Laser Scanning Data Segmentation in Urban Areas by a Bayesian Framework

Transcription

1 Laser Scannng Data Segmentaton n Urban Areas by a Bayesan Framework Ednéa Aparecda dos Santos GALVANIN, Alur Porfíro DAL POZ and Aparecda Donset Pres de SOUZA, Brazl Key words: Condtonal Autoregressve models, Bayesan approach, Dgtal Elevaton Model, regon segmentaton, quad tree. SUMMARY In ths paper s presented a regon-based methodology for segmentaton of Dgtal Elevaton Model (DEM) obtaned from laser scannng data. The methodology s based on two sequental technques,.e., a recursve splttng technque usng the quad tree structure followed by a regon mergng technque usng the Markov Random Feld (MRF) model (Condtonal Autoregressve model CAR). The recursve splttng technque starts splttng the DEM nto homogeneous regons. However, due to slght heght dfferences n DEM, regon fragmentaton can be relatvely hgh. In order to mnmze the fragmentaton, a regon mergng technque based on the Bayesan framework s appled to the prevously segmented data. The resultng regons are frstly structured by usng the neghborhood structure. Thus, two regons have connectvty between them f correspondng regons share a common boundary. Next t s used a herarchcal model, whose heght values n the data depend on a general mean plus some random effect. Followng the Bayesan paradgm, t was consder for the random effects a CAR pror. The posteror probablty dstrbuton was obtaned by Gbbs sampler. Regons presentng hgh probablty of smlarty are merged. Experments carred out wth laser scannng data DEM showed that the methodology allows to obtan the objects n the DEM wth a low amount of fragmentaton. 1/13

2 Laser Scannng Data Segmentaton n Urban Areas by a Bayesan Framework Ednéa Aparecda dos Santos GALVANIN, Alur Porfíro DAL POZ and Aparecda Donset Pres de SOUZA, Brazl 1. INTRODUCTION Segmentaton n computer vson and mage analyss s the term used to denote the process of groupng parts of a generc mage nto homogeneous unts wth relaton to one or several characterstcs (or attrbutes), resultng n a segmented mage (Ballard and Brown, 1982). Feature segmentaton s of fundamental mportance n the context of spatal data capturng and updatng for GIS (Geographc Informaton Systems) applcatons. Several mage analyss technques are used to segment the objects of nterest, among them s the regon segmentaton. Regon segmentaton, dependng on the purpose, can be defned as preprocessng for subsequent mage analyss steps. In any case, n order to obtan the desred result, the object detecton strategy must be effcent and relable. Substantal work on mage segmentaton has been developed to segment an mage or a group of data to obtan hgh-level nformaton on the regons or objects contaned on the mage to facltate the nterpretaton of those objects. Ths stage s crtcal n some processes of mage analyss. Some work has been done on segmentaton usng texture (Tuceryan and Jan, 1998), and others usng color (Cheng et al. 2001). However, the combnaton of these two propertes can supply more precse nformaton to support the descrpton of regons (Palm 2004). In relaton to arborne laser scannng technologes, some works can be quoted. In Lohmann (2002) and Voegtle and Stenle (2003) segmentaton s performed on the pont cloud and not n a raster mage. Tóvár and Pfefer (2005) present a combnaton of two approaches. The frst works drectly on the pont clouds usng geometrc crtera to decde f a pont s on the ground or an buldng. The second approach frstly segments the data and then make a classfcaton based on segmented data. Schenk and Csatho (2002) descrbe a possble combnaton of aeral magery and LIDAR data. Planar surface patches are extracted wth regon-growng segmentaton. Possble adjacent planes are ntersected whle mage edges are detected wth a Canny operator. Some plane ntersectons are checked by mergng edge nformaton. McIntosh and Krupnk (2002) propose to detect (wth an optmal zero-crossng operator) and match edges n aeral mages to refne the dgtal surface model produced from arborne scanner data. Bretar and Roux (2005) present an approach for combnng LIDAR data and aeral mages. At frst, LIDAR data are processed to extract buldng planar prmtves. These prmtves are nserted nto a hybrd mage segmentaton algorthm based on a regon-mergng scheme. 2/13

