Measurements of Rainfall Rates From Videos

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1 Measuements of Ranfall Rates Fom Vdeos Dong, R., Lao, J., L, B., Zhou, H., & Cookes, D. (07). Measuements of Ranfall Rates Fom Vdeos. In 0th Intenatonal Congess on Image and Sgnal Pocessng, BoMedcal Engneeng and Infomatcs (CISP-BMEI 07): Poceedngs IEEE. Publshed n: 0th Intenatonal Congess on Image and Sgnal Pocessng, BoMedcal Engneeng and Infomatcs (CISP- BMEI 07): Poceedngs Document Veson: Pee evewed veson Queen's Unvesty Belfast - Reseach Potal: Lnk to publcaton ecod n Queen's Unvesty Belfast Reseach Potal Publshe ghts 07 IEEE. Ths wok s made avalable onlne n accodance wth the publshe s polces. Please efe to any applcable tems of use of the publshe. Geneal ghts Copyght fo the publcatons made accessble va the Queen's Unvesty Belfast Reseach Potal s etaned by the autho(s) and / o othe copyght ownes and t s a condton of accessng these publcatons that uses ecognse and abde by the legal equements assocated wth these ghts. Take down polcy The Reseach Potal s Queen's nsttutonal epostoy that povdes access to Queen's eseach output. Evey effot has been made to ensue that content n the Reseach Potal does not nfnge any peson's ghts, o applcable UK laws. If you dscove content n the Reseach Potal that you beleve beaches copyght o volates any law, please contact openaccess@qub.ac.uk. Download date:03. Ap. 09

2 Measuements of Ranfall Rates Fom Vdeos Rong Dong, Juan Lao, Bo L, Huyu Zhou 3, Danny Cookes 3 School of Electoncs and Infomaton, Nantong Unvesty, Nantong, Chna School of Electonc Scence and Engneeng, Nanjng Unvesty, Nanjng, Chna 3 School of Electoncs, Electcal Engneeng and Compute Scence, Queen s Unvesty Belfast, Belfast, Unted Kngdom Abstact Measung anfall ates fom vdeos s a novel eseach topc. Due to an moton, eflecton of lght and backgound clutte, t s extemely challengng to obtan accuate measuements. In ths pape, we popose a new technque fo measung anfall ates fom vdeos, whch conssts of the followng techncal steps: fst, we detect andops n an mage usng gay-tone functons and decton of an steaks; we then select the focused andops, based on two featues: aveage colo tenso esponse and aveage ntensty dffeence. Aftewads, the sze of the andops s estmated and a andop sze dstbuton (RSD) cuve s ceated accodng to the use of the RSD n meteoology. Fnally, a anfall ate s obtaned by fttng the RSD cuve wth a Gamma dstbuton model. In the expement secton pesented n ths pape, the poposed algothm s evaluated unde dffeent lght, modeate and heavy any condtons. The measuement esults of the poposed algothm ae consstent wth those of a can-type an gauge. Keywods- colo tenso; logathmc mage pocessng; an detecton; anfall ate; andop sze dstbuton I. INTRODUCTION Measuement of anfall ates ae vey mpotant fo clmate analytcs, wate esouces utlzaton and flood dsaste peventon. Many types of nstuments o methods fo anfall ates measung ae avalable nowadays. Geneally, they can be dvded nto manual, mechancal, mcowave-based and optcal categoes. The wdely used cantype an gauge s a manual and conventonal pluvomete. Though t s vey smple and non-automatc, t has been and stll used at many meteoologcal statons n the wold. In the mechancal categoy, tppng-bucket an gauge o electomechancal nstuments [][] s commonly used. In the mcowave-based categoy, weathe ada s wdely used to estmate pecptaton [3-6]. In the optcal categoy, lase systems o cameas ae used. Lase-based systems [7-9] measued an ates by detectng the coheence degadaton of a lase beam caused by popagatng though an. The best known camea-based an gauge system s the D-Vdeo- Dstomete (DVD) whch uses two hgh speed lne scan cameas and backgound llumnaton [0][]. Besdes the lne scan cameas, matx cameas have also been used n the measuement of meteoologcal paametes [-5]. All of those camea-based system eque a specalzed llumnaton