IMPROVING AND EXTENDING THE INFORMATION ON PRINCIPAL COMPONENT ANALYSIS FOR LOCAL NEIGHBORHOODS IN 3D POINT CLOUDS Davd Belton Cooperatve Research Centre for Spatal Informaton (CRC-SI) The Insttute for Geoscence Research (TIGeR) Department of Spatal Scences, Curtn Unversty of Technology Perth WA, Australa - d.belton@curtn.edu.au Commsson V, WG 3 KEY WORDS: Laser Scannng, Pont clouds, Curvature Approxmaton, Surface Normal Estmaton, Prncpal Component Analyss ABSTRACT: Prncpal Component Analyss (PCA) s often utlsed n pont cloud processng as provdes an effcent method to approxmate local pont propertes through the examnaton of the local neghbourhoods. Ths process does sometmes suffer from the assumpton that the neghbourhood contans only a sngle surface, when t may contan multple dscrete surface enttes, as well as relatng the propertes from PCA to real world attrbutes. Ths paper wll present two methods. The frst s a correcton method to flter out the presence of multple surfaces through an teratve process. The second s to combne the PCA preformed on the neghbourhood of pont coordnates and normal approxmatons n order to estmate the radus of curvature n the maxmum and mnmum curvature drectons.. INTORDUCTION Pont cloud processng reles on the analyss and examnaton of dfferent observed attrbutes such as poston, ntensty and colour. Although these attrbutes are sampled drectly from the laser scanner, attrbutes are more often derved from the examnaton of the local neghbourhood surroundng a pont of nterest. These estmated attrbutes, whch nclude curvature, surface normal and geometrc surface propertes, are of great mportance n pont cloud-processng procedures such as for surface classfcaton and segmentaton. Often these attrbutes are estmated wth the use of Prncpal Component Analyss (PCA) performed on the local neghbourhoods of ponts, as t effcently retreves the local propertes of a neghbourhood (Gumhold et al., 00). Some common uses have ncluded approxmatng the normal drecton (Mtra et al., 004), fttng frst order planar surfaces (Wengarten et al., 003), approxmatng surface curvature (Pauly et al., 00), defnng the tensors for tensor votng (Tong et al., 004) and provdng a local pont coordnate systems (Danels et al., 007). There are two problems that can occur when usng PCA. The frst s that a neghbourhood may contan multple dscrete surface enttes. For most attrbutes, they are calculated under the assumpton that there s only one surface structured. The affect of multple surfaces can cause bases n the attrbutes e.g. the surface normal approxmaton. Whle deceasng the sze of the neghbourhood may help n reducng the probablty that a neghbourhood contans more than one sampled surface, the neghbourhood needs to be of suffcent sze n order to reduce the effect of random errors and nose. The other problem s how to relate the PCA results to the surface attrbutes. Often nformaton can be lost, such as the approxmaton of curvature through surface varaton (Pauly et al., 00) where the comparable level of curvature s ndcated, but there s no drectonal component or unt of measurement assocated wth the approxmaton. It s the am of ths paper to present an teratve method of adjustng the neghbourhood to remove effects of multple surface enttes. In addton, a formula between the egenvalues of the PCA and the surface propertes such as the radus and drecton of local curvature wll be presented. From ths formula, the maxmum and mnmum curvature drectons can be also calculated n a closed form soluton and ths nformaton provdes a novel and detaled nformaton of the neghbourhood of the pont of nterest.. PRINCIPAL COMPONENT ANALYSIS PCA s performed by frst calculatng the covarance matrx Σ by the formula: Σ = ( x c0 )( = x c ) () T 0 where x s defned as the vector form of the poston of the th pont n the neghbourhood contanng the nearest ponts and c 0 represents the centrod of the neghbourhood calculated as the mean of the neghbourhood. Snce Σ s a symmetrc and postve sem-defnte matrx, t can be decompled by egenvalue decomposton such that the real postve egenvalues, λ 0, λ and λ, along wth the correspondng 477
