Transform Clustering for Model-Image Feature Correspondence

En this paprr we present a novel technique for establishing a rohusl a n d arrurat~ rorr~spondence between a 3d model and a 2d image. \Vt. present a transform clustering approach to i so l a t~ the transformation that maps the mad01 f ~ a t t ~ r e n to the image featur~s . Tt is shown that this transform clustering techniqu~ alleviates the prohIerns with using the traditional Hough transform techniqr~es used 'by previous researchen. dV'r dcmonstra t~ the ~ffectiveness of our approach irk ~st imat ing the position and and pose ofan autonomous rnohilp rohot navigating in an outdoor urban environn~ent. We prespnt experimental results of test in^ this approach using a model of an airport scone. Thc task of establishing a reliable and acri~rate correspondence between an image of x scene and a stored model of it ocrl~ra in a large n u m b ~ r of computer vision problems. Autonomous navigation of a mobile robot given n priori modd nf the pnvisonment and modelbased object recognition at0 two ~xarnples of romputcr vision tasks in which t h ~ niodel-image correspondence needs to be addressed. In the contpxt of autonomous navigation, the robot is provided with a preloaded world model of t h e environment. The world modcl could be in direrent forms, such as a Digilal Elemtian Map IDEM), a CAD description, or a flour map. The robot uses a n onboard camcra t o image the environment . Oncc we establish a carr~spondence bei w w n the image and the model, the robot's position and pose can be drtprmined. This position information can bp used by the robot to SZICCPI(SIUIJ~ navigate in its environmmt . In the r o n t ~ x t of model-based o b j ~ c t recognition, WP are given a geometric description of the object to be recognised and an image or the scene in which the object is prcs~n t . The task i s to isolate the object in the scene by using the image. Mod~l-image correspondenc~ are particularly diffiri~lr because the image and the model are usually in diffccsent formats. diRercnt ro-ordinate frames and of different dimensions. h popular approach to solving this problem is t o extract features from the image and search the model description for the corresponding set of features. The type of It=al~rr~e required and the number oS features used dppends on the rnod~l description and what is assumed to be knnwu ahout the scene. For example, in navigating the Thi* m a r c h war nupported bv in part by Army R e a r c h OF fice contract UAAL03-9 1-I;-0050 and in part by Air Force Ofice or Scicntifir Heu~arch (AFSC) contract E49620-8PCO04-4. rohot in an indoor s t r r i r t r~ r~d rnvironm~nt with a g i v ~ n CAD n ~ o d ~ l of the environment, it is common prart ire to ~ I S P l i n ~ SPgrnPntc a5 feat I I ~ W 131. On the ot h ~ r hand, in navigating the robot in an outdoor mountainous l ~ r r a i n givm a D E M nr the ~nvironmcnt, using curves may be a 10~icd choice [9]. TypicaUv, in t h ~ s e prohl~rns t h ~ modrl and tlir camera (rottot) are sppcifipd in two different ro-ordinate systems. O n c ~ we exlract t h ~ rel~vant featurcs from the image and identify the corresponding Fcatures in the model, WP can romputer the transformation 7 that maps Ihc model f~atztr~s into thp image fpatures. The pararnetcrs of this transformation are the rcquirrd position and pose of the camrra [robot ) with respect to the model. Solving for the pxrarneters of 7 , once a set of model-image irature corrtspondences is rstablished, is a very WPII studied problem ['Zj. Therefore, t h ~ crucial txsk to be accomplished is that of establishing a reliable and accurate correspondence. Xoise, occlusions, errors in feature detrction and inaccurate modcl dcscriptions further complicate this cor~espondence problem. Transfarm Cluatering: Previous r~searchers h a v ~ considered the technique o l matching a key model feat u r ~ , such as a long e d ~ e or a set of lines in specific orientations. t o establish an initial transtormation [ l , fi]. Suhwqrtrnt assignmpnts are thrn used