component. As an altenatve to the above methods, n ths pape we popose to measue anfall ates fom CCTV cameas. As CCTV cameas become moe and moe popula, such a anfall measuement method s an economc and easly mantanable technque wth hgh tempoal esoluton. In spte of ts pomse, howeve, as a Vdeo Based Measuement (VBM) [6], vdeo based anfall ate measuement technques had to deal wth two majo poblems: () Image analyss: to accuately detect andops fom vdeos and () Measuement: to establsh a coect elatonshp between the quanttes of the detected an pxels and the coespondng an ates. To handle the fst poblem, we take advantage of a an detecton algothm. Randops have complcated effects on mages. To date, many eseach studes have been conducted n ode to solve ths challengng poblem, e.g. [7-6]. All of them detect andops use athmetc opeatons fo eal numbes. In ths pape, we popose to detect andops n a Logathmc Image Pocessng (LIP) famewok. In tems of the second poblem, we need to know the actual sze of a an steak detected on the mage n ode to calculate anfall ates. Unfotunately, the 3D depth of a an steak s had to obtan and consequently the eal sze of the coespondng andop cannot be computed wthout ths depth nfomaton. One of the solutons s to popely adjust the paametes of the used camea so that all the focused an steaks ae nealy at the same depth (.e. at the poston of the known focal plane). Aftewads, the sze of the e-focused an steaks can be calculated usng an affne tansfomaton based appoach. To acheve ths taget, focused and defocused andops must be dscmnated appopately befoehand. In the lteatue, thee s vey lttle eseach wok on ths dscmnaton poblem. Saylo and Svasubamanan [4] used the exstence of a bght hole n the cente of a andop to judge whethe the dop s n focus o not; howeve, the system needs a specalzed lght souce to llumnate andops whch s usually mpossble when usng CCTV cameas. Gag and Naya [7] attempted to solve ths poblem usng the velocty-sze elatonshp of andops. Howeve, ths method does not always wok because the wdth of a an steak n the mage appeas to be vey small and the estmaton can be seveely nfluenced by mage nose and backgound clutte. In ths pape, the photometc dffeence between focused and defocused andops s studed n-depth and a new algothm s developed usng aveage colo tenso esponse and aveage ntensty dffeence of andops fo dentfcaton of dffeent andops. The pape s oganzed as follows. In Secton, the poposed algothm s pesented. In Secton 3, a an detecton method usng gay-tone functons and the constant of anfall decton s ntoduced. In Secton 4, the photometc dffeence between the focused and defocused andops s exploed, whee featues ae used fo dscmnatng these andops. In Secton 5, we fstly dscuss how to geneate a Ths wok was suppoted by the Natonal Natual Scence Foundaton of Chna (No ), Poject of Industy and School and Reseach Insttuton of Jangsu Povnce (No.BY ), Key Suppot Poject of Natonal Natual Scence Jont Foundaton of Chna (No. U637). The coespondng autho s Rong Dong, dwstaa@63.com

3 RSD cuve fom the measuements, and then pesent a method fo measung an ates fom the ftted RSD cuve. Expemental esults ae shown n Secton 6 and conclusons ae dawn n Secton 7. II. DETECTION OF RAINDROPS It has been known that andops may efact lght fom the ambent envonment, and theefoe a andop tends to be much bghte than the backgound that t occludes [8]. On the othe hand, the speed of andops s so fast that usually a andop does not occupy the same mage aea n two consecutve mage fames. Fg. llustates the ntensty changes of a pxel n a an vdeo, whch s tempoally flutteng. Based on the above obsevaton, canddate andops n the mage can be selected usng the ules below: I I > I & I I > I () t t t t + th th whee I t-,i t, andi t+ ae ntensty values at the same pxel of thee consecutve mage fames. Ths method does not wok well as t has a congental defect due to the athmetc opeatons fo