Use of Digital Image Modeling for Evaluation of Concrete Pavement Macrotexture and Wear

Transcription

1 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Use of Dgtal Image Modelng fo Evaluaton of Concete Pavement Macotextue and Wea Saumya Amaas 1, Manjke Gunaatne, and Sudeep Saka 3 Abstact Modelng of the pavement mage fomaton pocess usng eflecton popetes of macotextue showed that dgtal mages of concete pavements can be used to monto pavement wea. The specfc optcal chaactestcs of mages and the optmum camea settngs that can be used fo ths pupose wee detemned by theoetcally fomulatng the Bdectonal Reflecton Dstbuton Functon (BRDF) of suface textue wth unfom colo. In the analytcal phase of the study, desed levels of pavement textue wee geneated by combnng a sees of 3-D sne sufaces of vayng wavelengths and ampltudes. The optmum specula settngs of the ovehead pont lght souce and the dgtal aea-scan camea fo effectve hghlghtng of the maged wheel path macotextue wee detemned wth an analytcal fomulaton based on a smplstc and physcally meanngful BRDF model. It was also shown that the mages obtaned by the theoetcal fomulaton closely esemble those captued fom a smlaly textued expemental suface unde dentcal lghtng and magng condtons. In patcula, the pavement mage fomaton model evealed that quantfable changes n the bghtness of mages do occu due to changes n textue depth and spacng (wavelength). In the next phase of the study, the taffc nduced pavement weang pocess was smulated by gadual smoothenng of the modeled sufaces and then mages coespondng to each weang stage wee geneated. The theoetcally pedcted vaaton of the mage bghtness due to wea was expementally vefed usng mages fom a gadually won out concete specmen. Fnally t was llustated how the bghtness evaluaton of wheel path mages has the potental to be a sceenng tool to monto the degadaton of macotextue and hence the skd-esstance of pavements at the netwok level. 1, Depatment of Cvl and Envonmental Engneeng, 3 Depatment of Compute Scence and Engneeng, Unvesty of South Floda, Tampa, FL

2 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Impotance of Suface Macotextue Evaluaton n Pavement Management A majo task of pavement management s to ensue adequate skd-esstance (fcton) on all pavements n a netwok. Gadual degadaton of skd-esstance on hghways and unways can be attbuted pmaly to pavement textue changes due to taffc nduced wea. Theefoe, a safe level of skd esstance can be ensued by egulaly montong pavement textue and takng coectve measues to estoe degaded textue n a tmely manne. Pavement fcton s known to ognate fom two levels of textue; (1) macotextue (depths fom 0.5 to 0 mm and wdths fom 0.5 to 50 mm) and () mco-textue (depths fom to 0.5 mm and wdths less than 0.5 mm) (Table 1, ISO 1997). The specfc nfluence of pavement textue on skd-esstance and te wea has been nvestgated by Btton et al. (1974), Leu and Heny (1978) and Balme (1978). A sngle model coelatng skd esstance to both macotextue and mcotextue evaluatons was fst ntoduced by Leu and Heny (1978). Moe ecently, Gendy and Shalaby (007) found that the complete chaactezaton of skd esstance must nvolve all thee attbutes; sze, spacng and shape of both macotextue and mcotextue. Mcotextue whch can be detected ndectly n the feld by the Btsh Potable Skd Teste (BPT) (ASTM E ) govens the dy fcton poduced by adheson at low te speeds. On the othe hand, macotextue poduces hysteess fcton at hgh te speeds and n addton educes the possblty of hydoplanng by facltatng the danage of wate. Macotextue can be evaluated usng the mean textue depth (MTD) o the mean pofle depth (MPD) (ASTM E ). The wet skd-esstance of localzed aeas of hghway pavements can be evaluated by the Locked-wheel Skd-Teste (LWST) at a slp speed of 65 km/h (ASTM E 74-06), whle the Runway Fcton Testes (RFT), Gp testes and mu metes can be employed to evaluate the wet skd esstance contnuously ove lmted length of unway sectons at desgnated slp speeds. Although hghway agences have used hgh-speed skd testes fo many yeas they ae not sutable fo netwok level analyss. Snce the wet fcton estmates vay fom one devce to anothe, the spot-measung and elatvely pecse Dynamc Fcton Teste (DFT) s consdeed to povde the standad fcton values at a slp speed of 60 km/h (ASTM a).

3 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Sceenng of pavements wth espect to skd-esstance can only be acheved wth technques that can monto the changes n skd-esstance along an ente pavement netwok based on evaluatng the degadaton of ts maco-textue n patcula. The lase evaluaton of macotextue does not have the capablty to detemne whethe the suveyed pofle s fomed by the pavement mateal tself o the deposted contamnants. Howeve, f the lase technology s used n conjuncton wth a contamnaton detecto, then the contamnated locatons can be dentfed fst. The DSC111 ( MONITORING:-Lase-system-montos-slppeness-of-oadway) s a oad-suface senso that has been ceated usng lases and tansmtte optcs to obtan shot-ange spectoscopc measuements of the wate and ce on a oad suface. Usng ths devce fost, snow, slush, and black ce on the oad suface ae dffeentated by d dstngushng between the specfc wavelengths of wate and ce. Theefoe, the advantage of usng dgtal mages s that they can be used to fst dstngush the contamnated locatons fom the othes. The INO LCMS ( system employs hgh speed cameas, custom optcs, and lase lne pojectos to acque D mages and hgh esoluton 3D pofles of oad sufaces that allow fo automatc detecton of cacks and the evaluaton of maco-textue and othe oad suface featues. The potental also exsts fo usng only appopately calbated mages of wheel paths to pedct the coespondng changes n maco-textue and skd esstance. Acquston of pavement dgtal mages Pavement evaluaton based on automated dgtal mage analyss has been eplacng the manual pavement evaluaton due to ts mpoved effcency and opeatonal safety. Whle lnescan cameas ae wdely used n state-of-the at pavement evaluaton vehcles to monto the pavement dstess (cackng) condton at egula tme ntevals (Wang 007, Huang and Xu 006, Maz et. al. 006, Amaas et. al. 007), aea-vew dgtal cameas ae employed fo magng oadway sgns and safety featues (Maz et al, 005). Typcal hghway magng systems nclude an exteo lght souce and a dgtal camea and the assocated acquston, stoage and the pocessng system mounted nsde the magng vehcle. In the latest magng vehcles, the lamp-based atfcal llumnaton s eplaced 3

4 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; by lase lghts to ovecome the ssues of non-unfom llumnaton and shadows. Aeavew cameas can also captue gayscale mages whee the optcal textue vaaton on the pavement suface s manfested by a wde ange of pxel ntensty values fom 0 to 55, whee 0 epesents black and 55 epesents whte. Most state-of-the-at cameas possess the esoluton to captue a 1mm x 1mm pavement aea at each pxel level wth the ntensty of a pxel dependng on the vaaton of the pofle and the colo of the suface. Thus, the optcal textue vaaton of an mage due to pavement macotextue nduced suface pofle vaaton can be used to detect the changes n macotextue. The cuent pavement magng technology has been lmted mostly to detecton and evaluaton of cacks and othe dstesses. The authos have not found publshed evdence of any attempts to use dgtal mages fo macotextue detecton. By applyng appopate modfcatons wth espect to the nstallaton of the exstng dgtal magng equpment, pavement macotextue changes can also be captued n the mages. Hence the netwok level evaluaton of sgnfcant pavement wea and changes n skd esstance can be facltated by the magng technology. Objectves of the nvestgaton The focus of ths pape s to theoetcally model the wea nduced ntensty changes n dgtal mages of pavement locatons whch ae deemed to be uncontamnated and evaluate the above changes expementally. In the pelmnay study epoted n ths pape, fst the geometcal eflecton popetes of macotextue would be used to model the dgtal mage fomaton of pavement sufaces of unfom colo. Second, the above magng model would be used to dentfy (1) the changes n optcal popetes of dgtal mages that eflect pavement wea and () the optmum specula settng equed by the magng system to detect the above changes. Then a smple expemental study would be set up to vefy the theoetcal fndngs. Fnally, t would be llustated how the detectable changes that occu n the optcal popetes of dgtal mages due to the pavement wea can be coelated to degadaton of macostuctue and consequent loss of skd-esstance. 4