to refine this transformation. New assignments arc S C ~ P C ~ P ~ on predictions of a model feature, projected into the image using tlre cnrrent transformat ion. t lowev~r , these techniques assume that it is possible to initially sderi a correct key m o d ~ l Feature. which may not alwavs be possiblc. Some sesearch~rs used the generalized H o u ~ h transform and its related parameter hashing techniques to perform fmnsJom rlr~st~ring to isolate the transformation mapping the modpl f e a t ~ ~ r ~ s into the image featur~s 16, 5, ID]. The g ~ n ~ r a l i z ~ d tlough transform works by first quantizing the n-dimmsional parameter spare in to discrete huckets or bins. Thc param~ters are the components describing 7. From thtgiven image. Sraturcs arc extracted using a feature extractor. Thpn all the possible modcl-image f ~ a t u r e cotrespondences are hypothesized and, for each hypothesis, the parameter vector is computed. For each parameter vector so computed, its n components are quantized a r~d used as indices to vote in one of t h ~ n-dimensional buckets. S~arching for large cIustrts is then accomplished by finding the buckets with a large nurnhprs of entries. Sometimes it is possible that one correspondence may not give explicitly aU the components of the parameter vector. but may only give a rangp of possible va lu~s far ~ a r h component. In this case. entries ate ma& into all the buckets within range. The a d v a n t a ~ r of this approach i s that c l u s t ~ r i n ~ provides a robust criterion b r firlrrting d i d m o d ~ l fcaturr assignrnmts. The cfbcts of miwing or inrotrpcf roature due to occlusion, ahadnws, or Inw rontra5t. arp not bit. The prohlema associat~d with using the H o u ~ h transform approach to transform rlueterinq are that l a r g ~ transform clust~ra may occur randomly. IT thesc clustrra are as l a r g ~ or I a r ~ o r than those due to the correct transrorm. the estirnalinn proc~durr that reFica only on the H o u ~ h transform will tw Prronmus. If t h ~ nllrnher of hucketrr is incrrased, thpn t h ~ po~~ihi!ity of random large c lus t~rs is aIlrviatrd but t h~ ni lmb~r of corn put ations grows rapidly. Grimson [1] summarizes t h ~ s ~ problems with the RFnPralirrd 1io11gh transform, This pappr pr-pnta a rnrthod to r e d u r ~ t h ~ probl ~ m r ~ s o c i a t ~ d with thr tfough transform approach to tmnsiorrn c lus t~t ing hy ilning a partition of thc paramet r r space. whirh is not nrcrssarily uniform. The partition is, in fact, ~nt~l l tgrnl and uses a pnon rnodrl information, Due to tttp gmmrtric constraints irnposd hy the model and thp campra ~eornetry. not all model features may he t.r*tbkr in dl camera positions. Typically orclusions b ~ t w r m the model i ~ a t u r w affect their visibility at rariour po~ir ions. However, since wr know the 3d dwctip tionfi of tho rnodpl f~at r l rm, t h r s ~ ~ ~ o m e t r i l : consttainta can br prr-computed and uard t o partition the pasame tor sparr to reduce I ~ P probability of the ocrurrrnrr of random transform cluatrrs. demonstrate t t ~ c k t i v e n e s s of our approach in ~stirnating t h ~ pmition anrl a n d pose of an autononious rnohilc robot. The robot is assumed to be navigating in an outdoor, urban environm~nt. The 3d description of the lines lt hat constitun* the rooftops of the buildin~s is given m a aorid modrl. Tbp position and pose of the robot are estimated by ~atahlishing a cortespondpncp between the linw pxtractpd from the imagc (image fratures) and the lines that constitute rooftops of the 1)uildin~s (model teat u r ~ s ) . tly rxploiting t he visibility conatrainf s imposed by i h r 3d world niodel and the camera Emmetry, we partition t h p paramrtrr space i n t o into disrinct, non-overlapping w~ i 0 n s callrd Fdge I'esrbrlity Hegtons (EYRs) [7]. In rach of thrsp r~gions , w e also Rtarr thr list of model featuwri that arp visible from within that region. If'e then hypothesite a correspondence b ~ t w w n all pairs of model and i m a g ~ featurm and romptltr I ~ P range of possiblc traasiwrmations