3 In recent years the se of the Bayesan approach has attracted the attenton of researchers from the mage processng area. Applcatons nvolvng the Markov Random Feld (MRF) for mage processng, such as segmentaton and mage restoraton (Geman and Geman, 1984; Szrány et al., 2000; L, 2003) have been dscussed thoroughly. However, MRF models have been recently used n hgh-level mage analyss (Km and Yang, 1995; Modestno and Zhang, 1992; Kopparapu and Desa, 2001; Andersen et al., 2002), for nstance, mage nterpretaton. Recently, the ISPRS (Internatonal Socety for Photogrammetry and Remote Sensng) Commsson III ncluded MRF models as a reference term, whose man objectve s to nvestgate applcatons n mage analyss n Photogrammetry. The man advantage of MRF s that t provdes a general and natural model for the nteracton among spatally related random varables on the mage (Dubes e Jan 1989). The task of object segmentaton n urban areas, due to scene complexty, requres the development of specfc methods that ntegrate the neghborhood nformaton and the doman knowledge of characterstcs of the nterest objects. Thus, ths paper proposes a methodology for laser data segmentaton n two stages. In the frst stage, the recursve splttng technque based on the quad tree structure s used to accomplsh ntal DEM (Dgtal elevaton Model) segmentaton. A regon mergng technque usng a Bayesan approach to mprove the qualty of the ntal segmentaton used n the sequence. Ths paper s organzed n four sectons. Secton 2 presents the methodology proposed for regon segmentaton, whch s essentally based on a recursve splttng technque followed by a regon mergng technque usng the Bayesan approach. Results and analyss are presented n the secton 3. The concluson and future perspectves are provded n Secton DIGITAL ELEVATION MODEL (DEM) SEGMENTATION BY RECURSIVE SPLITTING AND BAYESIAN MERGING We propose a methodology for laser data segmentaton that s based on regular grd,.e., a DEM. A recursve splttng and Bayesan regon mergng are sequentally used for DEM segmentaton wth a mnmum fragmentaton level. In other words, regons compatble wth the objects on the scene are sought. Object recognton s not the objectve of ths methodology. 2.1 Methodology Fgure 1 shows the man stages of the proposed methodology. 3/13

4 Pont cloud data Regular grd generaton Recursve splttng segmentaton Regon mergng by Bayesan approach Regon extracton Polygons representng regons Fgure 1 Proposed methodology. The laser scanner data are ntally nterpolated to generate a regular grd (DEM). After ths stage, recursve splttng s performed usng the quad tree structure. The recursve splttng technque conssts of splttng the DEM nto four homogeneous subregons of dentcal sze. Each subregon s checked for homogenety usng a predefned threshold based on pror knowledge of objects presented n the scene. The splttng process proceeds recursvely untl no regons can be subdvded. In the end, the result s the nput DEM organzed accordng to the quad tree structure, where all homogeneous regons are explctly represented. In order to mnmze the fragmentaton, a regon mergng technque by CAR model s appled to the prevously segmented data. After ths stage, the regons can be extracted. A contour followng algorthm was used for regon contour extracton, followed by the recursve subdvson polygonzaton technque (Jan et al., 1995). Some addtonal detals on recursve splttng and regon mergng are presented n the followng sectons. 2.2 Recursve Splttng usng the Quad Tree Structure The laser scanner pont cloud conssts of randomly dstrbuted laser ponts. In ths case t was necessary to nterpolate the data to generate a regular grd (Morgan and Tempfl, 2000). A varety of nterpolaton methods exst n the related lterature for DEM generaton, ncludng splnes, fnte elements, least squares, krgng, and nearest neghbor. The method used was the nearest neghbor because t makes possble the preservaton of the orgnal heght values on DEM, and t s computatonally effcent. 4/13

5 A regon n a DEM s a groupng of ponts wth smlar propertes. DEM Subdvson nto regons requres several decsons. However, the problem s n decdng whch property to use n the subdvson. Ths queston usually requres knowledge of the characterstcs of the objects present n the scene. In that applcaton, the varance of the heght values s used as a measure of the dsperson of the values n a certan regon. A technque used to splt regons s the recursve regon dvson, usng the quad tree structure. In the recursve splttng technque usng the quad tree structure a regon s splt nto subregons of dentcal sze f the values of heght varaton n ths regon do not exceed a specfed threshold. Each subregon s analyzed n relaton to ts homogenety usng a threshold based on knowledge of the objects present n the scene. The splttng process s repeated untl there are no regons n the tree to be subdvded. The result s an organzed DEM accordng to the quad tree structure, where all homogeneous regons are represented explctly. Fgure 2 shows an example of ths technque, and more detals can be found n Jan et al. (1995) (a) (b) (c) (d) Fgure 2 The buldng of a quad tree. (a) Orgnal Image. (b) Orgnal splttng nto four subregons (the left node n the tree corresponds to the top left regon n the mage). (c) Splttng the regons from (b) nto four subregons. One of these regons s stll a gray regon. (d) Splttng of the last gray regon and the fnal quad tree (Source: Adapted from Jan et al., 1995). In ths applcaton, R represents the DEM, R s each DEM subregon and P a property (for example, the varance n heghts of the ponts). Ths splttng s based on a hypothess testng H P( R σ =λ (where λ s a prestablshed value n agreement wth the values of heght of 0 : ) 0 2 5/13