eal numbes [8]. In ou appoach, the gay tone functons n the LIP famewok ae used to detect canddate andops. A. Gay Tone functons LIP was ntoduced by [9, 30] as a famewok fo epesentaton and pocessng of ntensty mages wth values bounded n a cetan ange. The LIP theoy was consstent wth human bghtness pecepton. Ths theoy has been used n seveal mage pocessng aeas such as edge detecton, mage segmentaton, and mage enhancement [3, 3]. In the LIP famewok, an ntensty mage s epesented by ts assocated gay-tone functon G(x,y), whch s elated to the ncdent lght ntensty functon I(x,y) by Eq. (). λ ΔI Fg.. Dagam of poposed algothm Fg.. Intensty changes of a pxel n a an vdeo acqued by a statonay camea. I( xy, ) Gxy (, ) = M( ) () Imax I max s the satuatng ntensty level n the human vsual system. M s the uppe bound of gay-tones. Image pocessng opeatons such as addton, subtacton and opposte n the LIP famewok ae defned n a new style. Addton of two gay tone functons G (x,y) and G (x,y) s denoted by Eq. (3). G( x, y) G( x, y) G( x, y) G( x, y) (3) = G( x, y) + G( x, y) M It s wtnessed that fo any two gay-tones n the ange [0, M), the esult of the addton s stll a gay tone n the ange [0, M). Ths s dffeent fom the addton opeaton of ntensty values. The opposte (Eq. (4)), subtacton (Eq. (5)) and modulus (Eq. (6)) of the gay-tone functons ae espectvely defned as: G(x, y) Θ G( x, y)=-m (4) M -G(x,y) G( x, y)- G( x, y) G( x, y) Θ G( x, y)= M (5) MG - ( xy, ) G( x,y); f G( x,y) 0 Gx,y ( ) = E (6) Θ Gx,y ( ); f Gx,y ( ) < 0 The subscpt E epesents the gay-tone space. Snce the gay tone functon coesponds to the ntensty functon n an nveted scale, an canddates ae selected usng Eqs. (7) and (8): t t t t+ G < G & G < G (7) G Θ G > G & G Θ G > G (8) t t t t + E th E G t-, G t and G t+ ae the gay-tone functons of thee consecutve fames. th

4 Compaed wth the use of mage ntensty, the advantage of usng gay-tone s shown n Fg. 3. It s obvous that the esults of usng gay-tone (Fg. 3(b)) shows cleae an steaks than that of usng nomal ntensty (Fg. 3(c)). Ths s because the opeaton of usng gay-tone s nonlnea and elevant to the gay tone tself, whle the ntensty subtacton s to handle all the ntensty values lnealy and equally. (a) (b) (c) Fg. 3. Dffeent esults of an canddate detecton usng the LIP model and usng the nomal ntensty. (a) Cuent any fame. (b) Subtacton of cuent fame and next fame n the LIP famewok; only pxels whch satsfy (7) ae shown. (c) Result of the same opeaton but usng the coespondng ntensty nstead of gay tone. M s set to be equal to Imax = 55 n ode to opeate and dsplay n the same scope. B. Constant of Decton Ran steaks usually have the same decton as the wnd. The constant of decton may help us emove nose. Fndng the tlt angle of a an steak s equvalent to fndng the decton that maxmzes the vaance of the steak, whch can be egaded as the fst pncpal component decton, as n Fg. 4. Fg. 4. Pncple component dectons of a an steak Let N epesent the numbe of the mage pxels fo a andop. X denotes the N * matx composed of N pxel coodnates elatve to the cente of the steak. Assume u = [u x, u y ] T, u =[u x, u y ] T ae egenvectos that espectvely coespond to egenvalues λ, λ (λ >λ ) of the covaance matx X T X, whee u s the fst pncpal component decton, and the tlt angle can be calculated as follows: u y θ =tan ( ) (9) u x On the othe hand, the vaances along the two pncpal component dectons can be used to epesent the length a and beadth b of the steak: ( λ ) ( λ ) a = s, b = s (0) N N whee s s a systematc constant. Consdeng that the estmaton of ndvdual andop dectons may be dstubed by nose, a dstbuton of dectons f(θ) s constucted as follows: N x θ θ f ( θ) = C0 k( ), k( x) = e () π h h whee C 0 s a nomalzaton coeffcent. h s used to descbe the uncetan degee of θ. Consde that the tlt angle s uncetan f the andop s length and beadth ae close to each othe, h s defned as: b h = C + B () a whee C s a