Research Article 3D Reconstruction of Tree-Crown Based on the UAV Aerial Images

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1 Mathematcal Problems n Engneerng Volume 2015, Artcle ID , 8 pages Research Artcle 3D Reconstructon of Tree-Crown Based on the UAV Aeral Images Chao Xu, 1 Zepng Lu, 1 Guangquan Xu, 2 Zhyong Feng, 2 Hongyan Tan, 3 and Hafeng Zhang 1,4 1 School of Computer Software, Tann Unversty, Tann , Chna 2 School of Computer Scence and Technology, Tann Unversty, Tann , Chna 3 Hgh Performance Network Lab, Insttute of Acoustcs, Chnese Academy of Scences, Beng , Chna 4 Space Star Technology Co., Ltd., Beng , Chna Correspondence should be addressed to Guangquan Xu; xuguangquan@tu.edu.cn Receved 11 June 2015; Accepted 21 July 2015 Academc Edtor: Krshnayan Thulasraman Copyrght 2015 Chao Xu et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. The algorthm for 3D reconstructon of tree-crown s presented wth the UAV aeral mages from a mountanous area n Chna. Consderng the fact that the aeral mages consst of lttle tree-crown texture and contour nformaton, a feature area extracton method s proposed based on watershed segmentaton, and the local area correlaton coeffcent s calculated to match the feature areas, n order to fully extract the characterstcs that can reflect the structure of tree-crown. Then, the depth of feature ponts s calculated usng the stereo vson theory. Fnally, the L-system theory s appled to construct the 3D model of tree. The experments are conducted wth the tree-crown mages from UAV aeral mages manually. The experment result showed that the method proposed n ths paper can fully extract and match the feature ponts of tree-crown that can reconstruct the 3D model of the tree-crown correctly. 1. Introducton In recent years, Unmanned Aeral Vehcle (UAV) magng has become the rreplaceable mappng tool. We can get multple magng from multangle and multposton durng a voyage of UAV[1]. Processng on the UAV sequental mages wth some related theores and technologes of 3D reconstructon, we can obtan the 3D models target on the ground. It s obvous that the heght, color, texture, and outlne nformaton of the tree-crown from the mages of hghalttudesfuzzy.andthetter,offset,androtaton of the arcraft can cause the moton and rotaton of the camera. Furthermore, wth the nfluence of many factors, the structure of the tree-crown has a lot of uncertanty, and t s dffcult to establsh emprcal knowledge [2]. All these reasons make t very mportant theoretcal gudance and practcal sgnfcance to reconstruct the 3D model of treecrown from UAV aeral sequental mages accurately. In ths paper, a tree-crown 3D reconstructon algorthm s proposed based on UAV aeral mages, and our feature pont extracton and matchng method are fully consdered the characterstcs of the aeral mages and the target to be reconstructon whch can provde reference value to the future research. The modelng approach takes nto account thestructuralcharacterstcsofthecanopy,andthefulluse of the exstng nformaton on more dffcult ssues as good canopy modelng s appled to acheve better results. A bref revew of relevant researches s presented n the second part. Then on the bass of the predecessors, the detals of the algorthm are descrbed n the thrd part, whle n the fourth part, the experments are demonstrated to valdate the algorthm and to make a concluson and dscusson. 2. Related Work In present, most researches of the 3D reconstructon are focused on the stereo vson prncple to process two or more mages from dfferent angles of the same target and to reconstruct the 3D shape of the target. Sun and Bergerson [3], Lu et al. [4], and Hapca et al. [5] proposedrelated

2 2 Mathematcal Problems n Engneerng reconstructon method and models of tree obect n ths dea. Wth ths dea n the 3D reconstructon of aeral mages, the tter and translaton of UAV can be consdered to mprove the whole model and results. Compared wth ther researches concernng the backbone and structure nformaton of tree, our research consdered the detaled nformaton of the treecrown contour and the nternal texture. Tan et al. [6] proposed a 3D tree reconstructon method to predct the obscured branches wth the vsble branches, and Tang et al. [7] proposed a 3D tree reconstructon method based on areas layered, so as to calculate the bologcal parameters of the tree. However, our method s concerned wth the branches and also the characterstcs of the outlne. Cheng et al. [8] provded us wth a good dea to determne the entre tree model wth the help of determnng the tree skeletons. There are many other researches on 3D tree reconstructon, such as [9 11], and