5 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Advances n suface chaactezaton usng dgtal mages The dentfcaton of object chaactestcs fom the mages has been made possble by ecent advances n the mage pocessng technology. Tamua et. al. (1978) modeled optcal textue of a physcally textued object usng ts eflecton popetes and llustated how t facltates mage classfcaton, mage segmentaton, and mage encodng. Optcal textue models have also been used to eceate depth and oentaton of objects and to geneate desed synthetc mage textues by adjustng model paametes (Tamua et. al. (1978)). It was shown by Shapo et. al.(001) that the optcal textue of pavement mages can also be fomed fom mage pmtves of vayng shape o by usng stochastc assumptons. In the above wok, pavement macotextue and mcotextue wee consdeed to be composed espectvely of elatvely lage and small optcal textue pmtves. The ntensty of each pxel n the mage space has also been consdeed a andom vaable wthn a ange of ntenstes defned by the neghbong pxels. Consequently, ths elatonshp of ntedependence of ntenstes has been modeled usng the Makov andom feld theoy to detemne the pavement mage textue paametes and hence evaluate the specfc paametes elevant to pavement fcton (Rado (1994)). Rado (1994) used the above model to coelate the macotextue to mage ntenstes of local neghbohoods usng actual mages of pavements and the coespondng mean textue depths measued fom those pavement pofles. Moe ecently Khoude and Bochad (004) have studed the changes n mage popetes due to weang of pavement sufaces based on the statstcal popetes of the mage gadent, the cuvatue map of the gay level mages, and the devatve of the autocoelaton functon of seveal lnes of the mages. Howeve n Khoude and Bochad (004) wok, the ntensty of lght eflecton n a gven decton was consdeed to be govened by the eflected angle only thus neglectng ts sgnfcant dependence on the ncdent angle and the suface popetes. In the wok pesented n ths pape the ntenstes of ncdent and eflected lght as well as the eflecton popetes of sufaces of unfom colo ae used n modelng the weang of pavement macotextue. 5

6 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Modelng of the pavement mage fomaton pocess Sufaces whee eflecton of lght s lmted to the exact opposte decton as dctated by the law of eflecton ae known as specula sufaces whle sufaces that eflect lght n all dectons ncludng the specula decton ae temed dffusve ones. Geneally most pavement sufaces have both specula and dffusve popetes dependng on the geomety of the suface textue fomed by the mateal consttuents. Theefoe, the chaactestc eflecton popetes can be exploted to model the mages of textue and dstess featues of pavements. Bdectonal Reflecton Dstbuton Functon (BRDF) The ntensty of specula and dffusve eflecton (adance) fom any pont on a suface must be consdeed as a functon of the ntensty of ncdent lght (adance), the local eflecton popetes and the oentaton of the suface to the decton of ncdence. Ths complex elatonshp between the adance and adance of a suface can be best descbed by the Bdectonal Reflecton Dstbuton Functon (BRDF) (Ngan et. al., 005). BRDF of a suface s defned as the ato of adance n a gven decton (R) to the adance on that suface fom anothe decton (I) (Eqn. 1(a)). L ( R) BRDF( I, R) ( I, R) (1a) L ( I)cos d whee L (R) s the adance (eflected flux pe unt nomal aea pe unt sold angle) L (I) s the adance (ncdent flux pe unt nomal aea pe unt sold angle) s the pola angle between the ncdent vecto and the suface nomal d s the sold angle subtended at the suface pont by the ncdent lght souce The total adance at a pont on the suface n the decton R due to lght enteng the ente hemsphee suoundng that pont can be expessed as, L ( R) ( I, R) L ( I) cos d (1b) 0 6

7 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Snce, d sndd, whee s the azmuth angle of the ncdent vecto pojected on the suface plane, the 3-D fom of the above elatonshp s based on two ncdent and two eflected angles defnng the dectons I and R as expessed n Eqn. a, / L (, ) (, ;, ) L (, )cos sndd (a) 0 0 whee s the pola angle between the eflected vecto and the suface nomal s the azmuth angle of the eflected vecto pojected on the suface plane L, ) s the eflected adance (watts/steadan/mete ) ( L, ) s the ncdent adance (watts/steadan/mete ) (, ;, ) s the BRDF (steadan -1 ) gven by equaton 1(a) ( The total adance n the decton R fom a gven pont due to a sngle lght souce that subtends a sold angle of Δω on a dscete aea used fo computng the ρ value of that pont can be obtaned fom Equaton (1a) as; L (, ) L (, ) (, ;, ) cos (b) Tadtonally the BRDF of a desed object o a suface s measued usng a gonoeflectomete (Maschne et. al., 000). The most common functons that ae used to epesent BRDF of a suface ae the tenso poducts of the sphecal hamoncs, Zenke polynomals, and sphecal wavelets (Rusnkewcz S.,1998). Howeve, most of the above basc functons eque a lage numbe of coeffcents to descbe even modeately specula BRDFs. In addton, the above methods do not eque any less stoage even unde sotopc BRDF condtons. Rusnkewcz (1998) poposed a method fo decomposng BRDFs by changng vaables moe effcently. In the Rusnkewcz (1998) tansfomaton, the BRDF s epesented n tems of half angle between ncdent and eflecton dectons, and the dffeence angle between the half angle and ncdent angle ( hn Fg. 1). Kautz and McCool (1999) used sngle value decomposton (SVD) and nomalzed decomposton (ND) fo the BRDF functon. On the othe hand, smplfed models ae also avalable fo appoxmate evaluaton of BRDF such as Phong (1975), He (1991), Cook et al (1981), and Wad (199) models. 7

8 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Wad s eflecton model fo BRDF In the mage modelng pesented hee, the Wad s eflecton model (Wad, 199) s used due to ts smplcty and physcally meanngful paametes. Although Wad (199) fomulated eflecton models fo both ansotopc and sotopc sufaces, fo most pavement sufaces, the sotopc model gven by Equaton (3a) would suffce. d 1 exp tan / (, ;, ) s.. (3a) cos cos 4 Whee s the dffuse eflectance of the suface (steadan -1 ) s d s the specula eflectance of the suface (steadan -1 ) s the angle between vectos nˆ and ĥ n Fgue 1 ( nˆ s the unt nomal to the suface, ĥ s the half vecto between the unt ncdent vecto llustated and defned n Eqn. (3b)). dˆ as d ˆ and unt eflecton vecto h d d (3b) s the standad devaton of the suface slope o the squae oot of the slope vaance. Selecton of suface paametes fo the eflecton model The thee domnant paametes n the Wad s eflecton model (Eqn. 3a) ae, and. Of these epesents the changes n the suface slopes o the andomness n the oentaton of tny suface factals that can be attbuted to both macotextue and mcotextue. Theefoe, at a patcula pavement locaton, the decton of lght eflecton can be consdeed to be totally specula at the mnute factal level. Smooth sufaces that ae chaactezed by low slope vaances (α) eflect lght mostly n the specula decton wth much lowe eflecton components n the othe dectons. As α nceases, moe and moe lght eflects n the dectons othe than the specula decton and the suface assumes dffusve chaactestcs. Theefoe, when the neghbohood of any pont s obseved as a sngle unt, lght eflecton appeas to be dffusve due to the specula scatteng of lght caused by the dffeences n oentaton of the multtude of tny factals that compose that neghbohood. The decton of scatteng follows a Gaussan dstbuton wth the vaance expessed by the local slope vaance. Thus, a non- d s 8

