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1、Statistics in the Image Domain forMobile Robot Environment Modeling,L.Abril Torres-Mndez and Gregory DudekCentre for Intelligent MachinesSchool of Computer ScienceMcGill University,Our Application,Automatic generation of 3D maps.Robot navigation,localization-Ex.For rescue and inspection tasks.Robots
2、 are commonly equipped with camera(s)and laser rangefinder.Would like a full range map of the the environment.Simple acquisition of data,Problem Context,Pure vision-based methods Shape-from-X remains challenging,especially in unconstrained environments.Laser line scanners are commonplace,butVolume s
3、canners remain exotic,costly,slow.Incomplete range maps are far easier to obtain that complete ones.Proposed solution:Combine visual and partial depth Shape-from-(partial)Shape,Problem Statement,From incomplete range data combined with intensity,perform scene recovery.,Overview of the Method,Approxi
4、mate the composite of intensity and range data at each point as a Markov process.Infer complete range maps by estimating joint statistics of observed range and intensity.,What knowledge does Intensity provide about Surfaces?,Two examples of kind of inferences:,Intensity image Range image,What about
5、Edges?,Edges often detect depth discontinuitiesVery useful in the reconstruction process!,Intensity Range,edges,Isophotes in Range Data,Linear structures from initial range dataAll normals forming same angle with direction to eye,Intensity Range,Range synthesis basis,Range and intensity images are c
6、orrelated,in complicated ways,exhibiting useful structure.-Basis of shape from shading&shape from darkness,but they are based on strong assumptions.The variations of pixels in the intensity and range images are related to the values elsewhere in the image(s).,Markov Random Fields,Related Work,Probab
7、ilistic updating has been used for image restoration e.g.Geman&Geman,TPAMI 1984 as well as texture synthesis e.g.Efros&Leung,ICCV 1999.Problems:Pure extrapolation/interpolation:is suitable only for textures with a stationary distributioncan converge to inappropriate dynamic equilibria,MRFs for Range
8、 Synthesis,States are described as augmented voxels V=(I,R,E).Zm=(x,y):1x,ym:mxm lattice over which the image are described.I=Ix,y,(x,y)Zm:intensity(gray or color)of the input imageE is a binary matrix(1 if an edge exists and 0 otherwise).R=Rx,y,(x,y)Zm:incomplete depth values We model V as an MRF.I
9、 and R are random variables.,R,I,vx,y,AugmentedRange Map,Markov Random Field Model,Definition:A stochastic process for which a voxel value is predicted by its neighborhood in range and intensity.,Nx,y is a square neighborhood of size nxn centered at voxel Vx,y.,Computing the Markov Model,From observ
10、ed data,we can explicitly compute,Vx,y,Nx,y,This can be represented parametrically or via a table.To make it efficient,we use the sample data itself as a table.,Estimation using the Markov Model,Fromwhat should an unknown range value be?For an unknown range value with a known neighborhood,we can sel
11、ect the maximum likelihood estimate for Vx,y.,Interpolate PDF,In general,we cannot uniquely solve the desired neighborhood configuration,instead assume,The values in Nu,v are similar to the values in Nx,y,(x,y)(u,v).Similarity measure:Gaussian-weighted SSD(sum of squared differences).Update schedule
12、 is purely causal and deterministic.,Order of Reconstruction,Dramatically reflects the quality of result Based on priority values of voxels to be synthesize Edges+Isophotes indicate which voxels are synthesized first,Region to be synthesized(target region)The contour of target region The source regi
13、on=i+r,Priority value computation,Confidence value:,Data term value:,Experimental Evaluation,Scharstein&Szeliskis Data Set Middlebury College,Input intensity image,Intensity edge map,Ground truth range,Input range image65%of range is unknown,Input data given to our algorithm,Isophotes vs.no Isophote
14、s Constraint,Results without isophotes,Results using isophotes,Synthesized range images,Ground truth range,More examples,Initial range data.79%of range is unknown.,Synthesized result.MAR error:5.94 cms.,More examples,Initial range data.70%of range is unknown.,Synthesized result.MAR error:5.44 cms.,M
15、ore examples,Synthesized result.MAR error:7.54 cms.,Initial range data.62%of range is unknown.,Adding Surface Normals,We compute the normals by fitting a plane(smooth surface)in windows of mxm pixels.Normal vector:Eigenvector with the smallest eigenvalue of the covariance matrix.Similarity is now co
16、mputed between surface normals instead of range values.,Adding Surface Normals,Initial range scans,More Experimental Results,Synthesized range image,Ground truth range,More Experimental Results,Synthesized range image,Ground truth range,Conclusions,Works very well-is this consistent?Can be more robu
17、st than standard methods(e.g.shape from shading)due to limited dependence on a priori reflectance assumptions.Depends on adequate amount of reliable range as input.Depends on statistical consistency of region to be constructed and region that has been measured.,Discussion&Ongoing Work,Surface normals are needed when the input range data do not capture the underlying structureData from real robot Issues:non-uniform scale,registration,correlation on different type of dataIntegration of data from different viewpoints,Questions?,