ther work gves mportant constructve advce to our work. Our research s more concerned wth the unque features of the target tree-crown. Although most of the researches are concerned wth the backbone and structure nformaton of tree, we consder the detaled nformaton of the tree-crown contour and nternal texture. It s very mportant to extract and to match the feature ponts of the target for 3D reconstructon. In our model and method, process s desgned and conducted to fully extract the ponts that can reflect the structural characterstcs of the targetandtocorrectlymatchthefeaturepontswhchdrectly affect the accuracy of the fnal results of 3D reconstructon. Commonly used methods of correspondng ponts matchng can be classfed as feature-based and regon correlaton coeffcent based on matchng method [1]. SIFT and SURF are typcal matchng methods based on typcal features; for example, Hou et al. [12], Cobanu and Côrte-Real [13], and Bellava et al. [14] all used SIFT algorthm to extract feature ponts and to match them n 3D problems so as to acheve good results of the robustness and stablty. Such algorthms have good reslence, stablty and robustness for mage rotaton, zoomng, and other changes, but these algorthms can only extract lmted ponts when there are mages wth lmted texture nformaton. Many scholars extract and match feature ponts based on regon correlaton coeffcent; for nstance, We et al. [15] put forward a method based on regon correlaton coeffcent of gray mage to match the feature ponts. Regon-based correlaton method s performed well n accuracy, but the calculate tme s long. Further mprovement s conducted; for example, Yang [16], Mor and Kashno [17], and Zhang et al. [18] haveputforwardsomemprovementsontemplate matchng method based on normalzed correlaton coeffcent (NCC). These methods do not need complex preprocessngonmages,andtheyonlyusethegraystatstcs of mage tself [19]. Based on the analyssabove, we select the approprate feature extracton methods and effcent scannng methods to save up the tme consumpton. In addton, consderng the complex structure of the tree, 3D modelng approaches are commonly based on grd, snce the canopy structure characterstcs of aeral mages are lmted. L [20] and Shlyakhter et al. [21] used Lndenmayer system (L-system) to automatcally generate models of tree, whch was appled to buld complex models of trees n our proposed method. On the bass of the current researches, a tree-crown 3D reconstructon algorthm s proposed. Frstly, feature ponts are extracted based on the watershed to match features by calculatng the local area correlaton coeffcent (LACC) n the RGB color space; secondly, the depth nformaton s acheved based on the prncple of bnocular stereo vson; fnally, L-system s appled to the 3D modelng of the treecrown. 3. 3D Reconstructon Algorthm The flow of the proposed algorthm n ths paper s presented n Fgure 1, whch s dvded nto sx parts ncludng mage acquston, preprocessng, feature extracton and matchng, camera parameter estmaton, depth calculaton, and 3D modelng. To gnore the mpact from other parts for the 3D reconstructon, we ntercept the same sze of as the crown area of two successve aeral mages manually, and GrabCut and BgCut [22] algorthm are appled to remove the background from tree-crown, leavng only the crown area Feature Extracton and Matchng. Feature extracton and matchng s a crucal step n 3D reconstructon, and the accuracy of matchng feature ponts affects the fnal results drectly. Due to the complexty of UAV aeral mages, t s dffcult to match the feature ponts as the ncreased pont extractons. Basedontheanalyssonthetree-crownmagecutfrom the aeral mages, we found that UAV aeral mages contan scarce nformaton of a sngle tree relatvely, and the texture nformaton of a tree-crown s smlar, or nearly no texture, whle the same area of the two mage has great relevance. In response to these fndngs, a feature pont extracton and matchng method s desgned wth four parts as: feature extracton based on watershed; regon matchng based on LACC; elmnaton of the fault matchng; mean geometrc regstraton error Feature Extracton Based on Watershed. Snce the two mages were captured durng a short nterval, the llumnaton changes are small between the two mages. And n the tree-crown mages, area at the top of the trunk s relatvely brghtwhlethebottomareasrelatvelydark.soweuse the watershed segmentaton method to separate the lght and dark areas n order to further extract the feature ponts that reflect the trunk structure of the tree 3D reconstructon. Watershed segmentaton algorthm usually takes gradent mage as nput, whch can get the closed areas quckly. However, there s often oversegmentaton phenomenon [19]. In ths paper, the oversegmentaton of watershed segmentaton algorthm s ust sutable to our requrements of fully separatngthelghtanddarkareasofthetree-crown. The classc watershed segmentaton algorthm s proposed by Vncent and Solle [23], and the algorthm s

