DIAGNOSTIC-ROBUST STATISTICAL ANALYSIS FOR LOCAL SURFACE FITTING IN 3D POINT CLOUD DATA

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1 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia DIAGNOSTIC-ROBUST STATISTICAL ANALYSIS FOR LOCAL SURFACE FITTING IN 3D POINT CLOUD DATA Abdul Nuruabi a, *, David Belto b, Geoff West b a, b Departmet of Spatial Scieces, Curti Uiversity, Wester Australia, Australia a abdul.uruabi@postgrad.curti.edu.au, b {D.Belto, G.West}@curti.edu.au a,b Cooperative Research Cetre for Spatial Iformatio Commissio III/4 KEY WORDS: 3D Modelig, Feature Extractio, Geometric Primitives, Laser Scaig, Local Normal Estimatio, Photogrammetry, Plae Fittig, Surface Recostructio ABSTRACT: This paper ivestigates the problem of local surface recostructio ad best fittig for plaar surfaces from uorgaized 3D poit cloud data. Least Squares (LS, its equivalet Pricipal Compoet Aalysis (PCA ad RANSAC are the three most popular techiques for fittig plaar surfaces to 3D data. LS ad PCA are sesitive to outliers ad do ot give reliable ad robust parameter estimatio. The RANSAC algorithm is robust but it is ot completely free from the effect of outliers ad is slow for large datasets. I this paper, we propose a diagostic-robust statistical algorithm that uses both diagostics ad robust approaches i combiatio for fittig plaar surfaces i the presece of outliers. Recetly itroduced high breakdow ad fast Miimum Covariace Determiat (MCD based locatio ad scatter estimates are used for robust distace to idetify outliers ad a MCD based robust PCA approach is used as a outlier resistat techique for plae fittig. The beefits of the ew diagostic-robust algorithm are demostrated with artificial ad real laser scaig poit cloud datasets. Results show that the proposed method is sigificatly better ad more efficiet tha the other three methods for plaar surface fittig. This method also has great potetial for robust local ormal estimatio ad for other surface shape fittig applicatios. 1. INTRODUCTION I may fields such as photogrammetry, reverse egieerig ad computatioal geometry, surface recostructio ad fittig for geometric primitives is a fudametal task with poit cloud data. Much use is made of accurate local surface fittig ad local ormal estimatio ad the fact that these are related to each other. I surface recostructio, the quality of the approximatio of the output surface depeds o how well the estimated ormals approximate the true ormals of the sampled surface (Tamal et al., 5. Most ma-made objects cotai plaar surfaces. Fittig a plaar surface is closely related to local ormal estimatio for surface recostructio, poit cloud segmetatio, classificatio ad rederig (Schabel et al., 7; Pu et al., 11. I fact, plae detectio ca be regarded as the first step i segmetatio. I poit cloud data aalysis local ormal estimatio from a fitted local plae is used frequetly (Hoppe et al., 199; Wag et al., 1. The Least Squares (LS method, Pricipal Compoet Aalysis (PCA ad RANdom Sample ad Cosesus (RANSAC are the three most popular techiques for fittig plaar surfaces to 3D data (Hoppe et al., 199; Schabel et al., 7. Tarsha- Kurdi et al., (7 show that the RANSAC is more efficiet tha the well-kow Hough trasform ad ote that the Houghtrasform is very sesitive to the segmetatio parameters values. Hece we compare RANSAC with our techique. The majority of poit cloud data is acquired by various measuremet processes usig a umber of istrumets (sesors. The physical limitatios of the sesors, boudaries betwee 3D features, occlusios, multiple reflectace ad oise ca produce off-surface poits that appear to be outliers (Sotoodeh, 6. Robust statistical approaches are regarded as oe of the most effective solutios to the problems of outliers. Stewart (1999 states i his review paper: It is importat for the reader to ote that robust estimators are ot ecessarily the oly or eve the best techique that ca be used to solve the problems caused by outliers ad multiple populatios (structures i all cotexts. The ecessity of robust methods has bee well described i the literature (e.g. Hampel et al., The goal of robust multivariate methods should be twofold: to idetify outliers ad to provide a aalysis