9 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; sngulaly low value such as (based on Eqn. 3a) defnes a suface wth hgh speculaty, whee as a elatvely hgh value of (ex. above 0.) potays a hghly andom factal oentaton and hence a dffusve suface fo all pactcal puposes. Howeve, once a lmtng value of α s exceeded, one can expect the adance to be cutaled n all dectons due to obscuty and ntenal eflecton caused by the ntefeence wthn the suface pofle tself. In ths analyss was computed fom the vaaton of suface slopes n the neghbohood suoundng the nodal pont of nteest. Fo the assumpton of local speculaty to be vald n the neghbohood of any node and the value of to captue the mcotextue, the nodal spacng was selected as 0.05 mm n both x and y dectons (Table 1). In the magng systems cuently used n pavement suvey vehcles manufactued by the state-of the-at ndusty, the pxel esoluton that coesponds to the optcs and nstalled heghts fom the pavement suface, allows them to acheve a pavement esoluton of only 1 mm. Thus, although theoetcal modelng of the textue magng can each the mcotextue level, any efnement n the fneness of the nodal mesh beyond 0.5 mm would only make the computaton of nodal α values moe accuate and poduce mages that show moe textue detals than eal mages. Snce the eflecton at each local node s consdeed to be specula, and (Eqn. 3a) ae assgned values of 1.0 and 0 espectvely. Smulaton of the pavement textue pofle s d In the modelng of mages of pavement macotextue, the pavement pofles wee epesented n tems of 3-D sne functons. Ths epesentaton can be justfed based on the pncples of Foue decomposton, wheeby most pavement textue pofles can be appoxmated wth a sees (n) of fnte 3-D sne waves vayng n wavelengths and ampltudes as shown n Eqn. (4). z n 1 Whee and x y amp sn amp ae the espectve wavelength and ampltude of the th component. (4) 9

10 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Evaluaton of the eflectance of the pavement suface The textue pofle of the maged pavement and the locatons of the lght souce and the camea wee defned usng a 3D catesan coodnate system (Fg. ). Then the BRDF vaaton of the suface due to the dect llumnaton fom the lght souce can be computed, dsegadng the nte-eflecton and llumnaton fom othe souces such as sunlght. Pat of the lght fom the llumnatng souce gets eflected fom evey pont on the pavement such as R (x,y,z), scattes due to the dffusvty caused by the slope vaance ( ) of the neghbohood of R and eaches dffeent locatons of the camea lens. Theefoe, BRDF of R (Eqn. 3a) wth espect to a numbe of small elements (A c ) that consttute the camea lens aea (A c ) must be evaluated and ntegated to detemne the aveage adance fom R wth espect to the camea. It has been shown n the Appendx A that the aveage BRDF at R wth espect to the ente camea can be detemned as, 1 d 1 exp tan / s AC ( x, y, z) avg (5) AC, cos cos 4 Whee, ĥ= Unt vecto bsectng the ncdence and eflecton dectons (Fg. 1) nˆ = Unt vecto nomal to the suface at R (Fg. 1) cos hˆ. nˆ, cos RL u. nˆ and cos RPu. nˆ LR u = Unt vecto n the decton of ncdence (Fg. ) RP = Unt vecto n the decton of eflecton (Fg. ) u The appopate expessons fo the above vectos ae also deved n the Appendx A. The BRDF at any pont on the suface (.e, R) wth espect to camea apetue segments of 0.5 mm and 30 0 ncements n the adal and angula dectons espectvely, can be evaluated numecally usng Equaton (5). The ncdent lght fom the souce does not each cetan locatons on the suface due to occluson by the suface pofle and smlaly the eflected lght fom cetan othe locatons s pevented fom eachng the camea. 10

11 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Both of the above condtons wee ncopoated when the BRDF fo maged suface was evaluated usng Equaton (5). Conveson of pavement adance to mage ntensty The mage of a pavement featue s fomed when the lght eflected fom that featue (object) entes the camea lens and efacts on to the CCD senso. A schematc dagam of the optcs of mage fomaton s shown n Fgue 3. The elatonshp (Eqn. 6) between the adance fom any suface pont (R) and the ntensty of ts mage ( E) has been deved n the Appendx B. 3 L c E h L * cos cos cos. AL... 4 AC (6) D f Whee f,, L *, and c ae the focal length of the lens, BRDF at R wth espect to one camea element A C, ntensty of adance mmedately below the lght souce (at Q), and the angle between the nomal to the camea apetue and the lne RC, espectvely. The emanng symbols n Eqn. (6) ae llustated n Fg. 3. If the lght souce and the camea ae placed at a elatvely lage heght compaed to the dmensons of the maged aea, and θ L C would not change sgnfcantly wthn one mage. Futhemoe, snce h, L*, A L and f ae constants, Eqn. (6) can be e-wtten as, 1 (7) D E K cos. A 4 C Whee K ncludes the constant quanttes n Eqn. (6). Fnally, the total ntensty E of the mage fomed by the suface pont R due to lght enteng the ente lens (of aea A c ) can be detemned by combnng Eqns. (5) and (7) as: cos E K AC ( x, y, z) (8) 4 avg D 11

12 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Theefoe, Eqns. (5) and (8) can be used to obtan the pxel ntensty dstbuton n the pavement suface mage. Expemental vefcaton of the mage fomaton model The accuacy of the mage fomaton model developed n Secton.0 was vefed expementally usng a sngle wavelength peodc suface (n=1, 1=6mm and amp =3mm n Eqn. (4)) molded fom clay. The lght souce was set up above the molded 1 suface wth the nomal to ts suface ntesectng the pofle at a hozontal dstance of 380 mm fom t. The camea was placed 500 mm away fom the lght souce and oented n such a way that the nomal lnes to the camea apetue and the lght souce ntesected the pavement pofle at the same locaton. Then the suface was maged at two dffeent camea heghts of 305 mm and 610 mm. The actual and smulated mages coespondng to the two condtons ae shown n Fgues 4(a)-(f). When compang Fgs. 4(a) wth 4(b) and Fgs. 4(d) wth 4(e), t can be obseved that the mages ceated by the BRDF model (Eqns. (5) and (8)) esemble those of the actual suface. Futhemoe, the mages of the same suface mathematcally smulated unde the same lghtng and magng condtons usng the Phong (1975) model pogammed n a wdely used compute gaphcs softwae, Maya 7, ae also shown n Fgs. 4(c) and 4(f). Maya s an nbult pogam n a commecal package, whch s fomulated based on the Phong (1975) eflecton model. When the postons of the camea and the lght souce and the suface pofle ae nput, Maya automatcally ceates the mages. Because of Maya s wdespead use, n ths wok t was used to confm the elablty of the Wad s model smulatons. Howeve the authos own codng of the Wad s model was pefeed ove Maya n the cuent eseach because of the fome s flexblty n pogammng dffeent pavement sufaces, lghtng and magng condtons compaed to the latte. In ode to quantfy the compason between the mages developed based on the Wad s model and the expemental countepats (Fgue 4), sectons of equal szes wee selected fom Fgue 4(a) and Fgue 4(b). Then, the esemblance of the two mages was expessed quanttatvely by the aveage dffeence n ntenstes between the two mages expessed as a pecentage of the ange of ntenstes.e. 56. Snce ths value was 1