for each hypothesis. lt'c vote in all thp r r~ ions in the pararnetpr sparv wlrer~ this ~ransfotmaiinn I R d i d . Alter consider in^ all t hc pair~ngs. u * ~ spIprt t htr ~ ~ i o n s in the parameter space with the I a r g numbers of votes the candirlat~ EV Ks lot position estirnafion, The actual correspondence and position estimation are then pcrfotmcd hy a ronstrairl~d search prncrsfl within thesp EVRs us in^ a i n t ~ r p r ~ t a t i o n t r w search paradigm. PARTITIONING THE PARAMETER SPACE Consider I he world coordinate system OXJ'i! and the robot coordinate system O'X7"Zr shown in F i g u r ~ 1. Generally, thp transformation 7 that transforma 0 4 Y 2 into O'.YfY'%' has six dwltes of freedom: t h r e e rotational and t hrpp translational. Sometimes, depending on the applita! ion, somc or these d q r m of Irm-dorn can be elirniFigure 1: Tbr world and robot co-ordinatr systems nated. Most mohilr robot self-location tmks make the assumptinn rhat t h ~ rohot is on t h ~ gro~tnd (04Y plane), so the Z-translation (the h ~ i ~ h t aT the rohot above the round) is assumed to be known or to he zero. The ramora on tho robot is assi~rned t o have zero roll (rotation about X-axis),.and the tilt a n ~ l r : of the camera, (rotation about the Y i s ) is asurnrd to be meuurable. So, thrrc arr rffrrf ivdy t hrw pararnr t r t~ in the transformat ion: two translational (X, Y ) and one rotatianal B [the pan angle of tlir camera. wh i rh is r rotation about the Z-axis). Likrwise. in this paper wp havr only three parametprs of 7: X, Y and 8. Thr parametrr space of tbc trannformatioa is thus the r n t i r ~ CIXY plane and f he r a n p of mbot orientation B is 0 t h r o u ~ h 360 degrw. In this sr r t~on. we bri~flg we dwcribe a method for partitioning thr O.YY plane into rq ions cdled Edge Visibility Hqions ( E V R s ) using thc ~ i w n world model d+ srription. f'nr more details sw [TI. A ~ s o c i a t d with each EV It is a list or the world model irati~tes crslbre in that t~ gian, cal ld thc t-iaibility Itnt (\'I,). No two adjacent EVRR havp the same 1'L. A150 stored lor each entry in the 1'1, or an EYR is the range or rohot orientations from which the f ra t i~re i s visiblr. Thus, rach EVR is a region of mpare which has the topnlo~ical property that from i ta pointn, t hr same set of rrlgrs of the model are visible through a complete rirrt~lar $can. The EVR repm~ntat ion pattitions t h ~ n t i r r parameter space of (X,Y.B) and capturm thr vicihility constraints h ~ t w r e n thr world model features. The a l~or i tkm that divides the OXY plane into the dmirrd EVfls. along with thrir maociatrd VLs, usw thrw suhproc~sacs cdEed Split. Pmj~ct, and ,Werqe. The a l p rithm's b a s ~ r idca is to start with theentire OXY plano as onr EVR with a NITLL vi*ihili ty list. Each of t he polygons that makes up the build in^'^ rooftop in the world model is ronsidtrcd in turn by extcndiag its edges, and the EVRs that ate interseri~ti arp d i r i d ~ ~ l into two new onm. The nrw EVRs then r ~ p l a c ~ the old one, and the Vl-s of the new IlYRs a r ~ ilpdatr*tl to account fat the viaihility of this d g e by cansid~ring it t o be visible in onp half-plane, say thp half-planr into the left of the edge, and invisible in the ofhpr. Thp Split process handles thin updating. For each nPuroortop considered, thc mutual occlusion 01 the mart op's P ~ R P R with the other existing rooftops is handled by forming the .*hadow wgion of t hmo erlgs on the other existine, rooftaps. The Pmj~rt process handles the forming aT thrsp shadow regions. Finally, the M r y e process con. ratt-natrs all the adjacent 13'Ra with identical \'LR into nnr CVU. After parfitioning the OXY plane into Ei'R.s, Figure 2: (a) World model (b) Robot view the range of the robot's orientations for which each model feature in the VL of an EVR is visible, is also computed and stored. An efficient method to compute these ranges is also developed. Figure 2(a) shows the world model and Figure 5(b) shows the EVR description computed from this world model.