that has greatly reduced sesitivity to outliers. It is well-kow that the LS ad PCA methods are very sesitive to outliers ad fail to reliably fit plaes (Mitra ad Nguye, 3. The RANSAC algorithm is ot completely free from the effect of outliers ad requires more processig time for large datasets. Moreover, RANSAC is very efficiet i detectig large plaes i oisy poit clouds but very slow to detect small plaes i large poit clouds (Deschaud ad Goulette, 1. I this paper, we cocetrate o plaar surface fittig ad local ormal estimatio of the fitted plae. Robust PCA ofte gives a accurate portrayal of the uderlyig data, but eve so, it does ot idetify particular outliers that may be sigificat i their ow right. To get more effective results, alog with a robust versio of PCA, it is importat to have a complemetary outlier idetificatio method. We propose a ew diagostic-robust statistical techique for plaar surface fittig i 3D poit cloud * Correspodig author. 69

2 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia data, which is able to fid outliers ad robust estimates at the same time. We compare the ew method with LS, PCA ad RANSAC. The robustess of the methods is compared with respect to size of the data, outlier percetage ad poit desity. The remaider of the paper is arraged as follows: Sectio briefly discusses the three related methods. I Sectio 3, we propose our techique for fittig plaes ad for local ormal estimatio from the best fitted plae. Sectio 4 cotais results, ad aalyses the performace of the proposed techique through compariso with the other methods usig simulated ad real (mobile mappig laser scaig datasets. Sectio 5 cocludes the paper.. RELATED WORKS AND PRINCIPLES I this sectio, we briefly discuss the basic otios of the related methods used i this paper..1 Least Squares The same basic priciple of the LS method has bee used i differet ways for plae fittig. The priciple is to miimize the sum of the squared residuals. Assume a sample of data poits {p i (x i, y i, z i; i 1,,..., } belog i a 3D poit cloud ad used to fit a plae. The plae equatio is: ax by cz d, (1 where a, b, c ad d are the parameters. The LS method is used to express the data poits i the form ( x, y, f ( x, y z ad to miimize the sum of squared residuals (r, ri mi i i,..., i1 i 1 z z, i 1, where r is the distace betwee poits ad the fitted plae. The i th residual is a vertical distace ad cosidered oly i oe (vertical directio (z here (Kwo et al., 4. To overcome the bias to oe directio, the approach of Total Least Squares (TLS is proposed that miimizes the squared sum of the orthogoal distaces betwee the poits ad the plae. I TLS, if the positio (cetre of the plae is defied as c ad is the uit ormal to the plae, the parameters of the plae ca be determied by solvig: where mi c, 1 i 1 T ( p c, i 1,,..., i ( (3 p c T ( is the orthogoal distace betwee a plae i ad a poit p i of the data. Hoppe et al., (199 ad later may use this idea for fittig a plae. The other way of parameter estimatio is miimizig the orthogoal distace usig the Sigular Value Decompositio (SVD of the data matrix.. Pricipal Compoet Aalysis PCA is a statistical techique that is typically used to idetify a small set of mutually orthogoal variables which explai most of the uderlyig covariace structure of a dataset. Pricipal Compoets (PCs are the liear combiatio of the origial variables that rak the variability i the data through the variaces, ad produce the correspodig directios usig the eigevectors of the covariace matrix. So, the first PC correspods to the directio i which the projected observatios have the largest variace, the secod PC correspods to the ext directio ad so o. Every PC describes a part of the data variace ot explaied by those with larger variaces. Usig oly the top raked PCs eable a reduced represetatio of the data. PCA miimizes the variace from the data by subtractig the mea from the correspodig variables ad the performs SVD o that covariace matrix. This way PCA fids the required umber of PCs. I the case of plae estimatio, the first two PCs form a basis for the plae ad the third PC is orthogoal to the first two ad defies the ormal of the fitted plae. Sice the first two PCs explai the