6 the scene objects) aganst the hypothess H 1 : P( R ) > σ If H 1 : P( R ) > σ 0, H s accepted 1 and H 0 s rejected. The segmentaton of R s performed from successve subdvsons. Thus, f the H 1 hypothess s accepted, then the DEM s splt nto smaller subregons. Ths technque generates a quad tree data structure,.e., a tree n whch each node s ether a leaf node or has four chldren. Ths approach can be summarzed n the followng stages: 1) Splt the DEM nto four regons. 2) For each regon compute the varance of the heght values. 2 3) If P ( ) > σ, splt the regon nto four subregons. R 0 Whenever the H1 hypothess s accepted the second and the thrd stage should be recursvely performed for all DEM regons. The process s concluded when the H 0 hypothess s accepted for all regons. That means that the strategy should be performed recursvely untl there are no regons n the tree to be subdvded. Thus, the algorthm s concluded and a structure s generated. That structure corresponds to a segmented DEM, where each R s labeled wth the mean heght level of the correspondng regon. 2.3 Regon mergng technque usng the Bayesan approach Let X be a segmented DEM over an ( m n ) lattce defned on a regular grd D = {(, j) : 1 m and 1 j n }, where each regon X, j has a fnte confguraton of mean heght. We assume that each X, j s a realzaton of a normal random varable whose mean s modeled n functon of a common factor ( μ ) plus random effects ( ε ),.e., j 2 ( ) X ~ σ (1), j Normal μ, j, μ = μ + ε, (2), j, j Spatal dependence among observatons s made assumng as pror dstrbuton for the random effectsε, j the CAR model, ncludng the spatal dependence among observatons. Accordng to Schmdt, Nobre and Ferrera (2003) ths dstrbuton s defned as ( ε ε ) ~ N( m, υ ) j j, (3) 6/13

7 m = j δ W j δ j W ε j j * υ e υ =, (4) W j δ j where δ represents the set of the neghborng regons to. Ths specfcaton results n the followng jont probablty dstrbuton forε, 2 ε. (5) * * υ 2υ = 1 j< 1 n * 1 1 ( υ ) exp Wj ( ε ε j ) n n The specfcaton s complete when the neghbor matrx W = [ wj ] and the pror dstrbuton * for varance υ are performed. In ths case, we assume that W j = 1 f shares boundares wth j and W = 0, otherwse we then have j m = j δ W ε n j j e * υ υ = n, (6) where n s the number of neghbors of the th regon and for υ * we assume the Inverse Gamma pror dstrbuton (Schmdt, Nobre and Ferrera, 2003). Once the model and respectve pror dstrbutons were defned, the next stage s to obtan the posteror dstrbutons. In order to get the regon mergng, the posteror dstrbuton characterstcs (e.g., maxmum a posteror MAP estmate) for random effects are used. Smulated Annealng, Gbbs sampler and so on can be used for obtanng the posteror dstrbutons (Geman and Geman, 1984). 3. RESULTS AND ANALYSIS In ths secton the results of the proposed methodology usng DEM by laser scanner data (fgure 3) are presented. The threshold used n the recursve splttng was selected n accordance to the pror knowledge of the heght varance n the scene. In the regon mergng stage, the Gbbs sampler mplemented n the WnBUGS (Bayesan Analyss Usng Gbbs Sampler) software was used to obtan the posteror dstrbutons. 7/13

8 Fgure 3 Laser scanner DEM. The regon mergng methodology s appled to the results generated by the recursve splttng technque. Fgure 4 presents the results obtaned wth the Gbbs sampler algorthm. In ths fgure t s possble to observe the dscrmnaton of objects exstng n the urban block (fgure 3) as e.g., roofs and trees. The regons n green represent the hghest objects n the scene and the ones n other colors are assocated wth lower regons. The regons are classfed n functon of heght estmates. 8/13