scale facto to adjust the aspect ato. B epesents a basc bandwdth used n the kenel functon. Notce that Eq. () can be vewed as a one-dmenson kenel densty functon. The Mean-shft method [33] s an effectve method to detemne ts local maxma. It s woth notng that bandwdth h changes wth, so the deved Meanshft vecto m(θ) s slghtly dffeent fom the style shown n [33]: N θ θ f( θ) = C0 ( θ ) ( ) 3 θ g π h h N θ θ = C0 g( ) m( θ ) 3 π h h N θ θ θ ( ) 3 g π h h ' ( θ) = θ ( ) = ( ) N θ θ ( ) 3 g π h h (3) m, g x k x (4) The local maxma θ man can be estmated as follows: Step: Set an ntal θ 0 ; Step: Let θ =m(θ 0)+ θ 0; Step3: If θ -θ 0 <ε, stop and etun θ man=θ ; else let θ 0=θ and then go to step. Gven a local maxma θ man of the dstbuton, whch s the most pobable anfall decton n the mage, the pxel wth an oentaton devaton fom θ man of a theshold lage than θ th s consdeed as nose and should be ejected: θ θ > θ (5) j man th II. DISCRIMINATION OF FOCUSED AND DEFOCUSED RAINDROPS The andops detected by the famewok descbed above may contan both focused and defocused andops. In ode to elmnate the defocused andops, futhe pocessng s appled. Consdeng a vsble pont P n the scene, f t s not n focus, ts coespondng mage appeas to be a blued ccle. Accodng to geometc optcs, the blued mage of pont P s actually elated to the pont spead functon of the camea system, and the obseved mage s the esult of convolvng the focused mage wth the camea s pont spead functon [34]. A smple spead functon s:

5 4 f x + y d /4 c hxy (, ) = π dc (6) 0 othewse whee d c s the damete of the blued ccle. It has been shown that the ntensty values of a an steak depend on the bghtness of the statonay andop as well as the backgound s adance and the ntegaton tme of the used camea [8]: τ T I ( x, y) = E ( ) ( ) 0 x,y dt+ Eb x,y dt (7) τ whee τ s the tme when the mage pxel s occluded by a andop. T s the exposue tme of the camea. E s the adance due to the andop tself and E b s the adance due to the backgound. If the andop s not n focus, the adance that the mage plane eceves due to the andop s descbed by: ' E ( x, y) = E ( x, y)* h( x, y) = E ( x u, y v) h( u, v) dudv = E ( x u, y v) dudv π d c u + v dc /4 S = E ( x, y) S d (8) whee S s the aea of the ovelapped egon of the andop and the coespondng aea of the used pont spead functon. S d = π dc /4 s the aea of the pont spead functon. The convoluton pocess shown n Eq. (8) s llustated n Fg. 5. Note that E (x,y) deceases as d c nceases. If a andop s futhe away fom the focus plane, d c s lage and E (x,y) s lowe. When d c s lage enough, we have S < S d. Then: E ' ( xy, ) < E( xy, ) (9) In Eq. (7), E b and E ae assumed to be constant ove the ente exposue tme T. Theefoe I ( xy, ) = τe( xy, ) + ( T τ) E( xy, ) (0) b Consdeng the defocus effect, Eq. (0) can be modfed to be: I (, xy) = τe(, xy) + ( T τ) E(, xy) () ' ' b τ τ τ Fg. 6. Compason of colo vectos of focused and defocused andops Eqs. (0) and () can be extended to an applcaton n the colo space as shown n Fg. 6, whee I efes to R (I, I G, I B ), and E stands fo R (E, E G, E B ). In Fg. 6, two pncples can be appled to help dscmnate the focused and defocused andops: ) The focused andops have hghe E than the defocused ones. Howeve, t s dffcult to calculate the value of E because tme τ s unknown. Note that n Eq. (), τ s vey small, and E >> E b, so τe b can be gnoed. Theefoe, a hgh E also ndcates a hgh ntensty dffeence ΔI(x,y) =I (x,y) - I b(x,y)= I (x,y) - TE b(x,y)= τe. Accodng to [7], backgound ntensty I b(x,y) can be estoed usng two consecutve fames, and theefoe ΔI can be estmated by: t t+ t- ΔI=I ( I +I )/ () Fg. 5. Illustaton of the convoluton pocess of a defocused andop. When dc s lage, the aea Sd of the pont spead functon s bgge than the ovelap aea S, so the convoluton pocess educes the adance E(x,y) To make the featue moe obust, Δ I, whch s the aveage ΔI of a andop, s used as the fst featue that allows the focused and defocused andops to be dscmnated. ) The colo vecto dstance between the defocused andop and ts backgound s smalle than that between the focused andop and ts backgound. The edge of the focused andop n colo space s shape than that of the defocused one. In ode to descbe the ntensty of an edge n colo space, we use a colo tenso [35]. Assumng a colo mage I = (I R, I G, I B ), we have a colo tenso defned as: x x x y F I I I I = Iy Ix Iy Iy (3)

