EXTENDING GENERALIZED HOUGH TRANSFORM TO DETECT 3D OBJECTS IN LASER RANGE DATA

Transcription

1 ISPRS Woksho on Lase Sanning 007 and SilviLase 007, Esoo, Setembe -4, 007, Finland ETENDING GENERALIED HOUGH TRANSFORM TO DETET 3D OBJETS IN LASER RANGE DATA Kouosh Khoshelham Otial and Lase Remote Sensing Reseah Gou, Delft Univesity of Tehnology, Kluyveweg, 69 HS Delft, The Nethelands KE WORDS: Lase sanning, Point loud, Objet Reognition, 3D Genealized Hough Tansfom, Automation ABSTRAT: Automated detetion and 3D modelling of objets in lase ange data is of geat imotane in many aliations. Existing aoahes to objet detetion in ange data ae limited to eithe.5d data (e.g. ange images o simle objets with a aameti fom (e.g. shees. This ae desibes a new aoah to the detetion of 3D objets with abitay shaes in a oint loud. We esent an extension of the genealized Hough tansfom to 3D data, whih an be used to detet instanes of an objet model in lase ange data, indeendent of the sale and oientation of the objet. We also disuss the omutational omlexity of the method and ovide ost-edution stategies that an be emloyed to imove the effiieny of the method.. INTRODUTION Automated extation of objets fom lase ange data is of geat imotane in a wide ange of aliations. Revese engineeing, 3D visualisation, industial design monitoing and envionmental lanning ae a few examles of the aliations that equie 3D models of objets extated fom images o lase ange data. A 3D model ovides an abstat desition of the objet, whih an be oessed and visualised moe easily and effiiently. The oess of objet extation onsists of two main tasks. The fist task is detetion, in whih the esene of an objet in the data is veified, and its aoximate loation is found (usually by labeling the data oints that belong to the objet. The seond task is modeling, whee the deteted objet is eesented with a 3D geometi model that is most adequate in tems of suh iteia as auay, omatness, the domain of the objet and the aliation equiements. The detetion ste lays a key ole in the suessful modeling of the objet. If the objet is oely deteted in the data, the modeling an be aied out moe eliably and auately. Existing aoahes to the detetion of objets in ange data an be divided into two majo ategoies: data-diven aoahes and model-diven aoahes. Data-diven aoahes ae mainly based on segmentation (Khoshelham, 006; Rottensteine and Biese, 003; Sithole, 005, lusteing (Filin, 00; Vosselman, 999 and lassifiation (Folani et al., 006; Oude Elbeink and Maas, 000. While these methods have been ommonly alied to the lase ange data of.5d sufaes, thei aliation to moe omlex 3D senes is not always ossible. Fo instane, in lase ange data of industial installations many objets ae atially oluded and data-diven methods fail to oetly detet these objets in the data. Model-diven aoahes, on the ontay, ae moe obust in the esene of atial olusion, sine they inooate some fom of knowledge about the shae of the objet. The objet model an be eesented, among othe eesentations, as a set of voxel temlates (Geensan and Boulange, 999 o sin images (Johnson and Hebet, 999, whih ae mathed against the data o as a set of aametes that mathematially define the objet. In the latte ase, Hough tansfom (Duda and Hat, 97; Hough, 96 has been used to detemine the model aametes as well as the data oints that belong to the objet (Olson, 00. The aliation of Hough tansfom is estited to simle objets that an be eesented with few aametes, suh as lanes, shees and ylindes. Vosselman et al., (004 desibe a Hough-based method fo the detetion of lanes and shees in a oint loud. Rabbani (006 develoed an extension of this method that an be used fo the detetion of ylindes. Figue demonstates the aliation of Hough tansfom to the detetion of ylindes in a oint loud. As an be seen, the uved ats joining the ylindes have not been extated beause these ats annot be exessed in aameti foms with few aametes. This ae onentates on the detetion of 3D objets with abitay shaes in a oint loud. The objetive of this ae is to develo a new extension of Hough tansfom, whih an be used to detet instanes of a omlex objet model in lase ange data, indeendent of the sale and oientation of the objet. The ae has five setions. Setion ovides an oveview of the standad and genealized Hough tansfom as alied to D images. In setion 3, the iniles of the 3D genealized Hough tansfom is desibed. A disussion on the omutational omlexity of the method is esented in setion 4. onlusions aea in setion 5. 06