3 Mathematcal Problems n Engneerng 3 Image acquston Preprocessng Feature extracton and matchng Camera parameter calculaton Depth calculaton 3D modelng Fgure 1: The flow of 3D reconstructon. calculated through two steps: the frst one s the sortng process and the other one s the submergng process. Frst of all, the gray-level heght for each pxel s sorted from low to hgh. And then the process of submergng s acheved from low to hgh. For each local mnmum value n the nfluent doman of h-order heght, the frst n frst out (FIFO) structure s appled to archve the udgment and to complete the labelng process. The watershed algorthm transforms the nput mage to the basn mage. Then the boundary of the basn s the watershed. The gradent mage s calculated as the nput, and the gradent value s calculated as shown n (1); wheren, the f(x, y) s the orgnal mage, and the grad( ) s the gradent functon: The watershed segmentaton method used n ths paper s represented as follows: () Do gradent computaton on the longtudnal drecton wth the Sobel operator. And the horzontal and vertcal Sobel operator template are shown n (2), wheren A s the orgnal mage: G x = ( 2 0 2) A, G y =( ) A (2) () Smooth the gradent mage by makng openng and closng operatons as shown n open (src, element) = dlate (erode (src, element)), close (src, element) = erode (dlate (src, element)). () Segment the smoothed mages usng the watershed segmentaton algorthm as shown n (3) g(x,y)=max (grad (f (x, y)), g θ ). (4) Regon Matchng Based on LACC. As mentoned above, the regon matchng can be acheved based on the LACC values whch can be calculated n the RGB color space; please see Fgure 2. The LACC n the RGB color space s calculated n c =Rc +Gc +Bc, (5) g(x,y)=grad (f (x, y)) = [f (x, y) f (x 1,y)] 2 +[f(x,y) f(x,y 1)] 2. (1) wheren, Rc, Gc,andBc represent the three components R, G, andb, respectvely.andwecalculatethemn(6) wth R as an example: Rc = wn k= wn wm k= wm [R 1 (u (I) +k,v (I) R (u, V) = 1 n wn k= wn wm k= wm R 1 (u+k,v +l), +l) R 1 (u (I), V (I) )] [R 2 (u (II) +k,v (II) n δ 2 (R 1) δ 2 (R 2) +l) R 2 (u (II), V (II) )], (6) wheren, R 1 (u (I), V (I) ) and R 2 (u (II), V (II) ) represent the value of R from two mages, whle wn and wm represent the half wdthandthehalflengthofthesldngwndow.andwetake the sze of the rectangle crcumscrbed for the watershed area as the sze of the sldng wndow. R(u, V) represents the mean value of R for all the pxels n the sldng wndow, whch can be represented for the standard devaton wthn a sldng wndow as shown n δ (R) = 1 n wn k= wn wm k= wm (R 2 (u+k,v +l) R 2 (u, V)). (7)

4 4 Mathematcal Problems n Engneerng Watershed regon Scan area H u 1 u 1 u 1 d x Image 1 Image 2 Image 1 Image 2 H 1 Fgure 3: The prncple of mean geometrc regstraton error. d x Fgure 2: Regon matchng based on LACC. The values of Rc, Gc,andBc are ranged n ( 1, 1). If the current areas n the sldng wndows from the two mages are matched, the value correlaton coeffcent s closed to 1. The ultmate target of ths procedure s to get the matched feature ponts for the two mages. In ths paper, we calculate the centrod values of the matched areas as the matchng ponts, and ther coordnates are calculated n u = 1 n u n k, k=0 V = 1 n V n k. k=0 In order to reduce the tme consumpton, the mage dsparty constrants of two mages are taken nto account to restrct the searchng area. Durng the matchng process, the sldng wndow s moved only n ths area, not n the whole mage area Elmnate the Fault Matchng. In the matchng procedure, only the local nformaton of the area s consdered. So we get the correct matchng areas of the two mages as well as some fault matched areas. In order to mprove the results, we need to elmnate the fault matchng results. In ths paper, we calculate the rato of the bggest correlaton coeffcent value and the second coeffcent value to elmnate the fault matchng. Accordng to paper [24], we fnd that the fault matchng areas have many other matched areas wth the smlar correlaton coeffcent value. And then the rato value wll be bgger than the correct matched ones. So wesetathresholdasacrterontoelmnatethematchng process whch has a rato value hgher than the threshold MeanGeometrcRegstratonError. Ponts from the two mages can have a mappng relaton as n X 2 =HX 1, (9) wheren H s the homograph matrx of the two mages and X 1 and X 2 