6 whee the symbol ndcates the convoluton of the colo mage wth a Gaussan flte, and the subscpt x o y ndcates the spatal devatve along the x o y axs. The lagest egenvalue λ of F epesents the devatve enegy n the most pomnent decton whch s used to descbe the magntude of an edge n the colo space. Fg. 7(c) shows the λ esponse of the mage shown n Fg. 7(a) (λ s calculated only at the egon of the detected andops shown n Fg. 7(b)). It s notced that the esponse of the focused andop s geate than that of the defocused one. To make the featue moe obust, λ, whch s the aveage λ esponse aound the bounday of the andop, s used as the second featue that enables the focused and defocused andops to be sepaated. Fg. 8 shows the dstbuton of Δ I and λ obtaned fom 5 consecutve mages of a any scene. The blue astesks epesent the defocused andops and the ed ones epesent the focused ones. The focused andops ae chosen manually. It s obseved that the focused andops le manly n the fst quadant of the geen coodnate system, ndcatng that the two paametes Δ I and λ can be used to dscmnate the focused and the defocused an steaks popely. Theefoe, fo evey detected andop, ΔI and λ ae calculated and then used to detemne whethe the andop s n focus o not. In othe wods, f both of the two paametes ae hghe than a cetan theshold, ths andop s classfed as a focused one. (a) (b) (c) Fg. 7: Detected an dops n a fame and the λ esponse: (a) Cuent Fame. (b) Detected andops. (c) λ esponse of the cuent fame. concentaton N(d) [m 3 mm ], also called RSD, whee d [mm] s the equvalent sphecal damete of a andop. Once a focused an steak n the mage has been detected, ts length a s calculated usng a method of geometc moments pesented n [36]. Consdeng a an steak wth depth z and length a, and usng an affne tansfomaton, we have: z T v( d) = f a (4) whee T s the tme of exposue. The elatonshp between the damete of a andop and ts temnal speed (m/s) s [37]: 0.67 = d (5) vd ( ) The damete d can be calculated by: za d = ft 0.67 (6) Accodng to the defnton of RSD, N(d) s obtaned by fstly countng the numbe of andops whch have dametes fallng n the ange [d-/δd, d+/δd], whee Δd s the unt scale nteval (mm). Then we dvde ths statstcal esult by the space volume V, whch s appoxmated by the poduct of the depth of feld and the wdth and heght of the scene captued at the focal plane. In ode to obtan a coect esult, the countng pocess s mplemented ove multple consecutve fames. In meteoologcal scence, thee ae seveal well-known RSD models, such as Exponental dstbuton, Gamma dstbuton and M-P dstbuton [38]. It has been shown that Gamma dstbuton can poduce good pefomance fo dffeent knds of pecptaton and s hence wdely used [39]. In ths pape, we use a Gamma dstbuton model to ft the RSD cuve obtaned and then calculate anfall ates fom the model. The Gamma dstbuton s defned as: ( ) 0 N d = N d e μ ω d (7) whee N 0, μ and ω ae thee paametes whch can be solved by a moment method [40]. The th ode moment of the RSD s defned as: Fg. 8. Dstbuton of Δ I and λ obtaned fom 5 consecutve mages of a any scene. The blue astesks epesent defocused andops and the ed ones epesent focused ones. Focused andops le manly n the fst quadant of the geen coodnate system. Theefoe, focused and defocused an steaks can be dscmnated usng the popely defned Δ I and λ. III. MEASUREMENT OF RAINFALL RATES The numbe and the sze of andops wthn a unt volume and a unt scale nteval can be descbed by the numbe M = dnddd ( ) (8) 0 Substtutng N(d) nto Eq. (8) wth the Gamma dstbuton n (7), then we have: M ( ) = N Γ + μ + μ 0 ω + + N 0, μ and ω ae espectvely calculated by: (9)