13 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; computed to be only 1.19% pe pxel, Wad s eflecton model can be assumed to model closely the expemental mages obtaned unde smla llumnaton condtons. It s seen that Fgs. 4(b) and 4(e) compae easonably well wth Fgs. 4(c) and 4(f) as well. The pxel ntenstes of the synthetc (modeled) mage close to the camea wee seen to be hghe (Fg. 4(b)) as n the case wth ts expemental countepat (Fg. 4(a)). Howeve, Fgs. 4(b) and 4(e) show that thee s a shap ntensty educton fom the peak of the pofle n the modeled mages wheeas the ntenstes of the expemental countepats (Fgs. 4(a) and 4(d)) decease gadually fom the peak. Ths can be attbuted to the fact that the exact snusodal shape descbed by Eqn. (4) could not be acheved due to a mno flattenng effect poduced at the peaks dung moldng of the clay suface. Applcaton of the mage model n detecton of wea In the next phase of the study, the new eflecton model was appled to detect the degadaton of textue n pavements. Fo ths pupose, a 0.05m x 0.05m segment of a pavement suface was modeled mathematcally wth the lght souce and the camea placed on opposte sdes of the nomal to the cente of the suface, 0.05 m apat fom each othe at heghts of 0.5m and 1 m espectvely above the modeled suface (Fg. 5(a)). Possble optmum locatons of two such magng systems n a potental feld mplementaton of ths technque ae shown n Fg. 5(b). As mpled n Fg. 5(b) the pavement wea detecton can be lmted to the wheel path aeas whee weang of pavement textue due to taffc s pedomnant. Usng the above setup, the eflecton model descbed n Secton. was used to ceate the coespondng mages of the mathematcally epesented ognal and won pofles, as descbed late n Secton 4.. Tools fo assessng pavement wea usng dgtal mages Seveal mage chaactestcs can be used fo dffeentaton of dgtal mages of new and won out pavements and subsequent dentfcaton of the extent of degadaton of textue and fctonal popetes. The nomalzed pxel ntensty hstogam of a dgtal mage whch depcts the statstcal dstbuton of pxel ntenstes on the gay scale of 0 to 55 povdes the smplest tool to compae and contast mages. Khoude and Bochad (004) (Secton 1.3) have used specfc statstcal popetes and the autocoelaton 13

14 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; functon fo ths pupose. Altenatvely, an appopately defned bghtness functon of an mage can also be employed as a moe elable measue fo compason of mages. Howeve, the peceved bghtness of a gven ntemedate gay-scale ntensty between 0 (black) and 55 (whte) cannot be defned n a clea-cut manne. To addess ths ssue and defne a elable bghtness functon, eseaches (Cheng et. al., 1999) have consdeed mage bghtness as a fuzzy set. The membeshp functon (μ bght (x)) of the bghtness fuzzy set can be defned n the gay ntensty scale of 0 to 55 wth thee paametes a, b, and c. As llustated n Fg. 6, the ntenstes less than a have zeo membeshp and the ntenstes hghe than c have a membeshp of 1, n the bghtness fuzzy set. The degee of bghtness fo the ntenstes between a and c would vay gadually fom 0 to 1. Ths vaaton can be epesented usng a standad S functon descbed n Eqn. (9) (Cheng et. al., 1999). 0, ( x a) x a ( b a)( c a) a x b bght ( x) (9) ( x c) b x c 1 ( c b)( c a) x c 1 Then the bghtness of an mage can be expessed as a pobablty measue as follows: 55 P( bght) ( x). p( x) (10) x0 bght whee p(x) s the pobablty of occuence of any gven ntensty x n the evaluated mage as dsplayed n ts nomalzed hstogam. The optmum values fo paametes a, b and c can be found by maxmzng the entopy of bghtness (H(bght) n Eqn. 11) of a selected standad mage. H ( bght) P( bght)log( P( bght)) (1 P( bght))log(1 P( bght)) (11) 14

15 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; In the cuent nvestgaton a standad gay-scale taget (Edmund, 003) consstng of 17 evenly spaced patches wth ntenstes between 0 and 55 (Fg. 7) was used as the standad mage. Wth p(x) (Eqn. (10)) detemned fom the nomalzed ntensty dstbuton of an mage of the standad gay-scale taget, the maxmzaton of the bghtness entopy functon (Eqn. (11)) yelded the optmum a, b and c values of 45, 135 and 195, espectvely. Then, the bghtness evaluaton of any othe mage can be pefomed usng Eqn. (10) wth p(x) obtaned fom ts ntensty hstogam and μ bght (x) evaluated fom Eqn. (9) usng the optmum a, b and c values detemned above. Detecton of suface wea based on mage bghtness Case 1 Modelng of sngle sne wave pofles The effect of textue wea on the bghtness of the ognal and won out mages was nvestgated by modelng the mages of dffeent textue levels usng the eflecton model n Equatons (5) and (8) unde the lght souce and the camea postons llustated n Fgue 5(a). The bghtness of the modeled mages of sngle sne wave suface pofles (Equaton 4) wth pedefned ampltudes (MTD) vayng fom 1 mm to 5 mm and wavelengths (aveage textue spacng) vayng fom 1 mm to 10 mm wee detemned usng Equaton (10) and plotted n Fgue 8. Fom Fgue 8 t can be obseved that fo a constant wavelength the mage bghtness nceases wth deceasng mean textue depth (MTD) whle fo a constant MTD, the bghtness nceases wth nceasng wavelength. In both cases the ncease n bghtness can be attbuted to the smoothenng of the pofle. Based on the above pelmnay obsevatons t was decded that the consdeaton of the bghtness of pavement mages captued unde the specfc condtons defned n ths study (Fg. 5) could be pusued to detect suface wea. Case Modelng of complex pavement suface pofles In the next phase of modelng, two dffeent and moe complex pofles wee composed of multple sne waves to closely epesent actual textue pofles of elatvely ough and elatvely smooth pavements. In both pofles the wavelengths wee set to be 4, 1, 8, 6 and 4 mm. The wavelength to ampltude atos ( a n Equaton 1) of the oughe pofle wee set to be 10, 8, 5, 3 and espectvely, whle a fo the smoothe pofle was set at a 15

16 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; constant value of 10 fo all the wavelengths. Then the above pofles can be expessed mathematcally as, z whee 5 / a 1 x y sn (1) s the wavelength of th a s the wavelength( sne cuve ( = 1,5 mm) ) to ampltude ( amp ) ato of th snusodal cuve Thee stages of weang wee smulated on the compute by degadng the poton of the pofles above the mean levels by %, 4% and 6% of the ognal pofle heghts espectvely. Fgues 9(a) and 9(b) show the smooth and ough pofles espectvely, whle Fgues 9(c) and 9(d) show the dffeent levels of weang of selected sectons of the pofles shown n Fgues 9(a) and 9(b) espectvely. Fgues 10(a) and 10(c) show the espectve mages of the ognal pofles shown n Fgues 9(a) and 9(b) modeled usng Eqns. (5) and (8), whle Fgues 10(b) and 10(d) show the modeled mages of the 6% won countepats. The pa-wse compason of Fgue 10(b) wth Fgue 10(a) and Fgue 10(d) wth Fgue 10(c) shows an ncease n mage bghtness due to weang. Fg. 11 s a plot of the bghtness Vs the MTD fo both pavement sufaces unde dffeent stages of weang. It can be obseved fom Fgue 11 that the mages of the smoothe suface ae sgnfcantly bghte than those of the oughe suface at all stages of weang. Futhemoe, Fg. 11 shows the clealy nceasng tends of bghtness of both pofles as weang poceeds. The above obsevatons futhe suppot the nceasng tend of bghtness that was obseved n Fgs. 8 due to smoothenng of sngle sne waves. In summay, the esults ndcated n Fgs demonstate the vablty of settng up an optcal magng system n the manne specfed n Fg. 5 to dentfy the level of macotextue degadaton on a pavement. Expemental vefcaton of mage bghtness vaaton due to weang In the fnal phase of the nvestgaton, the theoetcal elatonshp between mage bghtness and the extent of wea developed n Secton 4. was expementally vefed usng a 460 mm damete laboatoy concete specmen made to be compatble wth the 16