represent the ponts from the two mages. We calculate the mean geometrc regstraton error accordng to the prncple of homograph as shown n Fgure 3 and En = 1 2n (dst (x,hx )+dst (x,h 1 x )), (10) n (8) wheren, dst( ) represents the dstance between the two ponts x and x. Thus,fthepontsarematchedcorrectly,thedstance between d and d wll be small, and t wll result n a small En. In other words, the value of En decreases when the veracty of the matchng ncreases Depth Calculaton. In ths paper, the whole camera model s appled. Assume there s a 3D pont X=(X,Y,Z) T n ths proecton model, and the correspondent pont x = (x, y) T s n the mage; the two ponts X and x have the relatonshp as shown n x = 1 λ P X = 1 λ K (R t) X, (11) where x and X represent the homogeneous coordnates of x and X; λ s the scale factor between the two sdes of the homogeneous vector equaton, also called the proectve depth; K s the ntrnsc parameter matrx; and R s the rotaton matrx and t s the translaton matrx. We calculate the proecton equaton of the two treecrown mages n (12); andtheequatonssolvedtogetthe world coordnates of the pont n (13): λ 1 (u 1, V 1, 1) T =K(R 1 t 1 )(X W,Y W,Z W, 1) T λ 2 (u 2, V 2, 1) T =K(R 2 t 2 )(X W,Y W,Z W, 1) T, X W = f VT y (u 1 u 0 ) f u (V 1 V 2 ) Y W = T y (V 1 V 0 ) V 1 V 2 Z W = f VT y V 1 V 2. The camera ntrnsc parameter s the matrx f u 0 u 0 (12) (13) K=( 0 f V V 0 ), (14) 0 0 1

5 Mathematcal Problems n Engneerng 5 whch gnores the small rotaton of the camera. Thus, we have the rotaton matrx as R 1 =R 2 =( 0 1 0). (15) U + \ / H We assume that the translaton vectors are of mage 1 T 1 = (0 0 0) and mage 2 T 1 = (T x T y 0). Therearesome methods to estmate the parameters of the camera. Wth these known parameters, we can get the 3D coordnates of the feature ponts D Modelng. L-system s proposed by bologst Lndenmayer [25]. L-system can be later developed ntoan effectve computer graphcs smulaton of nature scenery, and t s a language promptng system whch controls parameters of certan symbols and words. L-system s rght-hand Cartesan coordnate system s defned n Fgure 4,whchscomposed of three drectons defned by three vectors as H, L, and U [17]. Commonly used commands of L-system nclude 3D postonng commands, specal postonng commands, moble commands, structure commands, and ncreasng or decreasng commands. Afterthe3Dpontsareconfguredthroughthemethod descrbed above, we apply a specfc method to get the trunk nformaton of the tree-crown accordng to the ponts, and then we use L-system command to construct the trunk structure and further the whole tree wth leaves. Accordng to Fgure 5, the method we used to get the trunk structure s descrbed as follows: () Fnd the hghest pont and the lowest pont n the Z coordnate and get the dfference dz as the tree heght. () Select the hghest pont on the vertcal axs as the center trunk of the tree, and set ts depth as 1. Add the trunkto TrunkLst collecton, and add the hghest pont to trunk ponts set IncludePonts. () Scan the feature ponts whch are not n the collecton IncludePonts to fnd the pont wth a mnmum dstance to the trunks n the collecton TrunkLst,and add the pont nto the collecton IncludePonts. (v) Create a new trunk from the new pont to ts nearest trunk wth 30 degrees. The depth of the new trunk plusone(themaxmumdepthofthetreesrestrcted to less than 4), and add the new trunk nto the collecton TrunkLst. (v) Go back to Step () untl all the ponts are ncluded n the collecton IncludePonts. 4. Experment Basedontheabovealgorthm,twosuccessvemagesare obtaned durng a voyage of UAV, whch s manually cut for thetree-crownmagewth thesamesze as as shown n Fgure 6(a). L & Fgure 4: The coordnate system of L-system. Start Fnd the hghest pont p1 and lowest pont p2 n Z coordnate Get the dfference between p1 and p2 dz as tree heght. Add frst trunk from p1 to p2 to set TrunkLst and ponts to IncludePonts Fnd the nearest pont p to the trunks n TrunkLst set, and add p to IncludePonts Are there ponts whch are not n IncludePonts set? No End Yes Fgure 5: The constructon process of the trunk structure. In order to avod the mpact of nose outsde the canopy regon, we use BgCut [22] algorthm to remove mage background, as shown n Fgure 6(b). For the next step, the lght areas and dark areas of the tree-crown are separated on mage 1 wth the watershed segmentaton algorthm. After obtanng the lght and dark areasofthetree-crown,thenumbersofpxelsofeacharea are recorded, and the centrod of the areas s calculated as the feature ponts of mage 1. In Fgure 7, we can extract more brght ponts and dark ponts for the tree-crown, whch can reflect the trunk structure of the tree.