variability as much as possible with two dimesios, the fitted plae is the best D liear approximatio to the data. Sice the third PC expresses the least amout of variatio, it ca be used as the estimate of the coefficiets of fitted plae. Hoppe et al., (199 use the third PC as the ormal of the plae. Later, may others use the PCA approach i differet ways (Pauly et al., as a equivalet to LS. Although PCA is a powerful tool, it is well-kow that the results are affected by aomalous observatios..3 RANSAC The RANSAC algorithm, itroduced by Fischler ad Bolles (1981, extracts shapes ad estimates the parameters of a model by radomly drawig a subset of data from the dataset. It is a iterative process cosistig of two steps: hypothesize ad test. First, a miimal subset (three poits for a plae is radomly selected ad the required parameter estimatio computed based o the subset. I the secod step, the estimates are tested agaist all the data poits to determie how may of them are cosistet with the estimates. RANSAC divides data ito iliers ad outliers ad yields parameters computed from the miimal set of iliers by usig LS estimatio with maximum support. It is coceptually simple, very geeral ad ca robustly deal with data cotaiig more tha 5% of outliers (Schabel et al., 7. May authors use RANSAC for plaar ad local surface fittig (e.g., Schabel et al., 7. Sice its iceptio, may versios of RANSAC (e.g., Torr ad Zisserma, ; Michaelse ad Stilla, 3 have bee proposed. Torr ad Zisserma ( poit out that RANSAC ca be sesitive to the choice of the correct oise threshold ad whe multiple model istaces are preset (see Zuliai, 11. Schabel et al., (7 state that lack of efficiecy ad high memory cosumptio remai its major drawbacks. 3. PROPOSED ALGORITHM The proposed Diagostic-Robust PCA (DRPCA algorithm is a combiatio of diagostics ad robust statistical techiques. First, we fid cadidate outliers usig Robust Distace (RD. This reduces some outlier effects ad makes the data more homogeeous. Secod, we use robust PCA to fid more cadidate outliers, if ay, ad fit the plae i a robust way. The steps of the algorithm are: i. calculate RD for the 3D poit cloud, ii. classify regular observatios ad outliers based o the RD, iii. perform robust PCA by usig the regular observatios from step (ii, iv. calculate orthogoal ad score distaces from step (iii, ad classify the observatios as outliers ad regular observatios by usig orthogoal distace, 7

3 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia v. fid the first three robust PCs based o the regular observatios from step (iv, ad vi. fit a plae usig the first two PCs from step (v ad fid the third PC as the ormal. 3.1 Robust Distace I multivariate data, the distace of a observatio from the cetre of the data is ot sufficiet for outlier detectio as the shape of the data has to be cosidered. The shape of multivariate data is quatified by the covariace structure of the data. The Mahalaobis Distace (MD (Mahalaobis, 1936 is probably the most well-kow distace measure that cosiders covariace i the variables. For a m-dimesioal multivariate sample x i, MD is defied as: T 1 MDi ( xi c ( xi c, i 1,,..., (4 where c is the estimated arithmetic mea ad is the covariace matrix of the sample data. Although it is still quite easy to detect a sigle outlier by meas of MD, this approach o loger suffices for multiple outliers because of the maskig effect (Rousseeuw ad Driesse, Maskig occurs whe a outlyig subset goes udetected because of the presece of aother, usually adjacet, subset (Hadi ad Simooff, Hampel et al., (1986 poit out that the MD is ot robust because of the sesitivity of the mea ad covariace matrix to outliers. It is ecessary to use a distace that is based o robust estimators of multivariate locatio ad scatter (Rousseeuw ad Leroy, 3. May robust estimators have bee itroduced i the literature (see Maroa ad Yohai, Miimum Covariace Determiat (MCD is oe of the most popular oes because it is computatioally fast (Rousseeuw ad Drisse, The MCD fids a subset of h ( / observatios (out of, the total umber of observatios whose covariace matrix has the lowest determiat. The MCD estimate of locatio (c MCD is the the average of the h poits, ad the MCD estimate