17 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Ccula Tack Mete (CTM) (ASTM E ). The above concete specmen was gooved at unfomly spaced ntevals to obtan the textued suface seen n Fg. 1(a). Then, fou 50x50 mm sectons evenly spaced out along the CT mete tack wee eamaked on t as test sectons whee the expemental esults could be aveaged to emove any bas due to textue vaaton. These ndvdual sectons wee then maged usng the same optcal settngs used n the theoetcal study. Late, the suface of the concete specmen was gadually won wth sand pape and the won sectons wee emaged unde the same lghtng condtons. The CT mete pofles fo the ognal and won pofles ae shown n Fgue 13 fom whch the aveage MTD can be calculated at each weang stage as shown n Table. In the pelmnay expemental vefcaton epoted hee, textue was ceated by goovng the concete suface to appoxmately epesent a squae-waved suface. At each stage of sandng off, t was obseved that the edges of the gooves and the suface ponts wth the hghest elevatons wee won out fst. Weang ntates n actual pavements also at the suface ponts wth the hghest elevatons. Hence t s expected that the vaaton of dgtal mage popetes dung feld weang would follow a tend smla to that acheved n the expement. Ognal and won mages of one of the fou selected concete sectons ae shown n 1(a) and 1(b) espectvely, whle Fgue 1(c) shows the ntensty hstogams. Compason of the two hstogams n Fgue 1(c) shows that the oveall mage ntenstes have nceased due to weang. The computed aveage bghtness values of the mages ae also shown n Table. Fom the esults n Table and the coespondng plot n Fgue 14, t can be obseved that the bghtness of the mages of the fou sectons have nceased due to weang. A smla bghtness evaluaton was conducted on a feld concete slab at nght tme usng atfcal llumnaton. A selected locaton of the slab was maged fst and e-maged on two stages of weang caused by sand pape. The esults ae shown n Fgues 1(d)-1(f). Addtonal hstogams n Fgue 1(g)-1() show the ncease n the ntenstes due to gadual weang shown n Fg 1(d)-(f). Based on the laboatoy and 17

18 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; feld esults t can be concluded that the theoetcally pedcted ncease n mage bghtness due to weang s suppoted by the expemental esults. Applcaton of mage bghtness to evaluate pavement fcton The expemental elatonshp obtaned n Fg. 14 between the mage bghtness and MTD of a gven suface can be calbated usng Equaton (13). B n k ( MTD ) e (13) whee k and n ae assumed to be constants fo gven pavement and lghtng condtons. Fo the specfc Bghtness Vs MTD data set n Fg. 14, one obtans, B ( MTD ) e (14) On the othe hand, the Skd Numbe (SN) (ASTM E ) of a pavement can be evaluated usng as, SN SN 0 e sv S p Whee, s and V ae the slp ato and the speed of measuement. SN 0 s the fcton measuement coespondng to statc condtons. Fo the Locked-Wheel Fcton Testes (LWST) (ASTM E 74-06) and DFTs (ASTM E a), s=100%. Also, constant, can be elated to the Mean Pofle Depth (MPD) as, S p p (15) S, the speed a b(mpd) (16a) Whee a and b ae constants dependent on the method used to evaluate macotextue. Fo the CT mete measuements, ASTM E ecommended values ae a=14. and b=89.7. The followng elatonshp ecommended by ASTM E 157 has been used to convet MPDs to MTDs. 18

19 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; MTD = 0.947*MPD (16b) The skd-numbe (SN) of a pavement measued wth the LWST o DFT can be elated to the bghtness of the coespondng mages by combnng Equatons (13), (15) and (16) as follows: SN SN 0 e V b ln B k 1 / n a Fnally, Equaton (17) can be used to calbate the elatonshp between the pedcted SN at dffeent stages of weang of a gven concete pavement and the bghtness (B) of the coespondng mages. As an example, let the LWST measued SN of the ntally unwon concete suface fo whch the mage Bghtness and MTD vaaton s defned n Fg. 14 (wth k=.58 and n=0.67), be 4. Then the vaaton of SN wth the bghtness of mages captued at dffeent stages of wea shown n Table can be evaluated usng Eqn. (17). Ths vaaton s llustated n Fgue 15 fo the standad measuement speed of 65 km/h. The above example llustates the need fo calbatng Equaton (17) to detemne the specfc values of SN 0, k and n applcable fo a gven pavement and a lghtng system, po to feld mplementaton of the developed methodology on that pavement. Lmtatons of the new technque A majo lmtaton of the developed technque s ts napplcablty on wheel paths whee the deposton of te ubbe camouflages the textue, theeby offsettng any ncease n bghtness n the mages due to wea. In addton, the mages ceated usng the geometcal and eflecton models could dffe fom the actual mages due to camea atfacts and othe types of nose. Hence the mages collected fom suvey vehcles have to be pe-pocessed to emove any nose befoe they ae used to detect the changes n bghtness. Anothe possble lmtaton could be the complexty of the actual llumnaton condtons at the tme of mage captue. Ths effect can be especally ponounced when mages ae collected dung daytme n the pesence of sunlght and nte-eflectons fom (17) 19

20 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; othe souces whch ae not consdeed n the modelng. Howeve, ths ssue can be ovecome by magng dung the nght tme when the maged pavement suface would be llumnated mostly unde the nfluence of the pobe lght attached to the evaluaton vehcle. In ths pelmnay analytcal nvestgaton and ts companon expemental vefcatons, the mage ntensty contasts wee pedcted based on the suface elef vaatons only, thus dsegadng effects of colo vaaton ntoduced n the adant lght by dffeent consttuent mateals. Ths ssue would be ctcal n the applcaton of ths technque to detect wea n asphalt pavements n patcula, whch consttutes aggegate and bnde wth contastng colos. Howeve, ths technque can be efned futhe to ncopoate colo vaatons n the BRDF models (Amaas et. al, 010). Pavement cack evaluaton usng dgtal mages does not eque the detecton of featues smalle than 1 mm esoluton snce the wdest (halne) cack consdeed n pavement ehabltaton s 1 mm n wdth. Theefoe, thee has been no mmnent need fo futhe advancement n camea esoluton to acheve pecsons geate than 1 mm. Howeve, the esoluton becomes an ssue n the advanced textue analyss snce hghe esoluton cameas wth esolutons as small as 0.5 mm would be needed to detect the lowe end of macotextue fom mm. Fnally, the objectve of ths nvestgaton was to evaluate the wea nduced ntensty changes n dgtal mages of locatons whch ae deemed to be uncontamnated. As fo detemnng the textue changes at contamnated locatons, the ntensty dffeences nduced by the contamnants themselves must be accounted fo fst usng vefed eflecton and efacton popetes of the contamnants. Then, the wea nduced ntensty dffeences can be evaluated accuately. Suggestons fo feld mplementaton Vaatons due to () llumnaton and () seasonal effects could also cause changes n the mage bghtness. Theefoe, befoe evaluatng the wea-nduced changes, the ntensty effects due to llumnaton must be elmnated usng mage flteng technques. 0

