θ. Based on calculated ρ-θ, pxels n the group are checked whether all pxels are on the lne equaton or not. If all pxels are on the lne equaton, ths group s treated as straght lne. If not, the group wll be elmnated. Condtons for beng treated as straght lne are as follows; - Length of group s more than lmt - At least one pxel of group touches the boundary of search wndow - ρ-θ are calculated by usng any two pxels n the group and all pxels should le on ths lne (Tolerance s pxel. Extracted lne segments are shown n Fgure.. Domnant Drecton Detecton We wll subdvde an mage block (parent regon nto four quadrant mage blocks (chld regons f the parent regon has more than two domnant road drectons. To decde about splttng or not, we must calculate the number of domnant drectons n the regon of nterest. For determnng the domnant drecton n the scene, several approaches have been studed. Gettng domnant drectons n a scene s usually begun by straght lne detecton for most of the research groups. Then each lne s gradent s calculated and lne length s accumulated nto a hstogram. The problem s selectng domnant drectons n ths hstogram. Sohn and Dowman (00 used a herarchcal hstogramclusterng method to obtan domnant drecton. They derved lne angle nformaton and quantzed t nto a hstogram. Correspondng lne length of each angle s accumulated to make many pxels contrbute more to determne domnant angle peaks. Once the hghest peak angle s obtaned, angle dscrepances less than angle thresholds from peak angle are checked as one set. Ther geometres are modfed to conform to the peak angle. In subsequent searchng, these modfed and the checked sets are gnored. In ths paper, we propose a modfed herarchcal hstogram-clusterng method. We calculate the angle for each lne, elmnate some lnes wth 90-degree flterng, threshold to make angle-pxel on hstogram and then apply herarchcal hstogram-clusterng. To calculate each lne s angle, the Hough transform s used and Fgure 3a s the result of calculatng all lne s angle and length. In Fgure 3a and Fgure 3b, crcles represent each lne s angle from 0 to 90 degree on the X ax and length s represented by the Y axs. (a (b (c Fgure. Extracted lne segments wth proposed algorthm To get lne-shaped edges (lne segments, we propose followng method. We use polar coordnate, whch use ρ-θ, to parameterze the lne. Frst, we examne the search wndow, of sze 0 0 pxel. Ths search wndow wll adon ones by 3 pxels. Next, all components are 8-connected labeled to determne pxel groups Fgure 3. Angle length relatonshp for lne segments. (a Angle and length for all lne segments. (b Result after 90-dgree flterng. (c Hstogram after 90-dgree flterng and threshold. Our regon of nterest s an urban area and we already assume that urban roads form a knd of grd pattern. The grd s composed of two man drectons whch are perpendcular to each other. Also, because we searched a wde area, even f a certan lne segment has a perpendcular segment, the two segments may have no relatonshp wth the grd. Searchng all lne drecton we elmnated the lnes that have no

3 perpendcular par n regon of nterest. That s so called 90- degree flterng. Fgure 3b s the result for 90-degree flterng. After 90-dgree flterng, we make a length threshold. If the length of a perpendcular par s less than percent of regon s total length of lne segment that par s elmnated. Fgure 3c represents the fltered hstogram n whch the bn counts are the total number of pxels (length summaton of lne segments and t s used for determne domnant drecton of regon. By ths algorthm, we can expect non-road and non-buldng roof edges to be gnored. From the Fgure 3c, ths regon has four domnant drectons about 0, 45, 90, 35, by ntutve nspecton. We need mathematcally separate t to determne the number of domnant drecton. We used a herarchcal hstogramclusterng method to determne the domnant angle set. After makng domnant angle set we can calculate a representatve angle for each set by followng equatons. process proceeds untl all regons