of scatter ( MCD is the covariace matrix of the h poits. The Robust Distace (RD based o MCD is defied as: T 1 RDi ( xi cmcd MCD( xi cmcd, i 1,,...,. (5 Rousseeuw ad va Zomere (199 show that RD follows a Chi-square (χ distributio with m (umber of variables degrees of freedom ad the observatios that exceed (χ m,.975 are idetified as outliers. the data space to the affie subspace spaed by the observatios is especially useful whe m, but eve whe m, the observatios may spa less tha the whole m- dimesioal space (Hubert ad Rousseeuw, 5. Sice, PP uses trimmed global measures; it has the advatage of robustess agaist outliers (Friedma ad Tukey, The fast-mcd cotais time savig techiques; whe is large it fixes a lower umber (5 of radom subsets. Reductio of subsets has o effect because the algorithm uses outlyigess measure to use fewer subsets. I computatio, first the data is compressed to the pricipal compoets defiig potetial directios. The, each i th directio is scored by its correspodig value of outlyigess: T T xiv cmcd( xiv wi arg max, i 1,,..., T v 1 MCD ( xiv where the maximum is overall directios, v is a uivariate directio ad x iv T deotes a projectio of the i th observatio o the directio v. O every directio a robust cetre (c MCD ad scale ( MCD of the projected data poits (x iv T is computed. Secod, a fractio h (h should be greater tha /; i this paper we use h=.75 of observatios with the smallest values of w i are used to costruct a robust covariace matrix. Fially, robust PCA projects the data poits oto the k-dimesioal subspace spaed by the k (k= for plae fittig largest eigevectors (i.e., PCs of the ad computes their cetre ad shape by the re-weighted MCD. The eigevectors of the determie the robust PCs. While computig the robust PCA, we ca flag outliers i a diagostic way. Outliers ca be two types: orthogoal outlier that lies away from the subspace spaed by the k pricipal compoets ad is idetified by a large Orthogoal Distace (OD, which is the distace betwee the observatio (x i ad its projectio ( x oto the k-dimesioal PCA subspace. The i other type of outlier is idetified by the Score Distace (SD, which is measured withi the PCA subspace. The cut-off value for the score distace is (χ k,.975, ad for the orthogoal distace is a scaled versio of χ (see Hubert ad Rousseeuw, 5. We cosider oly the orthogoal outlier here because the poits that are far away i terms of score should ot be ifluetial for plae fittig. (6 3. Robust Pricipal Compoet Aalysis Geerally, robust PCA is performed by computig the eigevalues ad eigevectors of a robust estimator of the covariace or correlatio matrix. A umber of robust cetre ad covariace estimators have bee itroduced i the literature (e.g., M-estimators: see Maroa ad Yohai, 1998; S-estimators: Rousseeuw ad Leroy, 3. Recetly, Hubert ad Rousseeuw (5 itroduce a ew approach to robust PCA. The authors combie the idea of Projectio Pursuit (PP (Friedma ad Tukey, 1974 with the fast-mcd (Rousseeuw ad Driesse, The PP is used to preprocess the data so that the trasformed data are lyig i a subspace whose dimesio is at most -1, ad the the fast-mcd estimator is used to get the robust cetre ad covariace matrix. Reducig Figure 1. Fitted plae, gree poits are distat i terms of score ad red poits are orthogoal outliers I Figure 1, we see that the poits 8, 9 ad 3 (red poits are orthogoal outliers because they are away from the plae ad distat by OD. Note that poit 3 has low SD (projectio is i the cluster so would ot be idetified as a outlier without OD. Figure 1 shows clearly that poits 5, 6 ad 7 are i the plae although far from the mai cluster of poits, hece they are ot cosidered as outliers. We use the remaiig regular observatios to get the fial three PCs. The first two PCs are used for fittig the required plae ad the third PC is cosidered as the estimated ormal. 71