2 IAPRS Volume VI, Pat 3 / W5, 007 Figue. Detetion of ylindes in a oint loud using Hough tansfom (fom Rabbani (006. The uved ats joining the ylindes annot be extated using this method.. AN OVERVIEW OF THE STANDARD AND GENERALIED HOUGH TRANSFORM Hough tansfom is a well known method fo the detetion of objets in D intensity images. The standad Hough tansfom is aliable to objets with an analytial shae suh as staight lines, iles and ellises; wheeas, with the genealized Hough tansfom any abitay uve an be deteted in a D image. The following setions biefly desibe the standad and genealized Hough tansfom.. The standad Hough tansfom The idea of Hough tansfom fo deteting staight lines in images was fist intodued by Hough (96. In the oiginal Hough tansfom, a staight line is aameteized as y = mx+b with two aametes m and b. Aoding to the numbe of aametes, a D aamete sae is fomed in whih evey oint in the image sae oesonds to a line b = -xm+y. A set of image oints that lie on a same line y = mx+b in image sae oesond to a numbe of lines in the aamete sae, whih inteset at oint (m, b. Finding this intesetion oint is, theefoe, the basis fo line detetion in Hough tansfom. The aamete sae is ealized in the fom of a disete aumulato aay onsisting of a numbe of bins that eeive votes fom edge ixels in the image sae. The intesetion oint is detemined by finding the bin that eeives a maximum numbe of votes. In addition to staight lines, Hough tansfom has been used to detet also othe analytial shaes, suh as iles and ellises, in D images. The undelying inile fo the detetion of othe analytial shaes is the same as fo the staight line detetion, and is based on onstuting a duality between edge ixels in the image and objet aametes in the aamete sae. The dimensions of the aamete sae, howeve, vay with eset to the aameteization of the objet.. The genealized Hough tansfom Ballad (98 oosed a genealization of Hough tansfom to detet non-aameti objets with abitay shaes in D intensity images. In the genealized Hough tansfom, the objet model is stoed in a so-alled R-table fomat. An abitay efeene oint is seleted fo the objet, and fo evey ixel on the objet bounday the gadient dietion as well as the length and dietion of a veto onneting the bounday ixel to the efeene oint ae omuted (Figue. The gadient dietions,, seve as indies in the R-table to look u the length,, and dietion, β, of the onneting vetos. Table illustates a geneal fom of an R-table. Table : R-table Point 0 0 (, β 0 - (, β 0 - (, β 03 - (, β - (, β - (, β 3 - (, β - (, β - (, β 3 - The eonstution of the objet model fom the R-table is staightfowad: y os( β sin( β whee (x, y and (x, y ae esetively the oodinates of the efeene oint and a oint on the bounday of the objet. Fo the detetion of the objet model in the image, howeve, the oodinates of the efeene oint ae not known. A D aumulato aay is, theefoe, onstuted with the two aametes of the efeene oint as the axes. At evey image edge ixel the gadient dietion is obtained and then looked u in the R-table. The oesonding sets of and β values ae used to evaluate Equation, and the esulting x and y values indiate the aumulato aay bins that should eeive a vote. One this oess is omlete fo all edge ixels, the bin with the maximum vote indiates the efeene oint, and the edge ixels that ast vote fo this bin belong to an instane of the objet in the image. (, G β P( P, P Figue : Paametes involved in the genealized Hough tansfom. ( 07

3 ISPRS Woksho on Lase Sanning 007 and SilviLase 007, Esoo, Setembe -4, 007, Finland The genealized Hough tansfom an also be used to detet a otated and saled vesion of a model in an image. This is ahieved by sulementing Equation with a sale fato and a otation angle, and the aamete sae is exanded to a 4D aumulato aay. The eak of the aumulato aay detemines the sale and otation aametes in addition to the oodinates of the efeene oint, although at the ie of a highe omutational exense. n P( P, P, P (,,.3 Modifiations to Hough tansfom Seveal modified vaiations of the Hough tansfom have been oosed to imove the efomane of the method. Illingwoth and Kittle (988 ovide a suvey of these methods. Duda and Hat (97 suggested a modifiation of the standad Hough tansfom by substituting the oiginal sloeinteet aameteization of staight lines with a ola, angleadius, aameteization. The ola aameteization leads to a bounded aamete sae, unlike the oiginal aameteization, and is, onsequently, moe omutationally effiient. They also showed that standad Hough tansfom an be used to detet moe geneal uves in an image. Gadient weighted Hough tansfom, as aeas in Ballad s genealization, was fist intodued by O Goman and lowes (976. The deivation of edge oientation infomation imoses vey little omutational ost, but geatly ineases the effiieny of the method. Othe methods that have been shown to imove the efomane of Hough tansfom inlude Adative Hough tansfom (Illingwoth and Kittle, 987, Hieahial