7 ( + 4) 3M M 4M μ M ω μ M μ = ( M ) , ω=, N 0 = 3 M4M M 4 Γ ( μ + 4) (30) Accodng to [37], fnally, a anfall ate s gven by: 6 3 ( 4.67) R= π Γ μ+ N( d) v( d) d dd=0.007n0 μ (3) ω 0 IV. EXPERIMENT RESULTS The poposed algothm was tested on vaous any days wth lght, mddle o heavy an at Nanjng Cty n Chna. Ranfall ates calculated wee compaed aganst the gound - tuth data measued usng a can-type an gauge. The an gauge was used to collect anwate dung a cetan tme nteval and then the volume of an was conveted to the standad anfall ate values n mm/h. The vdeos wee taken by a SONY DSR-PD98P vdeo camea. A. Camea paametes adjustment In ode to get a good sze dstbuton cuve of a andop, the smallest andop should be able to be captued n the mage. To do so, the focal length and the focal plane of the camea must be adjusted popely. As shown n Fg. 9, the smallest andop should have occuped at least one pxel so as to be clealy vsble. Thus we have: z fd mn (3) In the expement, we obseve that the focused andops can be segmented bette as z becomes smalle. Ths s because f the focal plane s futhe away fom the camea, thee wll be moe defocused andops ovelappng the focused ones, whch make t moe dffcult to segment the focused andops fom the counte pats. In all the expements, we empcally set z = (m). When z s detemned, f has a lowe lmt accodng to Eq. (3). In fact, thee s also an uppe lmt fo f. The scene captued by the camea should be lage enough so that the lagest andop can be detected. Ths suggests that the heght of the mage should be lage than the length of the longest an steak. Suppose that d max s the damete of the lagest andop; then f must satsfy ths equaton: zh f T v( d ) (33) whee H s the heght of the mage, and v(d max) s calculated by Eq. (5). Usng the vaables detemned by Eqs. (3) and (33), we manually (o by emote contol) zoom n the camea vew when the an s lght, and zoom out when the an s heavy. Lage andops (e.g. the damete s geate than 5mm) appea n heavy an condtons, and small andops (e.g. the damete s smalle than 3mm) show up when an s lght. The apetue A of the camea s accodngly adjusted n ode fo us to obtan a small depth of feld. max Fg. 9. The smallest andop should be vsble n the mage. Ths means that the smallest andop occupes at least one mage pxel n the mage. B. Ran detecton and focused andops dentfcaton Typcal mages captued and the coespondng detecton esults ae shown n Fg. 0. The fst ow shows typcal mages coespondng to lght, modeate and heavy an stuatons espectvely. Notce that we manually zoom n the camea vew when the an s lght, and zoom out when the an s heavy, so the backgound sceney n a heavy an stuaton looks shape than that of lght an. Indvdual paamete settngs of these thee stuatons ae lsted n the next secton. Canddate andops detected usng gay-tone functons ae shown n the second ow. Randops can be detected coectly. Due to nose and backgound vaaton, a small amount of false detectons occus. Constucted dstbutons of anfall dectons fom the bnay mages of canddate andops ae shown n the thd ow. Usng the poposed mean-shft method, we detect the local maxma of the dstbuton functon θ man. The andop wth an oentaton devatng by moe than θ th fom θ man s consdeed as nose and wll be ejected. In all the expements, θ th s empcally set to be 0, whle the scale facto C and the basc bandwdth B ae espectvely set to be 30 and 5. The detected andops usng the constant of decton ae shown n the fouth ow. The algothm poposed n Secton 4 s used to futhe dscmnate the focused and defocused andops and fnally the focused andops ae shown n the ffth ow. At ths stage, two theshold values coespondng to aveage colo tenso esponse λ and aveage ntensty dffeence Δ I espectvely affect the fnal esult. Consdeng