4 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia 4. EXPERIMENTAL RESULTS We aalyse LS, PCA, RANSAC ad DRPCA usig artificial ad real mobile mappig laser scaig 3D poit cloud data. We also cosider Diagostics PCA (DPCA, which uses the RD for outlier detectio ad fit the plae usig PCA without outliers, ad MSAC from the RANSAC family. MSAC (Torr ad Zisserma, is a M-estimator based statistically robust versio of RANSAC. We fit the plaar surface ad fid ormal ad eigevalues respective to the fitted plae. We calculate the bias agle (θ (Figure betwee the plaes fitted to the data with ad without outliers, defied by Wag et al., (1 as: arccos ( 1 T, (7 where 1 ad are the two uit ormals from the plaes with ad without outliers respectively. (b Figure. Bias agles (θ betwee the fitted plaes with ad without outliers by differet methods (b variatio alog the ormal to the sample poits To compare results, we use the covariace techique ad calculate the variatio alog the plae ormal ad the surface variatio (see Pauly et al,. Variatio alog the ormal is defied by the correspodig eigevalue (λ of the plae ormal, ad the surface variatio at the poit p i is defied as: ( p i, 1 (8 1 where σ(p i measures the surface variatio alog the directio of the correspodig eigevectors, ad λ i is the i th eigevalue. 4.1 Artificial Data Radom 3D datasets are geerated from a multivariate Gaussia distributio. Regular poits have meas i 3D of (., 8., 6. ad variaces (5., 5.,.1. Outliers have meas (15., 15., 1. ad variaces (1.,., 1.. We simulate the datasets for various sample sizes ( =, 5, 1 ad ad outlier percetages (5, 1, 15, ad 5. We perform 1 rus (for statistically represetative results for each ad every sample size ad outlier percetage. We compute the θ, λ ad σ p as the performace measures Bias agle: Figure 3 shows the average bias agles (i radias for differet sample sizes ad outlier percetages. It shows the large differece betwee robust (RANSAC, MSAC, DPCA, DRPCA ad o-robust (LS, PCA methods. LS is less cosistet tha PCA, ad DRPCA has a lower bias agle tha LS, PCA, DPCA, MSAC ad RANSAC i most cases. Figure 3, for sample size, shows that MSAC ad RANSAC give icosistet results for differet percetages of outliers. To show the effect of poit desity variatio o bias agle, we create variatios i surface directios (i.e., i x-y axes. We Average bias agle = LS PCA DPCA MSAC RANSAC DRPCA (c = (b = Outlier percetage (d = Figure 3. Average bias agle versus outlier percetage for differet sample sizes ad outlier percetages Variace I II III IV V X (R,O 3, 8 5, 1 7, 1 1, 15 15, Y (R,O 3, 5, 7, 4 1, 7 15, 1 Table 1. Variaces for regular (R ad outlier (O data simulate 1 sets of sample with 5 poits i which % are outliers for differet combiatios of x, y variaces. The rows of Table 1 show the variace combiatios for regular (R ad outlier (O data. Other criteria are the same as for the previous datasets. The results preseted i Figure 4 show that robust methods are better tha o-robust methods. Agai the average bias agle for DRPCA is sigificatly less tha for LS ad PCA, ad also better (less tha DPCA, MSAC ad RANSAC. It is kow that surface thickess (roughess iflueces surface fittig methods. To see the effect of roughess, we chage the variace alog the z (elevatio axis. Agai we simulate 1 datasets of 5 poits with % outliers. The z variaces for regular observatios are.1,.1,.,.5,.1 ad.. The parameters for outliers (mea, variaces for x, y ad z are the same as for previous simulated datasets. Figure 4(b shows that MSAC ad RANSAC get worse compared to others with icreasig z -variace. Average bias agle LS PCA DPCA MSAC RANSAC DRPCA I II III IV V Variatios i X-Y (b Variatios i Z Figure 4. Average bias agle w.r.t. poit desity variatio (b z variatio The above results i bias agle show that RANSAC performs better tha MSAC i most of the cases, ad DRPCA out performs DPCA. I the iterests of brevity we do ot cosider DPCA ad MSAC i the rest of the paper. 7