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 egenvectors e 0, e and e form an orthogonal bass of the neghbourhood n R 3 (Golub and Loan, 989). respectvely. An nternal relatonshp of x to x 0 wll be equvalent to an external relatonshp of x 0 to x. The covarance matrx Σ can be decomposed as follows: Σ = = 0 λ T ee () where λ 0 λ λ. Note that egenvectors e represent the prncpal components, wth the correspondng egenvalues λ denotng the sgnfcance of each component n the form of the varance n these drectons (Golub and Loan, 989). For a local neghbourhood of a pont cloud, e 0 approxmates the the local surface normal, wth e and e approxmatng the tangental plane through c 0 (Pauly et al., 00). Ths result s equvalent to a frst order least squares plane ft (Shaarj, 998). 3. IMPROVING NEIGHBOURHOOD SELECTION The ntal neghbourhood can be selected n varous ways. The problem s how to ensure that the assumpton of the neghbourhood contanng only one surface entty s vald. Technques exst that remove multple surfaces or reduce them down to a sngle domnate surface. Many are based on random samplng technques, such as RANSAC (RANdom SAmplng Consensus) and ts varants (Bolle and Vemur, 99), outler detecton (Danuser and Strer, 998), votng methods (Page et al., 00) and flterng (Tang et al., 007). Ths secton ams to present a method that wll teratvely converge to the correct soluton for a neghborhood by adjustng the weghts of ponts wthn a neghbourhood dependng on the lelhood of that pont beng sampled from the domnate surface entty sampled wthn the neghbourhood. Ths wll be done by examnng the PCA of the neghbourhoods and, usng statstcal sgnfcance testng, determne and adjust weghts teratvely for each pont untl the method converges to a stable soluton (.e. the weghts reman constant). It wll be demonstrated that the soluton wll have an unform weghtng for those ponts that are determned to belong to a domnate surface structure present n the neghbourhood, and zero for those that do not. The frst stage of the proposed method s outlnng how to determne the relatonshp between two ponts wthn a neghbourhood and whether they belong to the same surface entty. Ths s separated nto two models: an nternal relatonshp between a pont and the neghbourhood beng corrected, and an external relatonshp between the pont of nterest and the neghbourhood of another pont. (a) Fgure : (a) Example of an nternal relatonshp of x to x 0. The threshold s defned n red by Eq. 5 wth all ponts nsde consdered to have an nternal relatonshp. (b) Example of an external relatonshp of x to x 0. The threshold s defned n red by Eq. 6. The man concept of ths method s that a geometrc attrbute of a pont x 0, whch s related to ts underlyng surface, s dependent on ts nternal and external relatonshp wth other surroundng ponts. In other words, the surroundng neghbourhood N 0 for the pont x 0 should not only reflect the attrbutes wthn the neghbourhood, but x 0 should also reflect the attrbutes for the neghbourhood around x f they are to be consdered to belong to the same surface entty. To determne these relatonshps, two defntons of dstance are utlsed. Let c 0 and n 0 denote the centrod and normal approxmaton for neghbourhood N 0 around pont x 0. The equaton for the dstance for the nternal relatonshp s defned as: dst r (b) = ( c0 x ) no (3) wth c 0 beng calculated from the mean of the neghbourhood and n 0 s specfed through PCA. In a smlar manner, let c and n denote the centrod and normal approxmaton for neghbourhood N around pont x. The equaton for the dstance for the external relatonshp s defned as: dst er = ( c x0 ) n (4) Agan, c s calculated from the mean of the neghbourhood and n s specfed through PCA. In order to determne f an nternal or external relatonshp exsts, the Boolean operators can be defned respectvely as: 3. Internal and external neghbourhood relaton between ponts An nternal relatonshp s defned as the relaton of a pont x to the neghbourhood N 0 surroundng a pont of nterest x 0 gven that x N 0. Conversely, an external relatonshp s defned as the relaton of a pont of nterest x 0 to the neghbourhood N surroundng x, gven that x N 0. Illustraton of the nternal and external relatonshp s gven n Fgure (a) and Fgure (b) true r = false dst dst for the nternal relatonshp and: r r t > t α υ, s0 α υ, s0 (5) 478