21 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Sgnfcant and unfom bghtness changes acoss wheel path and non-wheel-path aeas would ndcate llumnaton effects. Flteng technques ae avalable (Cheng et. al., 1999) to evaluate the aveage change n ntensty acoss the mage and standadze mage sets wth espect to the ntenstes. The effects of seasonal vaatons and even llumnaton to some extent can be mnmzed by lmtng the pavement wea nduced textue change evaluaton to mages captued dung the same season. Most tanspotaton agences such as DOTs conduct the netwok level evaluatons on an annual bass. Thus, even netwok level skd evaluatons can be scheduled n such a way that a gven pavement can be evaluated evey yea dung the same season. In addton, wea nduced bghtness changes n mages can be magnfed by employng moe sophstcated cameas that can potay a hghe numecal ange of ntenstes than the standad scale of Futhemoe, as hghlghted n the example on the applcaton of ths technque, any netwok-level mplementaton of ths methodology must be accompaned by an ntal set of calbaton tests fo each possble testng scenao assocated wth dffeent pavement types and llumnatons levels. Fo ths pupose, two ntal LWST measuements and bghtness evaluatons of the coespondng mages would suffce fo any gven testng scenao. Conclusons An mage modelng technque was used to exploe optcal popetes of dgtal mages that can quantfy the macotextue and skd esstance changes n pavements. In ths egad, a smplfed Bdectonal Reflecton Dstbuton Functon (BRDF) model wth physcally meanngful paametes was used to tansfom the macotextue of a pavement suface to the coespondng mages captued by a dgtal aea-vew camea. The modelng esults wee fst vefed by matchng the theoetcally smulated mages of a sngle wavelength 3-D snusodal suface wth those of a geometcally smla expementally molded suface. Next the mages of a famly of 3-D sngle sne waves wth vayng ampltudes and wavelengths wee modeled to exploe specfc mage 1

22 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; chaactestcs that would detect suface smoothenng caused by changes n the mean textue depth o the textue spacng (wavelength). The above nvestgaton was also extended to nclude appopate combnatons of 3D sne cuves that esemble actual pavement sufaces wth dffeent macotextue levels. Modelng of suface wea consstently evealed monotonc nceases n the bghtness of the coespondng mages captued by a well desgned magng system placed at an optmum locaton elatve to the pavement. Modelng esults wee vefed expementally by fst usng a laboatoy concete specmen compatble n sze wth the Ccula Tack Mete (CTM) and won out n stages usng sandpape. The nvestgaton was late extended to a feld concete slab as well. Pocessng of the mages of the ognal and won concete sufaces confmed the defntve ncease n mage bghtness due to weang. It was demonstated that once the bghtness vaaton tend of the mages coespondng to ntal stages of weang of a gven pavement s establshed, the model can be calbated to detemne the extent of pavement wea at any futue stage based on evaluatng the bghtness of the elevant mages. In addton, the conventonal coelaton between the skd numbe and MTD of a pavement was employed to llustate how the new technque can be extended to pedct the degadaton of skd esstance, based on evaluatng the bghtness of pavement mages. It s known that the use of devces such as Locked-wheel skd testes s mpactcal fo peodc netwok level sceenng of hghway pavements fo skd esstance defcences. On the othe hand, wth futhe efnement of the technque ntoduced n ths study, f the evaluated bghtness of pavement mages outnely collected by vaous tanspotaton agences can be used to pedct the degadaton of skd-esstance of pavements, t would povde a valuable tool fo netwok-level sceenng. Snce ths textue modelng appoach can even each the mcotextue of pavements, t could povde a valuable tool to nvestgate the types of nfomaton on pavement mcotextue that could also be evealed on futhe enhancement of camea esoluton.

23 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Acknowledgment The Natonal Aeonautcs and Space Admnstaton (NASA) gant NNL06AA17A s gatefully acknowledged Refeences Amaas S.P., Gunaatne M., Saka S. and Nazef A. (007). Chaactezaton of the textue popetes of pavement mages as an ad to automated compehensve pavement evaluaton. Pesented at the Tanspotaton Reseach Recod. Amaas S.P., Gunaatne M., and Nazef A. (010). Dffeentaton of cacks fom suface egulates n open gaded fcton couse (OGFC) pavements usng dgtal mage modelng Pesented at the Tanspotaton Reseach Recod. ASTM Standad E Standad Pactce fo Calculatng Pavement Macotextue Mean Pofle Depth ASTM Intenatonal, West Conshohocken, PA. ASTM Standad E a Standad Test Method fo Measung Paved Suface Fctonal Popetes Usng the Dynamc Fcton Teste, ASTM Intenatonal, West Conshohocken, PA. ASTM Standad E Standad Pactce fo Calculatng Intenatonal Fcton Index of a Pavement Suface, ASTM Intenatonal, West Conshohocken, PA. ASTM Standad E Standad Test Method fo Skd Resstance of Paved Sufaces Usng a Full-Scale Te, ASTM Intenatonal, West Conshohocken, PA ASTM Standad E Standad Test Method fo Measung Suface Fctonal Popetes Usng the Btsh Pendulum Teste, ASTM Intenatonal, West Conshohocken, PA. Balme, G. G. (1978). Pavement textue: Its sgnfcance and development. Tanspotaton Reseach Recod. 666, Tanspotaton Reseach Boad, Washngton, D.C., 1-6. Btton, S.C., Ledbette, W.B., and Gallaway, B.M. (1974). Estmaton of skd numbes fom suface textue paametes n the atonal desgn of standad efeence pavements fo test equpment calbaton. J. Test. Eval., (), Cheng, H.D., Chen, J.R., Glaze, C., and Hu, Y.G. (1999). Novel appoach to pavement dstess detecton based on fuzzy set theoy. J. Comput. Cv. Eng., 13(4), Cook R.L. and Toance. K. E. (1981). Reflectance Model fo Compute Gaphcs, 15(3), Poceedngs, Annual Confeence Sees, ACM SIGGRAPH, pp

24 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; DSC 111 (008). MONITORING:-Lase-system-montos-slppeness-of-oadway Edmund Industal Optcs (003), Lage Gayscale taget, Egun, M., Lynam, S., and Lynam, A.F. (005). Pedcton of oad suface fcton coeffcent usng only maco- and mcotextue measuements. J. Tansp. Eng., 131(4), Gould D (003). Complete Maya Pogammng: an extensve gude to MEL and the C++ API, Mogan Kaufman Publshes Gendy A El, and Shalaby A. (007). Mean Pofle Depth of Pavement Suface Macotextue Usng Photometc Steeo Technques, Jounal of Tanspotaton Engneeng, Vol. 133, No. 7, pp Huang, Y. and Xu B. (006). Automatc Inspecton of Pavement Cackng Dstess, Jounal of Electonc Imagng, 15(1) He X.D., Toance K.E., Sllon F.X., and Geenbeg D.P. (1991). A Compehensve Physcal Model fo Lght Reflecton. Compute Gaphcs, 5(4) Poceedngs, Annual Confeence Sees, ACM SIGGRAPH, pp Intenatonal Oganzaton fo Standadzaton (ISO) (1997). Chaactezaton of pavement textue by use of suface pofles Pat 1: Detemnaton of mean pofle depth, Intenatonal Standad No Kautz J. and McCool M. D. (1999). Inteactve endeng wth abtay BRDFs usng sepaable appoxmatons, Euogaphcs Rendeng Wokshop, pp. 47:60. Khoude M. and Bochad J. (004). Roughness Chaactezaton though 3D Textued Image Analyss: Contbuton to the Study of Road Wea Level, Compute-Aded Cvl and Infastuctue Engneeng, Vol. 19, pp Leu, M.C., and Heny, J.J. (1978). Pedcton of skd esstance as a functon of speed fom pavement textue. Tanspotaton Reseach Recod. 666, Tanspotaton Reseach Boad, Washngton, D.C., LRIS (Lase Road Imagng System). (008). Maschne S.R., Westn S. H., Lafotune E. P. F., and Toance K. E. (000). Imagebased bdectonal eflectance dstbuton measuement, Appled Optcs 39:16. 4