5 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia 4.1. Surface variatio: We simulate 1 samples of 5 poits with % outliers usig the same iput parameters as for previous experimets. Table shows the calculated descriptive measures of λ ad σ p for all the samples. Measures LS PCA RANSAC DRPCA Mea λ Media Outliers Mea σ p Media Outliers Lambda Table. Measures based o λ ad σ p from 1 rus LS PCA RANSAC DRPCA Sigma P (b LS PCA RANSAC DRPCA Figure 5. Box-plots for λ (b σ p from 1 rus All the measures i Table have larger values for o-robust methods. Every measure for DRPCA is better tha for LS, PCA ad the overall results are better tha for RANSAC. I Figure 5, both the Box-plots show that DRPCA is better tha classical PCA ad competitive with RANSAC Performace time: Although DRPCA takes more time tha LS ad PCA to ru, its computatio time is still sigificatly less tha for RANSAC. Table 3 shows the mea CPU time (i secods for various sample sizes (with % outliers based o 1 rus. Figure 6. Real poit cloud data (b LS plae (c PCA plae (d outliers (red poits detected by RANSAC (e RANSAC plae (f red ad blue poits (outliers detected by RD ad OD respectively (g DRPCA plae Cosiderig the real dataset as a populatio, we take 1 radom samples of 5 poits. We compute λ ad σ p values for LS, PCA, RANSAC ad DRPCA. To illustrate the robustess of the methods, we draw Box-plots for λ ad σ p from the 1 samplig results. Descriptive measures i Table 4 ad Figure 7 show that o-robust techiques always perform worse tha robust oes, ad betwee the robust techiques DRPCA is better tha RANSAC. For both λ ad σ p, DRPCA has the least umber of outlyig results. I the case of λ, RANSAC fails 54 times whereas DRPCA fails oly 7 times for 1 rus. Measures LS PCA RANSAC DRPCA Mea λ Media Outliers Mea σ p Media Outliers Table 4. Measures based o λ ad σ p from 1 samples Sample size LS PCA RANSAC DRPCA Table 3. Mea computatio time 4. Real Poit Cloud Data We use laser scaer 3D data (Figure 6 with 1,875 poits. This dataset represets a saddle-back roof of a road side house; we cosider it as a plaar surface. Figures 6 (b ad 6 (c show the poits fitted by plaes usig LS ad PCA showig that may outliers are take as regular poits i the plae. RANSAC fids 78 (14.8% outliers (red poits i Figure 6(d ad Figure 6(e shows that the RANSAC fitted plae is still ot completely free from outliers. DRPCA fids 5 (1% outliers marked as red poits by RD ad 73 (3.9 % outliers marked as blue poits by OD (Figure 6(f. I total 15.9% outliers are detected by DRPCA ad with the remaiig regular poits we fit the plae usig robust PCA. Figure 6(g shows there is o idicatio of outliers o that DRPCA plae. Log(Average Lambda Figure 7. Box-plots of λ (b σ p LS PCA RANSAC DRPCA Sample size log(average Sigma P (b Sample size Figure 8. Log average λ, ad (b σ p ; w.r.t. sample size 73

6 ISPRS Aals of the Photogrammetry, Remote Sesig ad Spatial Iformatio Scieces, Volume I-3, 1 XXII ISPRS Cogress, 5 August 1 September 1, Melboure, Australia To evaluate the impact of sample (eighborhood size variatio o λ ad σ p, we take 1 radom samples for each of, 3, 4, 5, 1 ad poits. We take log values o the average of λ ad σ p to emphasise the differece amog differet methods. Figure 8 shows that DRPCA performs the best for all sample sizes with all the values for the measures, ad gives more accurate results (less values for both λ ad σ p. 5. CONCLUSION AND FUTURE WORK This paper proposes a diagostic-robust PCA algorithm for fittig plaar surfaces. Experimets based o artificial ad real laser scaig datasets show that the proposed techique outperforms classical methods ad is competitive with RANSAC. It has more accurate ad robust results tha the other methods. It gives the lowest bias agle ad least amout of surface variatio from the best fitted plae. It is also faster tha RANSAC. Apart from accurately fittig plaes i the presece of outliers, DRPCA ca also geerate accurate local surface ormals. The techique has great potetial for local surface estimatio ad geometric primitives fittig. Similar to may other robust techiques, it is ot suitable for more tha 5% of outliers. Future research will ivestigate its potetial use for differet feature extractio, estimatio ad fittig tasks. ACKNOWLEDGEMENTS This study has bee carried out as a PhD research supported by a Curti Uiversity Iteratioal Postgraduate Research Scholarship (IPRS. The work has bee supported by the Cooperative Research Cetre for Spatial Iformatio, whose activities are fuded by the Australia Commowealth's Cooperative Research Cetres Programme. We are thakful to McMulle Nola ad Parters Surveyors for the real poit cloud dataset. We also thak the aoymous reviewers for their costructive remarks. REFERENCES Deschaud, J. -E., ad Goulette, F., 1. 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