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 true r = false dst dst r r t > t α υ, s0 α υ, s0 for the external relatonshp. Ths Boolean operators come from a statstcally sgnfcance test to determne f the relatonshp s lely to exst. s 0 and s are the error n the approxmate normal drecton for neghbourhood N 0 and N respectvely. These values can be set as λ 0 from the PCA of the respectve neghbourhoods. The value t s the test statstc from the t- dstrbuton wth υ degrees of freedom and a sgnfcance factor of α. 3. Iteratve generaton of pont membershp weghtng (6) so that the summaton of the weghts equal unty. p s then used as the weght n the recalculaton of the covarance matrx for the next teraton. 3.3 D case example In ths secton, a D example of an ntersecton wll be presented. The example s presented n Fgure. As can be seen, the surface normals for the ponts near the edges are ntally perturbed away from the normal drecton of the surface they are sampled from as the neghbourhood s affected by more than one dscrete surface structure. As defned method s appled, the weghts are teratvely updated untl they become stable,.e. that successve teratons do not effect the soluton and p p. The results are shown n Fgure 3. PCA s performed to obtan the ntal approxmaton for the varance and normal drectons. The proposed method wll use a slghtly modfed verson of the covarance matrx formula such that: Σ = = p ( x c )( T 0 x c0 ) (7) p s the weght of pont x n the neghbourhood. Intally, the ponts wll all be equally weghted as p = /, wth beng the number of ponts n the neghbourhood. In a smlar manner, the formula for the centrod value wll be modfed to: c 0 = = p x (8) Fgure : Example of correcton appled to a D ntersecton. The blue lnes represent the ntal normal approxmaton and red lnes represent the corrected normal approxmatons. If a pont p s not related ether nternally or externally to pont p 0, t s lely that t s not sampled from the same surface and the weght s decreased. Conversely, f a pont p has an nternal and external relatonshp to pont p 0, then t s lely that they belong to the same surface, and the weght s ncreased. If there s only one relatonshp, then t s lely that at least one of the neghbourhoods (N 0 or N ) s affected by multply surfaces, and as such the weghs are left as t s untl the neghbourhoods become more refned. From ths, the rules for updatng the weghts are specfed as: p' = p p + δ δ p ( r = true) and ( ( r = false) and ( er er otherwse = = true false where p are the adjusted weghts and δ s the small change to modfy t by. If p becomes a negatve, then t s set to be zero n order to ensure all weghts are non-negatve. The new weghts are then normalsed by: = ) ) (9) p" = p' p' (0) Fgure 3: Angle of the normal orentaton. The values for the surfaces should be approxmately -45 and 45 degrees. The blue lnes represent the orentaton of the ntal normal approxmaton and red lnes represent the corrected values. If the nternal relatonshps were solely used to update the weghts, the ponts whose neghbourhoods are only mldly affected by another surface structure are corrected as t behaves smlar to an outler removal process. If only the external relatonshps are used, whle the results are smlar to when both are used, the process can become unstable wth all the ponts n the neghbourhoods beng removed. If the weghts of the ponts are examned at every teraton, as shown n Fgure 4, t can be seen that they stablsed wth ether a zero value or an unform value for those that are non-zero. It should be noted that f the pont closest to the ntersecton dd not get corrected n order to conform to one of the surfaces. Ths s because the surfaces are equally represented n the neghbourhood and therefore one cannot be consdered better than the other. The normal can be forced to algn to one of the 479
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 surfaces by replacng the centrod c 0 wth x 0. Ths nstablty caused n the covarance matrx allows t to algn to one of the surfaces; however t can also affect the normal approxmaton detrmentally and provde based solutons. (a) (b) Fgure 6: (a) shows the Gaussan sphere of the uncorrected normal drectons and (b) the Gaussan sphere of the corrected normal drectons. The colour ndcates the densty of normal drectons from blue representng zero to red representng n excess of a hundred. Fgure 4: Trend of the weghts for ponts n a neghbourhood as the teratons progress. The neghbourhood s affected by the presence of multple surfaces wth the ponts belongng to the domnant surface tendng to a value of 0.077, and the others tendng to a value of zero. On examnng those ponts near a surface ntersecton Fgure 8(a) shows the orentaton angles for the uncorrected approxmatons and Fgure 8(b) for the corrected approxmatons. Ths llustrates an ncrease n the accuracy of normal algnment after the correcton wth approxmately 90% of the edge ponts now beng algned to wthn 5 degrees of ther correct orentaton. 3.4 Practcal Example Ths secton wll demonstrate the outlned correcton procedure as appled to a 3D pont cloud. The pont cloud, presented n Fgure 5, s scanned from a door arch wth a Leca ScanStaton wth a nomnal pont spacng of 0.0m. The correcton procedure s appled to the pont cloud wth a neghbourhood sze of 30 and the threshold for determnng nternal and external relatonshps set at a sgnfcance level of α = 0.5. (a) (b) Fgure 7: Hstograms for edge ponts of the orentaton angles for the normal drectons. (a) s the uncorrected normal approxmatons and (b) s the corrected normal approxmatons. Peas n the hstogram denote orentaton of the surface present n the pont cloud. 4. APPROXIMATING CURVATURE Fgure 5: Pont cloud sampled from a secton of a door archway wth a Leca Scanstaton. In Fgure 6(a), the ntal normal approxmatons are dsplay on a Gaussan sphere. The clusters on the sphere represent the presence of surfaces wth that normal orentaton. The strpng effect occurrng between the clusters represents normal approxmatons beng effected by more than one surface. Fgure 6(b) shows the Gaussan sphere of the corrected normal approxmatons usng the proposed method. As can be seen, the strppng effect s sgnfcantly reduced as those ponts affected by more than one surface are corrected to algn wth the domnant surface element n the neghbourhood. The neghbourhood weghts are stablsed wthn 50 teratons of the procedure. There are a varety of technques to approxmate curvature such as surface fttng (Besl and Jan, 988), varaton n surface normals (Jang et al., 005), tensor votng (Tong et al., 004), and angles between neghbourhood members (Dyn et al., 00). Two of the methods that nvolve PCA are gven n Pauly et al. (00) and Jang et al. (005). Pauly et al. (00) uses the percentage of total populaton varaton n the normal to determne the surface varaton as a measure of curvature for a local neghbourhood. However, there s no unt or drecton gven to ths curvature approxmaton. Jang et al. (005) provdes an approxmaton of curvature based on the varaton of the approxmate normal drectons n a local neghbourhood. Whle ths measure as a drectonal component, t does not have a unt of measurement. The advantages of both are ther robust nature and fast computatonal tme. A method wll now be presented to combne the PCA of the coordnates and the normal drectons for a neghbourhood to determne the prncpal drectons of maxmum and mnmum curvature, n addton to the radus of curvature approxmaton n these drectons. 480
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 4. Prncpal component analyss on pont coordnates The propertes that can be derved from PCA have been descrbed prevously. In the case of curvature, the value of λ 0 descrbes that amount of surface varaton n the normal drecton. Snce curvature can cause a varaton n the normal drecton, λ 0 can be used to measure the level of curvature. In most cases λ 0 s dvded by the total varaton to provde an approxmaton (Pauly et al., 00), otherwse the measure wll be dependant on the span of the neghbourhood (Belton and Lcht, 006). It s the span of the neghbourhood that s of nterest n ths method, and s descrbed by λ and λ. In the conc secton dsplayed n Fgure 8(a), f the dstance d and the angle θ s nown, then t becomes a smple matter of determnng the radus of curvature by the followng equaton: sn θ = d r () and d can be approxmated statstcally usng confdence nterval as: λ d = s () wth λ beng the standard devaton n ths drecton calculated from PCA of the neghbourhood, and s beng a scale factor or number of standard devatons on ether sde of the mean that covers the span of the ponts. Ths leaves the only unnown n the formula as θ. that λ 0 (n) λ (n) λ (n). In ths case, λ (n) represents the varaton of the normal drecton along the drecton of maxmum curvature (denoted by e (n) ) and λ (n) represents the varaton of the normal drecton along the drecton of mnmum curvature (denoted by e (n) ). The conc secton for the normals, dsplayed n Fgure 8(b) can be examned n a smlar manner to the conc secton for the pont coordnates. In ths case, θ s solved as: (n) snθ = d (4) wth d (n) beng approxmated as: d t λ = (5) (n) wth λ beng the standard devaton n ths drecton calculated from PCA of the normal, and t beng a the number of standard devatons that covers the span of the normal varaton. 4.3 Radus of curvature approxmaton If the value of θ s the same n Fgure 8(a) and Fgure 8(b), then t becomes a smple matter of solvng the radus of curvature. Assumng that there s only a sngle curved surface, by examnng Fgure 9, t can be seen that the neghbourhood for the normal drectons s a scaled down verson of the neghbourhood of pont coordnates by a factor of r. The reason for ths s that the scalng of the coordnate values would occur along the normal drecton for each pont. Therefore, the nformaton for the PCA on the neghbourhood of pont normals can be used to solve for the value of θ. (a) (b) Fgure 8: (a) Conc secton for the neghbourhood of pont coordnates. (b) Conc secton for the neghbourhood of pont normal drectons. 4. Prncpal component analyss on normal estmaton As llustrated n Jang et al. (005), the PCA performed on the normal drectons of a neghbourhood can also provde an approxmaton of curvature. In ths case, the covarance matrx Σ s defned as: Σ = ( )( = T n μ n μ ) (3) wth n denotng the normal drecton and μ (n) denotng the mean of the normal drectons. The results from the egenvalue decomposton wth the egenvalues λ (n) (n) 0, λ and λ (n), along wth the correspondng egenvectors e (n) (n) 0, e and e (n) such Fgure 9: Neghbourhood of pont normals overlad on the neghbourhood of pont coordnates. Depcts how neghbourhood of coordnates s scaled only along the normal drecton of each pont to get the neghbourhood of the normals. Combnng Eq. and Eq. 4 and rearrangng, the resultng equaton for the radus of curvature s: s λ r = (6) t λ 48
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 If t s assumed that they follow the same dstrbuton (whch s vald snce one s a scaled verson of the other), the values for s and t wll be equal, thus cancellng out to leave the approxmate radus of curvature as follows: r = λ λ (7) For the D case, ths s smple as the prncpal components wll be nomnally algned between the PCA on the neghbourhood of coordnates and normal. In the 3D case, they are often not algned. Therefore, n order to use the approxmaton, the varance n the neghbourhood of pont coordnates must be determned for the drecton specfed by e (n) and e (n), the two prncple curvature drectons. Ths can be done by usng the ellpsod defned by the egenvector decomposton (Golub and Loan, 989) to determne the varance n these drectons. If λ and λ denote the varance of neghbourhood of pont coordnates n the drectons of e (n) and e (n) respectvely, then radus of curvature n the mnmum curvature and maxmum curvature drecton can now be defned respectvely as: r r mn ' = λ λ (8) max ' 4.4 Practcal Applcaton = λ λ (9) Ths secton wll present the approxmate radus of curvature measure appled to a practcal data set. The pont cloud used s shown n Fgure 0 and was captured wth a Leca 4500. The results are shown n Table. r s the radus of curvature obtaned through the ppe fttng routne n Cyclone, μ r s the mean value for the approxmated radus of curvature on for the ppe secton and σ r s the standard devaton of the approxmated values. Whle smulated experments perform well, the nose n a practcal data set causes errors and varatons n the results. The results may be mproved by applyng a smoothng flter beforehand. 