Hough tansfom (Pinen et al., 990, and Randomized Hough tansfom (u et al., ETENSION OF GENERALIED HOUGH TRANSFORM TO 3D DATA In this setion we esent an extension of the genealized Hough tansfom to 3D data. The method will be efeed to as 3D GHT in the subsequent ats of the ae. The 3D GHT follows the same inile as genealized Hough tansfom as outlined in Setion.. The main diffeene is that the gadient veto is elaed with a sufae nomal veto. The nomal vetos an be obtained by tiangulating the sufae of the objet o by fitting lana sufaes to small sets of oints in a loal neighbouhood. Vetos onneting eah tiangle to an abitay efeene oint ae stoed in the R-table as a funtion of the nomal veto oodinates. A nomal veto is onstained to be of unit length and is, theefoe, defined by two oientation angles, and ψ, as deited in Figue 3. A onneting veto is defined by two oientation angles, α and β, as well as its length. These aametes an be deived fom the oodinates of the efeene oint and the objet bounday oint: = [( x x + ( y y + ( z z ] z z α = aos x x β = aos sin( α This fomulation esults in a D R-table whee all the onneting vetos,, ae stoed in ells whose oodinates ae the oientation angles of the nomal vetos. Figue 4 demonstates how suh a D R-table is onstuted. ( P( P, P, P ψ ψ 0 Figue 4: Stoing vetos in a D R-table. The eonstution of the objet model fom the R-table is aied out by extending Equation to 3D: sin( α os( β y sin( α sin( β (3 z = z os( α whee α and β denote the oientation angles of the veto that onnets a oint to the efeene oint. Fo the detetion of the 3D objet model in a oint loud the thee oodinates of the efeene oint ae unknown aametes. Thus, the equations given in (3 ae eaanged so as to exess the unknown aametes as funtions of the known vaiables: y z = z n sin( α os( β + sin( α sin( β + os( α P( P, P, P (,, Figue 3: Paametes involved in the 3D GHT method. Having obtained the objet model in the fom of the R-table, an algoithm fo the detetion of instanes of this model in a oint loud an be outlined as follows:. onstut a 3D aumulato aay with the thee aametes of the efeene oint as the axes; α β (4 08

4 IAPRS Volume VI, Pat 3 / W5, 007. omute the nomal veto fo evey oint in the oint loud and look u vetos at oodinates (, ψ of the D R-table; 3. Evaluate Equation (4 with the oesonding sets of, α and β values to obtain x, y and z; 4. ast a vote (an inement to the aumulato aay bin oesonding to eah set of x, y and z values; 5. Reeat the voting oess fo all the oints in the oint loud; 6. The bin with the maximum vote indiates the efeene oint, and the 3D oints that ast vote fo this bin belong to an instane of the objet in the oint loud. In atie, the objet aeas in ange data with an abitay otation and sale. To aount fo the additional otation and sale aametes, Equation (4 is modified as: = + sm M. M. (5 z. y x whee = ( x T, y, z, = ( x T, y, z, = ( sin( αos( β, sin( αsin( β, os( α T s is a sale fato and M x, M y and M z ae otation maties aound x, y and z axis esetively. The inooation of a sale fato and thee otation aametes esults in an exansion of the Hough sae to seven dimensions. To evaluate Equation 5 and ast votes fo the aumulato bins, a 4D sae iumventing the entie ange of sale fatos and otation angles must be exhausted. This imlies that the ude aliation of the 3D GHT method to objet detetion an be vey exensive. Theefoe, ost-edution stategies suh as adative, hieahial and andomized voting shemes ae of geat imotane in the 3D GHT algoithm. 4. IMPLEMENTATION ASPETS The 3D GHT method as desibed in Setion 3 is omutationally exensive when the objet aeas in data with an abitay sale and otation with eset to the model. The develoment of a ost-edution stategy is thus the main hallenge in the aliation of 3D GHT. In geneal, the exeution time of Hough tansfom is moe dominated by the voting oess athe than by the seah fo a eak in the aumulato. In the absene of abitay sale and otation, the numbe of equied oeations in the voting oess is O(M, whee M is the numbe of oints in the dataset. Thus, a desiable ost-edution stategy must aim to edue the numbe of oints that ae involved in the voting oess. Randomized (u et al., 990 and obabilisti (Kiyati et al., 99 vaiations of the Hough tansfom wok based on a andom seletion of a small numbe of data oints, and ae, theefoe, suitable otions fo ontolling the omutational ost of the voting oess.. In the esene of abitay sale and otation, a 4D subset of the aamete sae iumventing the entie ange of sale fatos and otation angles is exhausted duing the voting oess. onsequently, the numbe of oeations equied in the voting oess is O(M*N 4, whee N is the numbe of intevals along eah axis of the aumulato aay. lealy, a desiable