dffeent llumnaton condtons n dffeent any stuatons, the two theshold values ae taned n advance. We manually select the focused and defocused andops fom a secton of the tanng sequence and constuct a dstbuton map of Δ I and λ shown n Fg. 8, then detemne the theshold values. C. Ranfall ate measuement The measued N(d) and the ftted Gamma dstbuton model ae shown n Fg.. The countng pocess s mplemented usng 000 consecutve fames. Ths means that the system outputs an nstantaneous an ate evey 000 fames. Detaled paametes settngs ae shown n Table. The mean anfall ate s calculated by aveagng nstantaneous an ates dung a peod of tme (e.g. half an hou fo modeate an and the length of tme depends on the an stuaton at that day). It can be obseved that although thee ae mno dstubance, the measued RSD cuves unde

8 dffeent any condtons ae consstent wth those of the Gamma dstbutons. It s woth pontng out that unde heavy any condtons the densty of lage andops calculated usng ou appoach s hghe than the ftted Gamma dstbuton. Ths s manly because the occluson between two andop steaks becomes sevee when the an s heavy and the two shot steaks may jon togethe to fom a longe one, whch s dffcult to sepaate. In Table, we show that the calculated anfall ates also agee wth the ecods of the can-type pluvomete. The two esults ae not exactly the same because both methods have eos. The systematc eoes of the can-type pluvomete manly nclude: wettng loss caused by the wettng of the nne walls of both collecto and contane, wnd-caused loss because of wnd peventng small andops fom enteng the gauge and out-splashng loss caused by collson between andops and the nwall of the collecto. The total magntude of ts systematc eos may be up to 5% [4]. Besdes, eadng eo exsts because the can-type an gauge s a manual one. Most eos of can-type an gauge ae loss-type, that s maybe why the meansuement values by poposed algothm ae lage n modeate and heavy an stuatons. In the lght an stuaton, ou meansuement esult appeas to be lowe by contast wth the can-type. That s maybe because most an dops ae vey small n lght an so that the an steaks ae vey slende and the mage ntenstes ae low whch may cause moe steaks beak and mss detecton. Despte the mno dffeence, these esults show that ou algothm s capable of obtanng easonably coect anfall ates. TABLE PARAMETER SETTINGS AND MEASUREMENT RESULTS (d) (e) (f) (g) (h) () (j) (k) (l) (m) (n) (o) Fg. 0: Typcal mages captued and coespondng detecton esults. Fst ow: typcal mages coespondng to lght an, modeate an and heavy an stuatons espectvely. Second ow: canddate andops detected usng constants of gay tone. Thd ow: constucted dstbuton of oentatons. Fouth ow: andops detected afte constants of decton. Ffth ow: fnally dentfed focused andops. Weathe condton Lght an Modeate an Heavy an f A T[s] /5 /5 /5 z[m] Ranfall ate by pluvomete [mm/h] Mean Ranfall ate by pesented algothm [mm/h] (a) (a) (b) (c) (b)

9 (c) Fg. : Measued RSD cuve and ftted Gamma dstbuton unde dffeent any condtons: (a) lght an, (nstantaneous an ate.0 mm/h). (b) modeate an, (nstantaneous an ate 4.9 mm/h). (c) heavy an, (nstantaneous an ate.0 mm/h). CONCLUSIONS In ths pape, a method fo eal-tme anfall ate measuement has been pesented. The method we poposed s to count the focused andops n a small depth of feld and then ceate a RSD cuve. Aftewads, anfall ates can be estmated by fttng the cuve usng a Gamma dstbuton model. To acheve ths taget, accuate detecton of andops s the fst task, followed by the dscmnaton of focused and defocused andops. Detectng andops usng gay-tone functons demonstated the capablty to dentfy andops bette than usng mage ntenstes. The constant of decton helps to emove false detectons. It has shown that aveage colo tenso esponse and aveage ntensty dffeence of andops can be used to dscmnate the focused and defocused andops n the mages. 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