25 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Maz A, Gunaatne M., and Nazef A. (005). Gudelnes fo pefomance assessment of dgtal magng systems used n hghway applcatons, ASCE Jounal of Tanspotaton Engneeng, Vol. 131, No. 6, June. Maz A., Amaas S.P., Gunaatne M., and Nazef A. (006). An Innovatve Method fo Enhancng Pavement Cack Images. Pesented at the Tanspotaton Reseach Recod. Ngan A., Duend F. and Matusk W. (005). Expemental analyss of BRDF models, n Euogaphcs Symposum on Rendeng, Euogaphcs Assocaton, pp Phong B.T. (1975). Illumnaton fo Compute Geneated Images. Communcatons of the ACM, 18(6): , June. Rado Z. (1994). A Study of Road Suface Textue and ts Relatonshp to Fcton, Doctoal Dssetaton, Pennsylvana State Unvesty, PA. Rusnkewcz S. (1998). A new change of vaables fo effcent BRDF epesentaton, Euogaphcs Rendeng Wokshop, 1998, pp. 11:. Shapo L. G. and Stockman G. C. (001). Compute Vson, Pentce Hall Tamua H., Mo. S, and Yamawask T. (1978). Textual featues coespondng to vsual pecepton, IEEE Tans. Syst., Man, Cyben., vol. C-4, pp Wang K.C.P, Hou Z., Watkns Q.B, and Quchqulla S.R. (007). Automated Imagng Technque fo Runway Condton Suvey, pesented fo the Woldwde Apot Technology Tansfe Confeence Wad G.J. (199). Measung and modelng ansotopc eflecton. Compute Gaphcs, 6(), pp. 65-7, July. APPENDIX A Devaton of BRDF fo a suface pofle wth espect to an aeal-vew camea. Fom Fg., the ncdent lght vecto at R can be detemned as LR x y j ( h z) k D. LR u (A1) whee D s the dstance LR and LR s the unt vecto. In ode to compute the u adance (ncdent lght) on the camea, a tansfomaton can be used to convet the 5

26 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; apetue fom a 3D plane ccle n the (x,y,z) system to a D ccle n the x, y, z system as shown n Fgue A. If z s nomal to the apetue of the lens, then the camea plane can be dentfed by the unt vecto k along z defned by two of ts dectonal cosnes l and m as; k l m j 1 l m k (A) Then the unt vecto can be selected such that x axs les on the xy plane that ntesects the ccle. Snce and k ae pependcula to each othe (.e.. k 0), the tansfomed can be expessed usng the ognal and j as m l j (A3) l m l m C j, y' Φ k, z' FIGURE A Pola and Catesan Coodnate Systems fo the Camea Apetue Also snce the thd unt vecto j s pependcula to both and k (.e. tansfomed j can be expessed usng the ognal, j and k as A C dφ P d ΔA C, x' j k ), the l j 1 l l m m m 1 l l m m j l l m l m m k (A4) 6

27 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Usng the tansfomaton defned by Eqns (A)-(A4), the vecto CP (Fgue A) can be epesented n the (x,y,z) coodnates as, mcos l 1 l m lcos m 1 l m CP sn sn jsn l l m l m l m l m Let the vecto jonng R and the cente of the camea C (Fgue A) be, m k (A5) RC C C j C k (A6) Snce, RP RC CP x y z The eflected lght fom R to P can be epesented by the followng vecto mcos sn l 1 l m l cos sn m 1 l m RP C x C y j Cz sn l m k l m l m D. (A7) C RP u whee D c s the dstance RP and RP u s the unt vecto. Then usng the unt vectos n the RP and LR dectons, the half vecto between the ncdent and the eflected lght (Fgue 1) s defned by, h RP u LR = hˆ. h (A8) u If the unt nomal to the pavement textue pofle at pont R( x, y, z) s specfed usng two known dectonal cosnes N x and N y as follows, nˆ N N j 1 N N k (A9) x y x y Then, the angula paametes equed fo Wad s BRDF expesson (Eqn. (3)) to be appled at the suface locaton R can be detemned as, cos hˆ. nˆ (A10) cos LR u. nˆ (A11) cos RPu. nˆ (A1) 7

28 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Fnally, by applyng Eqn. (3a) to an element of aea A C of the apetue, the aveage BRDF at R wth espect to the ente camea can be detemned as, 1 d 1 exp tan / s AC ( x, y, z) avg (A13) AC, cos cos 4 Whee A c ( d)( d) (Fg. A) and A c s the aea of the camea apetue. APPENDIX B Relatonshp between the photo ntenstes of objects and the mages In Fg. 3, O s the aea of the neghbohood of R fom whch lght s eflected to the coespondng aea I of the mage. The flux leavng the pavement suface aea δo towad the camea s gven by F LR O (B1) whee L R s the adance at δo. The sold angle subtended by as, C A on R can be expessed cos Ac (B) D If no loss of photo enegy s assumed wthn the camea, and the ntensty caused by the lght efacted wthn the element A c at the mage aea I s E, then F E. I (B3) Substtutng fom Eqn. (B3) n Eqn. (B1), EI LR O (B4) Usng Eqn. (B), Eqn. (B4) can be ewtten as EI L ( O) A O R c cos D C c 8

29 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; O cos E LR Ac (B5) I D C Fom basc optcs t follows that the lght ognatng fom an object O and passng though the cente of the camea lens (C) contnues wthout efacton to fom ts mage I. Hence the sold angles subtended at the camea cente C by O and I ae equal and opposte. Then, by evaluatng each sold angle one obtans, ( O)cos O O I D / C / ( I )cos ( f / cos / C / C C ) 3 cos C. D (B6) f cos Whee θ C s the angle between the nomal to the apetue at C and the lne CR (Fgue 3) / and s the angle between the nomal to the modeled suface and CR. Snce the camea / / lens s elatvely small n aea, t can be assumed that = and D C =D C. Theefoe, by substtutng n Eqn. (B5) fom Eqn. (B6) cos 3 C E LR.. f A C Fom Equaton (1a) the eflected adance L R and the ncdent adance by, L R (B7) L ' can be elated L' cos (B8) cos L Whee AL. and s the nclnaton of the face of the lght souce to the L D plane nomal to RL Futhemoe, snce the attenuaton of adance s nvesely popotonal to the squae of the dstance, 9

30 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; h L' L * D (B9) Whee L* s the adance on the suface mmedately below the lght souce Q. By combnng Eqns. (B7), (B8) and (B9) one obtans, 3 L c E h L * cos cos cos. AL... 4 AC (B10) D f 30