have ther own par of domnant drectons or the regon reaches a lower threshold lmt. The regon threshold can be predefned as a cty block sze (Mn block. The regon segmentaton result s shown n Fgure 5. The red rectangle s the regon whch has one par of domnant drectons and the yellow regon denote that domnant drectons are not determned and splttng s stopped because the mnmum sze threshold has been reached. The reason why those regons don t have one par of domnant drectons s usually due to lack of lne segments. In such cases of too few lne segment we skp 90 degree flterng and proceed to hstogram clusterng. θ dom θ n n Where n s the length of lne. As a consequence, the study area has four domnant drecton and the angles are.9, 4., 9.5, and Image Splttng wth Quadtree Data Structure The obectve of Image splttng n ths paper s to partton an mage nto regons untl all regons have ther own sngle par of domnant drectons. To partton the mage, we appled the quadtree data structure. The followng basc formulaton s very smlar to Gonzalez (99 Regon-Orented Segmentaton method. Let R represent the whole mage regon and t s dvded nto n sub regons lker R, R,..... R n such that n (a R R, (b R s a rectangular regon,,,..... n, (c R R s null set for all and,, (d P(R TRUE f ths regon has only one par of domnant drecton. Regon s subdvded nto four dsonted quadrants regon f P(R FALSE. That means the R regon has more than one par of domnant drecton. Ths splttng technque has a convenent representaton form called the quadtree. Quadtree concept s represented n Fgure 4. Fgure 5. Image segmentaton based on road drectons 3. The poston of the lne on the road Each regon from the quadtree has ts own two domnant road drectons and, as mentoned above, those drectons are parallel wth road and buldng edges. Let s magne two vrtual needles that penetrate the two dmenson edge mage spaces and a compare a measure for both needles. We defne a free passage to quantfy ths concept. Specfcally, a needle whch meets many edges wll have a small free passage measure, whereas a needle whch meets few or no edges wll have a large free passage measure. Fgure 6 llustrate the needle percng process through an edge mage. Because of the analogy wth needle, we call ths process the Acupuncture Method. n R R R R3 R4 R R R R3 R4 Fgure 6. Penetratng needles on the edge mage m R3 R4 R43 R4 R44 R R R R4 R4 R4 R43 R44 Fgure 4. Concept for Quadtree mage splttng Let the sze of the entre mage be m n. Frst, calculate the entre mage (R s domnant drectons and f the entre regon has only one par of domnant drecton then mage splttng s stopped. Otherwse, ths regon s subdvded nto dsont four quadrant regons (R, R, R 3, R 4. Second, f each R has only one par of domnant drecton then splttng s stopped. Otherwse, each regon s subdvded agan nto four quadrant dsont rectangular regons of whch sze s m/ n/. Ths Replacng the needles as lne equatons on the edge mage algned wth the domnant drecton and steppng exhaustvely across the edge mage, we can compute a free passage measure for each canddate lne. We denote the two domnant drectons θ d and θ d. The free passage measure for a fxed domnant drecton and a gven ρ s generated by followng steps. Before mplementng the step the range of ρ s defned as ρ mn Mn (, NL cosθ ρ max Max (NS snθ, NL cosθ + NS snθ ρ mn ρ ρ max

4 where (NL, NS s the sze of mage (number of lne number of samples. Also, we defne the functon N(X whch represents total number of elements for set X. Wth ρ, calculate the lne coordnates set P wth pont coordnates (l, s, l NL (45 < θ < 35 P ρ l cosθ s snθ s NS. P ρ s snθ (0 θ 45 or 35 θ < 80 l cosθ Fgure 7d and Fgure 7e, the X axs represents the lne number and the Y axs s the free passage measure. From the graphs n Fgure 7a and 7d, we select the peaks usng modfed herarchcal hstogram clusterng method. Ths method requres the user to specfy a mnmal block wdth. Fgure 7b and 7e are the results for that method and determne the lnes selected as roads. The θ d graphs yelds 