9 Fgure 4. Results of regon mergng usng the heght estmates. Fgure 5 shows the result obtaned wth the recursve splttng process and wth the regon mergng process. Fgure 5(a) shows the result obtaned by the recursve splttng process for a whole DEM, and for a small zoomed area. In ths case the effect of the fragmentaton resultng from the process of recursve splttng can be observed. Vsually the dfferences among the color of the regons seem to be small but, however, the object (roof) s segmented n several subregons. The segmented DEM showed n fgure 5(a) s vectorzed and presented n fgure 5(b). Although the fgures 5(a) and 5(b) show an accentuated fragmentaton of the objects, a dstncton among subregon groups that compose the respectve physcal objects (for example, buldngs, trees etc.) and the bottom regon s evdent. The Bayesan mergng process seeks to fnd probablstc smlartes among predetected subregons, resultng n regons wth hgh compatblty wth the physcal objects. Fgure 5(c) shows, manly n the wndow where the same object selected n fgure 5(a) s hghlghted, a sgnfcant mprovement n the segmentaton level. It can be notced vsually that now the quadrants correspondng to the object possess smlar characterstcs, that s, the same heght. Fgure 5(d) shows the fnal result, obtaned by plottng the object contours n the segmented DEM by the proposed methodology. It can be stated that the object contours were usually extracted wth good qualty. 9/13

10 (a) (b) (a) (b) (c) (d) (a) (b) Fgure 5 Result of the DEM segmentaton usng the proposed methodology. (a) Result of recursve splttng. (b)contour obtaned by the recursve splttng. (c) Regon mergng result (d) Contour obtaned by regon mergng. 4. CONCLUSIONS AND FUTURE PERSPECTIVES Ths paper presented the theoretcal bases and expermental analyss regardng the process of regon segmentaton va recursve splttng wth regon mergng usng the MRF model. The steps n the process were descrbed and an experment was presented usng a laser scanner DEM. 10/13

11 Bayesan modelng allows a data spatal structure by ncludng a random effect nto the model. Consderng that ths effect, representng specfc characterstcs of the objects n queston, allows the ncorporaton n the analyss of the neghborhood relatonshp among regons, s obtaned a model that represents the behavor of the phenomenon under study n a more realstc way. The results obtaned showed that the proposed strategy allowed the generaton of regons closer to the physcal objects, that nclude the hghly desrable object (a roofs) and also undesrable objects, such as trees and vehcles. Among the objects detected, there can also be spurous ones, whch result from DEM rregulartes. REFERENCES Andersen, H.; Reutebuch, S.; Schreuder, G. 2002, Bayesan object recognton for the analyss of complex forest scenes. In: Arbone Laser Scanner Data. ISPRS, Symposum Photogrammetrc Computer Vson, Austra. Ballard, D. H.; Brown, C. M. 1982, Computer vson. Englewood Clffs, Prentce-Hall. Bretar, F.; Roux, M. 2005, Hybrd Image Segmentaton Usng Ldar 3D Planar Prmtves. ISPRS WG III/3, III/4, v. XXXVI, Part 3/W193, p , Workshop Laser scannng 2005, Netherlands. Cheng, H. D. et al. 2001, Color Image Segmentaton: Advances and Prospects, Pattern Recognton 34(12): p Dubes, R. C.; Jan, A. K. 1989, Random Feld Models n Image Analyss, Journal of Appled Statstcs 16(2): p Geman, S.; Geman, D. 1984, Stochastc relaxaton, Gbbs dstrbuton, and Bayesan restoraton of mages. In: IEEE Transactons on Pattern Analyss and Machne Intellgence, v.6, p Jan, R.; Kastur, R.; Schunck, B. G., 1995, Machne Vson, MIT Press and McGraw- Hll, Inc New York, 549p. Km, I. Y.; Yang, H. S., 1995, An ntegrated approach for scene understandng based on Markov Random Feld. In: Pattern Recognton. p Kopparapu, S. K.; Desa, U. B., 2001, Bayesan approach to mage nterpretaton. 127p. L, C.-T., 2003, Multresoluton mage segmentaton ntegratng Gbbs sampler and regon mergng algorthm. Sgnal Processng, v.83, Lohmann, P., 2002, Segmentaton and Flterng of Laser Scanner Dgtal Surface Models. IAPRS, v. 34, part 2, X an, p Mcntosh, K.; Krupnk, A., 2002, Integraton of laser-derved DSMs and matched mage edges for generatng an a accurate surface model. ISPRS Journal of Photogrammetry and Remote Sensng (56), p Modestno, J. A; Zhang, J., 1992, A Markov Random Feld model based approach to mage nterpretaton. In: Ieee Transactons on Pattern Analyss and Machne Intellgence, 6, p Morgan, M.; Tempfl, K., 2000, Automatc Buldng Extracton from Arborne Laser Scannng Data. IAPRS Internatonal Archves of Photogrammetry and Remote Sensng, v. XXXIII, Part B3, Amsterdam. 11/13