5. CONCLUSION AND FUTURE WORK PCA s an mportant tool for dervng the local pont propertes through the examnaton of a local neghbourhood. In ths paper, two methods were presented to utlse the nformaton ganed from PCA. The frst method was an teratve correcton procedure appled to a neghbourhood to flter out ponts deemed lely to belong to a dfferent surface. The second was a method to combne the PCA performed on the pont coordnates wth the PCA performed on the pont normal approxmatons to approxmate the maxmum and mnmum curvature drectons and the radus of curvature n each drecton. Whle these results are stll prelmnary, there s an ndcaton that these methods could be used to retreve nformaton for procedures such as classfcaton and segmentaton. Future wor wll focus on examnng the error propagaton of pont nose to ncrease the accuracy of the nformaton. ACKNOWLEDGEMENTS Ths wor has been supported by Curtn Unversty of Technology, the Cooperatve Research Centre for Spatal Informaton, who actvtes are funded by the Australan Commonwealth's Cooperatve Research Centres Programme, and The Insttute for Geoscence Research (TIGeR). REFERENCES Belton, D. and Lcht, D. D., 006. Classfcaton and segmentaton of terrestral laser scanner pont clouds usng local varance nformaton. Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences XXXVI(part 5), pp. 44 49. Besl, P. J. and Jan, R. C., 988. Segmentaton through varable-order surface fttng. IEEE Transactons on Pattern Analyss and Machne Intellgence 0(), pp. 67 9. Bolle, R. M. and Vemur, B. C., 99. On three-dmensonal surface reconstructon methods. IEEE Transactons on Pattern Analyss and Machne Intellgence 3(), pp. 3. Danels, J. D., Ha, L., Ochotta, T. and Slva, C. T., 007. Robust smooth feature extracton from pont clouds. In: IEEE Internatonal Conference on Shape Modelng and Applcatons 007 (SMI 07), Lyon, France, pp. 3 36. Fgure 0: Pont cloud sampled from an ndustral scene contanng multple ppe sectons. Colours are done based on a crude cluster analyss to dentfy dfferent ppe rad. Ppe Label r μ r σ r 0.5m 0.40m 0.047m 0.30m 0.40m 0.098m 3 0.588m 0.600m 0.000m 4 0.80m 0.83m 0.075m 5 0.630m 0.646m 0.0837m Table : Results for the approxmated radus of curvature. Danuser, C. and Strer, M., 998. Parametrc model fttng: From nler characterzaton to outler detecton. IEEE Transacton on Pattern Anaylss and MAchne Intellgence 0(), pp. 63 80. Dyn, N., Hormann, K., Km, S. J. and Levn, D., 00. Optmzng 3D trangulatons usng dscrete curvature analyss. In: Proceedngs of Mathematcal methods for curves and surfaces (Oslo 000), pp. 35-46. Golub, G. H. and Loan, C. F. V., 989. Matrx Computatons, nd edn, Johns Hopns Press, Baltmore, MD. Gumhold, S., Wang, X. and MacLeod, R., 00. Feature extracton from pont clouds. In: 0th Internatonal Meshng Roundtable. 48
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 Jang, J., Zhang, Z. and Mng, Y., 005. Data segmentaton for geometrc feautre extracton from ldar pont clouds. Geoscence and Remote Sensng Symposum, 005. IGARSS 05, pp. 377 380. Mtra, M. J., Nguyen, A. and Gubas, L., 004. Estmatng surface normals n nosy pont cloud data. Internatonal Journal of Computatonal Geometry and Applcatons 4(4,5), pp. 6 76. Page, D. L., Sun, Y., Koschan, A. F., Pa, J. and Abd, M. A., 00. Normal vector votng: Crease detecton and curvature estmaton on large, nosy meshes. Journal of Graphcal Models 64(3/4), pp. 99 9. Pauly, M., Gross, M. and Kobbelt, L. P., 00. Effcent smplfcaton of pont-sampled surfaces. In: VIS 0: Proceedngs of the conference on Vsualzaton 0, IEEE Computer Socety, Boston, Massachusetts, pp. 63 70. Shaarj, C. M., 998. Least-squares fttng algorthms of the NIST algorthm testng system. Journal of Research of the Natonal Insttute of Standards and Technology 03(6), pp. 633 64. Tang, Q., Sang, N. and Zhang, T., 007. Extracton of salent contours from cluttered scenes. Pattern Recognton 40(), pp. 300 309. Tong,W.-S., Tang, C.-K., Mordoha, P. and Medon, G., 004. Frst order augmentaton to tensor votng for boundary nference and multscale analyss n 3D. IEEE Transactons on Pattern Analyss and Machne Intellgence 6(5), pp. 94 6. Wengarten, J., Gruener, G. and Segwart, R., 003. A fast and robust 3d feature extracton algorthm for structured envronment reconstructon. In: Proceedngs of th Internatonal Conference on Advanced Robotcs (ICAR), Portugal. 483
The Internatonal Archves of the Photogrammetry, Remote Sensng and Spatal Informaton Scences. Vol. XXXVII. Part B5. Bejng 008 484