3 lnes chosen as roads. The θ d graphs yelds 4 lnes. Applyng the complete Acupuncture method to the study area yelds the results shown n Fgure 8. Those lne nterpreted as an urban road grd, wll be used as ntal approxmatons for the snake refnement. Next, we count the pxels where the edges concde wth the lnes ust descrbed. For each lne,, overlay wth each edge, k. The total number of concdent pxels (C wll be an ndcator of obstacles encountered by that lne. A large number of such obstacles wll ndcate that t s less lkely to be a road feature, whereas a small number of obstacles wll mean that t s more lkely to be a road feature. The number of lne/edge concdent pxels s C U ( P I Ek k where E k s an edge pxel. We characterze the degree, to whch the lne s free from obstructng edges a N( P N( C F 00 (0 F 00. N( P A hgh value (near 00 of F s an ndcator of a road. Repeatng ths process for each lne we can make a graph of the free passage measure vs. lne number. Peaks n ths graph wll very lkely correspond to roads. (a (b (c Fgure 8. Detected lnes on the road by acupuncture method 4. Adaptve Snakes Many research groups have tred to use snakes as a tool for rural area road extracton, and they have appled global energy coeffcents. Applyng global energy coeffcents should be on the assumpton that the lnear features have smlar curvature characterstcs through the curve. Snce the road structure for rural roads s not so complex, global energy coeffcents perform well. Here, we propose adaptve snakes for whch energy coeffcents vary locally to accommodate urban area road extracton. Frst, we ntroduce the general soluton for snakes and second, present the advantage of local varyng energy coeffcents. Thrd, we apply the proposed snakes to the study area wth ntal approxmatons whch are generated n prevous secton. In ths paper, we defne global energy coeffcents as applyng the same coeffcents to the all nodes n one curve whle local energy coeffcents means that coeffcents vary locally. 4. General Soluton for Snakes (d (e (f Fgure 7. Result of acupuncture method on small example regon. (a~(c are for θ d, and (a~(c are for θ d. (a and (d Free passage measure. (b and (e Clusterng result. (c and (f Detected lnes on the road. Fgure 7 s the example of applyng acupuncture algorthm to one of the regons. In ths regon, the predetermned domnant road drectons are.5 (θ d and 9 (θ d. Fgure 7a, 7b and 7c are for.5 case and others are for 9 case. Fgure 7a and 7d show the graph that represents the relatonshp between lne number and the free passage measure. In Fgure 7a, Fgure 7b, The orgnal concept for snakes (Actve contour models was ntroduced by Kass et. al(988, and they defne t as A snake s an energy-mnmzng splne guded by external constrant forces and nfluenced by mage forces. Also, t can be defned as a movable curve n mage doman controlled by nternal forces (elastc and bendng force etc. and mage forces whch attract or repel the curve. The Snakes can be modeled as a curve wth tme-dependent sequental lst of nodes n two dmensons and defne parametrcally lke v ( ( x(, y( 0 s (

5 ,where t s current tme or evoluton step, s s proportonal to the curve length, and x and y represent coordnates for nodes n the mage doman. In ths paper, the nternal and external energy at any node are determned throughout the curve, and we fnd the optmum poston of nodes wth energy mnmzng technques. The energy of the snake can be wrtten as a summaton of nternal and mage energy a E E ( v E ( v ( snake nt + The nternal energy controls the shape of the curve wth geometrc constrants and can be decomposed nto a frst and second order term a mg Ent ( v α( s vs ( + β ( s vss ( 0 ds. (3 Here, coeffcent α controls the elastc force of the curve and coeffcent β controls the bendng force of the curve. More detaled descrpton for the nternal energy wll be stated next secton. The mage energy attracts the curve to the salent features n the mage and s represented a 0 E mg ( v P( ds (4 where P( s functon value correspondng to the feature of nterest. In ths paper, we focus on the edges as the salent feature, so P( s the mage gradent. The total energy of the snake s wrtten as Esnake α vs ( + β vss ( P( 0 ds. (5 To mnmze the energy functonal, we use the Euler-Lagrange dfferental equatons of the functonal yeldng the followng smplfed Euler evoluton equaton, P( t γ + αvss ( + βvssss ( (6 t v where γ represents the vscosty of the curve. The hgher vscosty makes the evoluton of the curve slower. v ss s the second dervatves wth respect to s. The temporal dervatve can be numercally wrtten as v ( t. (7 t Assumng external forces are changed very slowly wth tme step, substtute equaton (7 to equaton (6, equaton (6 s rewrtten a P( t α vss( + βvssss( + γ ( t (8 v Let V t be a set of each nodes a V t {,,,... n} (9 where n s the total number of nodes n the curve. Then, wth equaton (9 equaton (8 can be rewrtten n matrx form as P( Vt γ I Vt γ Vt (0 v ( A + where the matrx A s a pentadagonal banded matrx composed of α and β, and I s an n n dentty matrx. Wth the ntal curve modeled by sequental lst of node the next curve s calculated by equaton (0 teratvely and teraton wll be stopped when total energy change s less than a threshold. Fnally, we can fnd an optmal poston of curve wth ths energy mnmzaton technque. 4. Local Energy Coeffcents for Urban cty block detecton As stated n the prevous secton, snakes have nternal energy components whch are controlled by coeffcents α and β. For accurate delneaton of cty block boundares of detected edges should reman n lnear form n the preserve of concavtes (parkng lot near the sde of cty block and convextes (parked car at the sde of a cty block. Wth the above mentoned characterstc we know that the corner regon s well suted for lower β compared wth the sdes of the block. Fgure 9 shows us the dfference between applyng global energy coeffcents (constants versus local energy coeffcents (context dependen. In Fgure 9, the target for snakes smulates the example of a cty block. The red lne s a curve whch s composed of blue nodes. Fgure 9b s a result of applyng global energy coeffcents (constants wth ntal contour n Fgure 9a. Here, the corner area s well delneated, however snakes s senstve to the concave and convex part. But applyng dfferent weghtng coeffcents to the corner and sde area, an mproved result s obtanng partcularly n the sde area. (a (b (c Fgure 9. Global and local energy coeffcents for snakes. (a Intal contour (b Global coeffcent wth α, β 0. (c Local coeffcent: α, β 0 for corner area and α 300, β 0 for sde area. To use local weghtng coeffcent we must have a pror knowledge about the pont context before mnmzaton. For our cty block case, the pont context (corner vs. sde s determned from the ntalzaton. Davs et al (995 tred to apply local coeffcents for the snake and they had a lttle success because ther resultant snake model dd not ft wth user expectaton. Man problem for ther approach s due to the unrelablty of expectatons for target shape. However, we can overcome that problem by usng the detected lnes on the road obtaned n the prevous secton. Detaled usage s descrbed n the next secton. 4.3 Applyng Adaptve Snakes to Cty Block Delneaton Generally, ntal curves for snakes are gven by manually. However, road ntersecton, whch are determned by detected lnes on the road, generate the ntal curves n our approach and also, they gve us the nformaton for the corner area. Seeng the result of detected lnes n Fgure 8, we focus on two facts; the

6 lne ntersectons mostly correspond for road ntersecton, and these also concde wth block corners. Energy mnmzaton starts from makng ntal curve and proceedng wth the refnement. Among all road ntersecton pont each four ponts become seed ponts for one ntal curve. Based on these seed pont we nsert nodes for whch spacng s proportonal to the dstance from one seed pont to another. Fgure 0a s a detaled example of one ntal curve wth dfferent pont classfcaton. A yellow dot s an ntersecton pont, all blue ponts are nserted node the large blue ponts are classfed as corner area, and all ponts comprse the ntal V t n equaton (9. We apply dfferent nternal weghtng coeffcents based on pont locaton. We apply α and β value for corner area as and 3, meanwhle gve α 300 and β 0 for sde area. Wth matrx A and the ntal V t, we teratvely solve for V t for each tme evoluton step untl the change of total energy s less than threshold. A result, whch represents the cty block s n Fgure 0b. To enhance the senstvty to mage force we use a spatal dffuson technque to spread the nfluence of the edges. Fgure s the result of applyng adaptve snakes to the study area. We elmnate the nonconverged curve durng mnmzaton. can obtan each regon s domnant road drectons even f the road network has multple grd patterns. The determned road drectons were used for road detecton. Searchng the regon wth ts road drecton we fnd the canddacy of lnes on the road by usng the acupuncture method. These detected lnes were used to construct ntal approxmatons for the subsequent snake refnement. Lne ntersecton were consdered as road ntersectons and used for seed ponts for the snakes. Applyng local weghtng coeffcents to the tradtonal snake we have developed an adaptve procedure well ftted for urban cty block delneaton. Our future work wll focus on achevng better stablty n the numercal estmaton, mprovng the adaptve algorthm, and comparng dfferent methods of computng the steps n the lne fttng. References Agour P., A. Stefand and S. Gyftak 00. Dfferental snakes for change detecton n road segment Photogrammetrc Engneerng & Remote Sensng, 67(: Baumgartner, A., C. Steger, H. Mayer, W. Ecksten, and H. Ebner, 999. Automatc road extracton based on mult-scale, groupng, and context, Photogrammetrc Engneerng and Remote Sensng, 65(7: (a (b Dav D.N., K. Nataraan, and E. Clardge, 995. Multple energy functon actve contours appled to CT and MRI mages of the bran, Proceedngs of the 5th IEE Conference on Image Processng and ts Applcaton Ednburgh, UK, pp Gonzalez, R., and R. Wood 99. Dgtal Image Processng. Addson Wesley Publshng Company, Readng, Massachusett 458 p. Fgure 0. Adaptve snakes for urban road grds. (a Local coeffcents. (b Detected cty blocks. Gruen, A., and H. L, 997. Sem-automatc Lnear feature extracton by dynamc programmng and LSB-snakes. Photogrammtrc Engneerng & Remote Sensng. 63(8: Hepke, C., C. Steger, and R. Multhammer, 995. A Herarrchcal Approach to Automatc Road Extracton From Aeral Image SPIE Aerosense 995 Symposum, 7- Aprl, Orlando, USA, Vol. 486, pp.-3. Hnz, S., A. Baumgartner, H. Mayer, C. Wdemann, and H. Ebner, 003. Road Extracton Focusng on Urban Area, Automatc Extracton of Man-Made Obects from Aeral and Space Images(III, (E. Baltsava A. Grün, and L. Van Gool, edtors, A.A. Balkema Publsher Lsse, The Netherland pp Kas M., A. Wtkn, and D. Terzopoulo 988. Snakes: Actve contour model Internatonal Journal of Computer Vson, (4:3-33. Fgure. Detected cty blocks n the study area 5. Conclusons In ths paper, we propose a new approach for urban road extracton. A basc assumpton s that urban road network has a nomnal grd pattern and a pror knowledge requred s the approxmate mnmum sze of the cty block and approxmate road wdth. In regon segmentaton, we subdvde the regon untl all regons have only two domnant drectons. By dong so, we Prce, K., 999. Road Grd Extracton and Verfcaton, Internatonal Archves of Photogrammetry and Remote Sensng, 3(Part 3/w5:0-06. Sohn, G., and I.J Dowman, 00. Extracton of buldngs from hgh-resoluton satellte data, Automatc Extracton of Man- Made Obects From Aeral and Space Images(III (E. Baltsava A. Grün, and L. Van Gool, edtors, A.A. Balkema Publsher Lsse, The Netherland pp Vosselman, G., and J. de Knecht, 995. Road tracng by profle matchng and Kalman flterng, Automatc Extracton of Man- Made Obects from Aeral and Space Images (A. Gruen, O. Kuebler, and P. Agour edtors, Brkhaeuser Verlag, Bern, Germany, pp

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