12 Palm, C., 2004, Color Texture Classfcaton by Integratve Co-Occurrence Matrces, Pattern Recognton 37(5): p Schenk, T.; Csatho, B., 2003, Fuson of ldar data and aeral magery for a more complete surface descrpton. Vol. XXXIV-3A/W3, Internatonal Archves of Photogrammetry and Remote Sensng, p , Graz. Schmdt, A. M.; Nobre, A. A.; Ferrera, G. S., 2003, Alguns Aspectos de Modelagem de Dados Espacalmente Referencados. Ro de Janero. Spegelhater, D.J.; Thomas, A.; Best, N.; Glks, W., 2002, Wnbugs (Bayesan Inference Usng Gbbs Samplng). Verson 1.4, Mrc Bostatstcs Unt, Cambrdge, Uk. Szrány, S. et al., 2000, Image segmentaton usng Markov Random Feld model n fully parallel cellular network archtectures. In: Real-Tme Imagng. v.6, p Tóvár, D.; Phefer, N., 2005, Segmentaton Based Robust Interpolaton A New Approach To Laser Data Flterng. ISPRS Wg III/3, III/4, V. XXXVI, Part 3/W19, Workshop Laser scannng 2005, p , Netherlands. Tuceryan, M.; Jan, A. K., 1998, Texture Analyss, n C. H. Chen, L. F. Pau e P. Wang (eds), The Handbook of Pattern Recognton and Computer Vson, World Scentfc Publshng Co., p Voegtle, T.; Stenle, E., 2003, On the qualty of object classfcaton and automated buldng modellng base don laserscannng data. In IAPRS, v. XXXIV 3/W13, Dresden, pp , Germany. ACKNOWLEDGEMENTS The authors thank the LACTEC for furnsh the data for ths research (LACTEC from Curtba - Brazl). BIOGRAPHICAL NOTES Ednéa Aparecda dos Santos Galvann s workng toward a Ph.D. n Cartographc Scences at Paulo State Unversty. She has receved her B.Sc. degree n mathematcs and the M.Sc. degree n Cartographc Scences from São Paulo State Unversty (UNESP), Presdente Prudente-SP, Brazl, n 2000 and 2002, respectvely. Her research nterests nclude nonlnear partal dfferental equatons, dgtal mage processng and mage analyss. Alur Porfíro Dal Poz s Assocate Professor of Department of Cartography at the São Paulo State Unversty, Brazl. He has receved hs Dpl. Eng. from the São Paulo State Unversty n 1987, hs M.Sc. degree from the Paraná Federal Unversty (Brazl) n 1991, and hs Ph.D. degree from the São Paulo Unversty (Brazl) n From July 1999 to March 2000 he joned the Department of Spatal Informaton Scence and Engneerng of Unversty of Mane (USA) as Vstng Researcher and was nvolved n research projects amng at automated object extracton for capturng and updatng of Geographc Informaton Systems (GIS). Hs expertse and current research actvtes are focused on the area of Image Analyss and Dgtal Photogrammetry. 12/13

13 Aparecda Donset Pres de Souza s Assocate Professor at Department of Mathematcs, Statstcs and Computer of the São Paulo State Unversty, Brazl snce She has receved her L.Sc. degree n Mathematcs from São Paulo State Unversty, Brazl n 1984, her M.Sc. degree n Statstcs and Ph.D degree n Operatons Research from Federal Unversty of the Ro de Janero, Brazl, n 1988 and 1999, respectvely. Her current research nterests nclude dynamc herarchcal models, spatal statstcs, stochastc smulaton and Bayesan nference. CONTACTS Ednéa Aparecda dos Santos Galvann São Paulo State Unversty Rua Roberto Smonsen, 305 Presdente Prudente BRAZIL Emal: ednea@pos.prudente.unesp.br edneagalvann@g.com.br Alur Porfíro Dal Poz São Paulo State Unversty Rua Roberto Smonsen, 305 Presdente Prudente BRAZIL Emal: alur@fct.unesp.br Aparecda Donset Pres de Souza São Paulo State Unversty Rua Roberto Smonsen, 305 Presdente Prudente BRAZIL Emal: adps@fct.unesp.br 13/13