6 6 Mathematcal Problems n Engneerng (a) (b) Fgure 6: The two tree-crown mages (a) wth wackground; (b) wthout background. Table 1: Mean geometrc regstraton error. Method En N Ponts SIFT-KNN [24] Our method wth (K 1) Our method wth (K 0.8) Our method wth (K 0.6) Our method wth (K 0.4) Fgure 7: The result of watershed on tree mage 1 and the center of the watershed areas. Fgure 8: The matched ponts on the two mages. Image 1 s separated nto 47 areas wth 47 feature ponts. Thenthelocalareacorrelatoncoeffcentscalculatednthe RGBcolorspacesoastofndthematchedareafrommage2. The rough matchng result s shown n Fgure 8. The ponts of mage 2 are roughly matched wth ponts of mage 1 ncludng some fault matchng nevtably. So we set dfferent thresholds descrbed n Secton 3 to fnd proper results to reconstruct the tree model. The average geometrc regstraton errors are calculated between the matched ponts, and the results are shown n Table 1. Wecanseefromthetable, comparedwththemethod proposed n paper [24], that the method we proposed can pck more feature ponts whch are enough to construct the tree model, and these ponts can be matched more accurately. To take the approprate threshold value K,a better reconstructon result can be acheved. The trunk structure nformaton of the tree-crown s calculated accordng to the method descrbed n the above secton, and the feature pont set and the correspondence trunk structure of the tree wth dfferent threshold values are shown n Fgure 9. As seen from the results n Fgure 9,fthethresholdvalue s taken too large, there are stll some false matchng ponts, then the remanng error wll affect the 3D modelng results, and f the threshold value s taken too small, there are some correct matchng ponts whch are removed, whch results n the loss of nformaton. So we use the threshold of 0.91, and the result s shown n Fgure 10.Fnally,theleavesofthe skeleton model can be reconstructed for the 3D model of the target tree. 5. Concluson UAV magng has great practcal sgnfcance n forestry and land plannng. However, two-dmensonal mages lack the necessary depth nformaton, whch wll be a lmtaton of the UAV aeral applcatons. In ths paper, 3D reconstructon of vson technology s proposed to obtan the depth nformaton from the 2D mages of the obect wth great advantages. The 3D reconstructon based on UAV aeral mage can be used n many practcal applcatons. In ths paper, feature extracton and matchng methods are proposed based on watershed segmentaton algorthm, and local area correlaton coeffcent s ntroduced n the RGB color space, whch can fully extract the feature ponts ofthemagessoastoreflectthestructureofthetargettreecrown. And reconstructon of the 3D model of the treecrown s desgned based on the prncple of stereoscopc vson from the lmted nformaton of the aeral mages. In theproposedmethodnthspaper,wemakeanefforttothe camera magng model of UAV. The method can apply to

7 Mathematcal Problems n Engneerng 7 (a) Threshold 0.93 (b) Threshold 0.92 (c) Threshold 0.91 (d) Threshold 0.90 Fgure 9: The result wth dfferent threshold; (a) wth threshold as 0.93, 28 feature ponts are selected, and the result s poor because of the remanng dsturbance; (b) wth the threshold as 0.92, 27 feature ponts are selected, and t has a smlar result as 0.93; (c) wth the threshold as 0.91, 23 feature ponts are selected, and the result has an effectve mprovement; (d) wth the threshold as 0.90, only one feature pont s lost aganst the result as the case of aeral mages taken wthn a small nterval, and the 3D reconstructon method has applcablty for tree-crown. Conflct of Interests (a) Fgure 10: 3D model of the target tree. (a) The sde vew of the tree model; (b) the top vew of the 3D tree model; (c) the orgnal treecrown mage. (b) (c) The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgment ThsworkspartallysupportedbyNatonalNaturalScence Foundaton of Chna (no ). References [1] L.-C. L, Reconstructon of Terran Based on Unmanned Aeral Vehcle Sequental Images and Its Applcaton n the Navgaton Research, Natonal Unversty of Defense Technology, Changsha, Chna, 2009.

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9 Advances n Operatons Research Advances n Decson Scences Appled Mathematcs Algebra Probablty and Statstcs The Scentfc World Journal Internatonal Dfferental Equatons Submt your manuscrpts at Internatonal Advances n Combnatorcs Mathematcal Physcs Complex Analyss Internatonal Mathematcs and Mathematcal Scences Mathematcal Problems n Engneerng Mathematcs Dscrete Mathematcs Dscrete Dynamcs n Nature and Socety Functon Spaces Abstract and Appled Analyss Internatonal Stochastc Analyss Optmzaton