31 Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; TABLE 1 Classfcaton of Textue based on Wavelengths (ISO, 1997) Type Wavelength (mm) Descpton of textue Mcotextue λ<0.5 Fomed by ethe fne aggegate patcles (sand) o suface oughness of the lage aggegate Macotextue 0.5<λ<50 Same ode of sze as coase aggegate o te tead elements Mega-textue 50<λ<500 Same ode of sze as te/oad contact aea Unevenness 500<λ Suface oughness that affects the de comfot TABLE Bghtness Vaaton due to Weang Suface Descpton Mean Textue Depth (MTD) mm Bghtness of Images Ognally gooved Afte weang stage Afte weang stage Afte weang stage Smooth suface

32 Fgue Captons Lst Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; LIST OF FIGURES FIGURE 1 Illustaton fo Wad s Reflecton Model FIGURE Illustaton of the Imagng System Setup FIGURE 3 Illustaton of the Image Fomaton Pocess FIGURE 4(a) Actual Image of the Pofle Taken at 305 mm Above the suface FIGURE 4(b) Modeled (Wad) Image of the Smulated Pofle Coespondng to Fg. 4(a) FIGURE 4(c) Modeled (Maya) Image of the Smulated Pofle Coespondng to Fg. 4(a) FIGURE 4d) Actual Image of the Pofle Taken at 610 mm Above the Suface FIGURE 4(e) Modeled (Wad) Image of the Smulated Pofle Coespondng to Fg. 4(d) FIGURE 4(f) Modeled (Maya) Image of the Smulated Pofle Coespondng to Fg. 4(d) FIGURE 5(a) Specula Setup of the Imagng System FIGURE 5(b) Optmum Aangements of Lght Souce, Camea and Imaged Secton FIGURE 6 Illustaton of the Bghtness of Gay-Scale Intenstes FIGURE 7 Standad Ffteen-wedge Gayscale Taget (Edmund, 003) FIGURE 8 3-D Plot of Bghtness Vaaton wth Wavelength and MTD FIGURE 9(a) Smooth Pofle FIGURE 9(b) Rough Pofle FIGURE 9(c) Weang of a Selected Secton n Smooth pofle n Fgue 9(a) FIGURE 9(d) Weang of a Selected Secton n Rough pofle n Fgue 9(b) FIGURE 10(a) Synthetc Image fo the Ognal Pofle of Fgue 9(a) FIGURE 10(b) Synthetc Image fo the Won Pofle (wea 3) of Fgue 9(a) FIGURE 10(c) Synthetc Image fo the Ognal Pofle of Fgue 9(b) FIGURE 10(d) Synthetc Image fo the Won Pofle (wea 3) of Fgue 9(b) FIGURE 11 Bghtness Vaaton of Smooth and Rough Pavement Sufaces due to Weang (Theoetcal Modelng Results) FIGURE 1(a) Ognal Image of the 50mm x 50 mm secton FIGURE 1(b) Image of secton n Fgue 1(a) afte weang FIGURE 1(c) Image hstogams fo ognal secton and won sectons shown n Fgues 1(a) and 1(b) FIGURE 1(d) Ognal pavement (bghtness = 0.310) FIGURE 1(e) Afte stage 1 weang (bghtness = ) FIGURE 1(f) Afte stage weang (bghtness = 0.385) FIGURE 1(g) Image hstogam fo ognal secton shown n Fgue 1(d) FIGURE 1(h) Image hstogam fo won secton shown n Fgue 1(e) FIGURE 1() Image hstogam fo won secton shown n Fgue 1(f) FIGURE 13 Ccula Tack Mete Results Showng the Vaaton of Suface Pofle due to Weang Fgue 14 Vaaton of Bghtness wth MTD Fgue 15 Vaaton of Skd Numbe wth Bghtness

33 FIGURE 1.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; d ˆ nˆ δ ĥ d ˆ FIGURE 1 Illustaton fo Wad s Reflecton Model

34 Fgue.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; z Lght Souce L (0,0,h) Nomal to the Apetue l m j 1 l m k Lens apetue C(c x,c y,c z ) P ΔA C D D c x Ogn of Coodnates O (0,0,0) y Obseved Pont R(x,y,z) FIGURE Illustaton of the Imagng System Setup

35 FIGURE 3.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; θ C Aea δi f CCD Senso plane Aea - A L L O θ L θ C A C, Element of Camea Apetue h D δω δω D c θ θ Q R, Aea δo FIGURE 3 Illustaton of the Image Fomaton Pocess

36 FIGURE 4.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; FIGURE 4(a) Actual Image of the pofle taken at 305 mm above the suface FIGURE 4(b) Modeled (Wad) Image of the smulated pofle coespondng to Fg. 4(a) FIGURE 4(c) Modeled (Maya) Image of the smulated pofle coespondng to Fg. 4(a) FIGURE 4(d) Actual Image of the pofle taken at 610 mm above the suface FIGURE 4(e) Modeled (Wad) Image of the smulated pofle coespondng to Fg. 5(d) FIGURE 4(f) Modeled (Maya) Image of the smulated pofle coespondng to Fg. 5(d)

37 FIGURE 5.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; L C 0.05 m FIGURE 5(a) Specula Setup of the Imagng System FIGURE 5(b) Optmum Aangements of Lght Souce, Camea and Imaged Secton

38 FIGURE_6.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; Bghtness Membeshp Functon a b c Intensty FIGURE 6 Illustaton of the Bghtness of Gay-Scale Intenstes

39 FIGURE 7.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; FIGURE 7 Standad Ffteen-wedge Gayscale Taget (Edmund, 003)

40 FIGURE 8.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; FIGURE 8. 3-D Plot of Bghtness Vaaton wth Wavelength and MTD

41 FIGURE 9.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; P o fle H eg h t/m m Dstance/mm P o fle H eg h t/m m Dstance/mm FIGURE 9(a) Smooth pofle Heght Pofle/mm Dstance/mm 100% 98% 96% 94% FIGURE 9(c) Weang of a Selected Secton n Smooth pofle n Fgue 9(a) FIGURE 9(b) Rough pofle Heght Pofle/mm Dstance/mm 100% 98% 96% 94% FIGURE 9(d) Weang of a Selected Secton n Rough pofle n Fgue 9(b)

42 FIGURE 10.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; FIGURE 10(a) Synthetc Image fo the Ognal Pofle of Fgue 9(a) FIGURE 10(b) Synthetc Image fo the won pofle (wea 3) of Fgue 9(a) FIGURE 10(c) Synthetc Image fo the Ognal Pofle of Fgue 9(b) FIGURE 10(d) Synthetc Image fo the won pofle (wea 3) of Fgue 9(b)

43 FIGURE 11.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; weang smooth hash Bghtness weang MTD (mm) 7 FIGURE 11 Bghtness Vaaton of Smooth and Rough Pavement Sufaces due to Weang

44 FIGURE 1.pdf Jounal of Tanspotaton Engneeng. Submtted August, 009; accepted Septembe 1, 011; FIGURE 1(a) Ognal Image of the 50mm x 50 mm secton FIGURE 1(b) Image of secton n Fgue 1(a) afte weang Numbe of Pxels (Nomalzed) 0.06 Ognal secton Won secton Intensty FIGURE 1(c) Image hstogams fo ognal secton and won sectons shown n Fgues 1(a) and 1(b) FIGURE 1(d) Ognal pavement (bghtness = 0.310) FIGURE 1(e) Afte stage 1 weang (bghtness = ) FIGURE 1(f) Afte stage weang (bghtness = 0.385)