ost-edution stategy in this ase must onentate on the N 4 fato. The adative Hough tansfom (Illingwoth and Kittle, 987 edues the numbe of intevals along axes sine it begins with a oase-esolution aamete sae and ineases the esolution only in the viinity of the eak. The andomized Hough tansfom (u et al., 990 also ovides an effiient stategy to edue the numbe of bins that eeive votes in the aamete sae. In the andomized voting, instead of woking with one oint at a time, a numbe of oints suffiient fo the omutation of all aametes ae seleted fom the data. One all the aametes ae omuted, only one bin in the aumulato aay eeives a vote. In the ase of a 3D objet with seven aametes, a set of thee oints must be seleted fom the data at eah time. These oints along with thei esetive vetos fom nine equations of the fom given in Equation 5, whih an be solved fo the seven aametes. Thus, fo eah andomly seleted set only one vote is ast fo a bin in the 7D aumulato aay. 5. ONLUSIONS In this ae we esented an extension of the genealized Hough tansfom to detet abitay 3D objets in lase ange data. The oedue of stoing a 3D model in a D R-table was demonstated, and a method fo the detetion of instanes of the model in a oint loud, based on a voting oess, was desibed. It was disussed that the voting oess an be omutationally exensive in the ase that the objet aeas in data with an abitay sale and otation with eset to the model. The emloyment of a voting oess based on the andomized Hough tansfom was, theefoe, suggested to edue the omutational ost of the method. REFERENES Ballad, D.H., 98. Genealizing the Hough tansfom to detet abitay shaes. Patten Reognition, 3(: -. Duda, R.O. and Hat, P.E., 97. Use of the Hough tansfomation to detet lines and uves in itues. ommuniations of the AM, 5: -5. Filin, S., 00. Sufae lusteing fom aibone lase sanning data, Poeedings of the Photogammeti omute Vision, ISPRS ommission III Symosium, Gaz, Austia, Folani, G., Nadinohi,., Saioni, M. and ingaetti, P., 006. omlete lassifiation of aw LIDAR data and 3D eonstution of buildings. Patten Analysis & Aliations, 8(4: Geensan, M. and Boulange, P., 999. Effiient and eliable temlate set mathing fo 3D objet eognition, nd Intenational onfeene on 3-D Digital Imaging and Modeling, Ottawa, anada, Hough, P.V.., 96. Methods and means fo eognizing omlex attens, US atent Illingwoth, J. and Kittle, J., 987. The adative Hough tansfom. IEEE Tansations on Patten Analysis and Mahine Intelligene, 9(5: Illingwoth, J. and Kittle, J., 988. A suvey of the Hough tansfom. omute Vision, Gahis and Image Poessing, 44: Johnson, A.E. and Hebet, M., 999. Using sin images fo effiient objet eognition in lutteed 3D senes. IEEE Tansations on Patten Analysis and Mahine Intelligene, (5: Khoshelham, K., 006. Automated 3D modelling of buildings in sububan aeas based on integation of image and height data, Intenational Woksho on 3D Geoinfomation (3DGeoInfo '6, Kuala Lumu, Malaysia, Kiyati, N., Elda,. and Bukstein, A.M., 99. A obabilisti Hough tansfom. Patten Reognition, 4(4:

5 ISPRS Woksho on Lase Sanning 007 and SilviLase 007, Esoo, Setembe -4, 007, Finland O'Goman, F. and lowes, M.B., 976. Finding itue edges though ollineaity of featue oints. IEEE Tansations on omutes, 5(4: Olson,.F., 00. A geneal method fo geomti featue mathing and model extation. Intenational Jounal of omute Vision, 45(: Oude Elbeink, S. and Maas, H.G., 000. The use of anisotoi height textue measues fo the segmentation of aibone lase sanne data, Intenational Ahives of Photogammety and Remote Sensing, 33 (Pat B3/, Pinen, J., Illingwoth, J. and Kittle, J., 990. A hieahial aoah to line extation based on the Hough tansfom. omute Vision, Gahis and Image Poessing, 5(: Rabbani Shah, T., 006. Automati eonstution of industial installations using oint louds and images PhD thesis Thesis, Delft Univesity of Tehnology, Delft, 54. Rottensteine, F. and Biese,., 003. Automati geneation of building models fom Lida data and the integation of aeial images, Intenational Ahives of Photogammety and Remote Sensing, Volume IV/3-W3, Desden, Sithole, G., 005. Segmentation and lassifiation of aibone lase sanne data. PhD Thesis, Delft Univesity of Tehnology, Delft, 85. Vosselman, G., 999. Building eonstution using lana faes in vey high density height data, ISPRS onfeene on Automati Extation of GIS Objets fom Digital Imagey, Munih, Vosselman, G., Gote, B.G., Sithole, G. and Rabbani Shah, T., 004. Reognising stutue in lase sanne oint loud, Intenational Ahives of Photogammety, Remote Sensing and Satial Infomation Sienes, Vol. 46, Pat 8/W, Feibug, Gemany, u, L., Oja, E. and Kultanen, P., 990. A new uve detetion method: andomized Hough tansfom (RHT. Patten Reognition Lettes, (5: