International Symposium of Robotics and Automation, August 25-27, 2004RangeSynthesisfor3DEnvironmentModeling三维环境建模的范围内的合成Stillwatersrundeep.流静水深流静水深,人静心深人静心深Wherethereislife,thereishope。有生命必有希望。有生命必有希望International Symposium of Robotics and Automation, August 25-27, 2004Our ApplicationAutomatic generation of 3D maps.Robot navigation, localization - Ex. For rescue and inspection tasks.Robots are commonly equipped with camera(s) and laser rangefinder. Would like a full range map of the the environment. Simple acquisition of dataInternational Symposium of Robotics and Automation, August 25-27, 2004Problem ContextPure vision-based methods Shape-from-X remains challenging, especially in unconstrained environments.Laser line scanners are commonplace, butVolume scanners 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 International Symposium of Robotics and Automation, August 25-27, 2004Problem StatementFrom incomplete range data combined with intensity, perform scene recovery.From range scans like thisinfer the rest of the mapInternational Symposium of Robotics and Automation, August 25-27, 2004Overview of the MethodApproximate 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.International Symposium of Robotics and Automation, August 25-27, 2004What knowledge does Intensity provide about Surfaces?Two examples of kind of inferences:Intensity image Range imagesurface smoothnessvariations in depthsurface smoothnessfarcloseInternational Symposium of Robotics and Automation, August 25-27, 2004What about Edges? Edges often detect depth discontinuitiesVery useful in the reconstruction process! Intensity RangeedgesInternational Symposium of Robotics and Automation, August 25-27, 2004Isophotes in Range Data Linear structures from initial range dataAll normals forming same angle with direction to eye Intensity RangeInternational Symposium of Robotics and Automation, August 25-27, 2004Range synthesis basis Range and intensity images are correlated, 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 FieldsInternational Symposium of Robotics and Automation, August 25-27, 2004Related WorkProbabilistic 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 equilibriaInternational Symposium of Robotics and Automation, August 25-27, 2004MRFs for Range SynthesisStates are described as augmented voxels V=(I,R,E).Z Zmm=(x,y):1x,ym=(x,y):1x,ym: mxm lattice over which the image are described.I = II = Ix,yx,y, (x,y), (x,y) Z Zmm: intensity (gray or color) of the input imageE is a binary matrix (1 if an edge exists and 0 otherwise).R=RR=Rx,yx,y, (x,y), (x,y) Z Zmm: incomplete depth values We model V as an MRF. I and R are random variables.RI vx,yAugmentedRange MapIRInternational Symposium of Robotics and Automation, August 25-27, 2004Markov Random Field ModelDefinition: 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.International Symposium of Robotics and Automation, August 25-27, 2004Computing the Markov ModelFrom observed data, we can explicitly compute intensityintensity & rangeVx,yNx,y This can be represented parametrically or via a table.To make it efficient, we use the sample data itself as a table.International Symposium of Robotics and Automation, August 25-27, 2004 Further, we can do this even with partial neighborhood information. Estimation using the Markov ModelFromwhat should an unknown range value be?For an unknown range value with a known neighborhood, we can select the maximum likelihood estimate for Vx,y. Even further, if both intensity and range are missing we can marginalize out the unknown neighbors. intensityintensity & rangeInternational Symposium of Robotics and Automation, August 25-27, 2004Interpolate PDFIn general, we cannot uniquely solve the desired neighborhood configuration, instead assumeThe values in Nu,v are similar to the values in Nx,y, (x,y) (u,v).Similarity measureSimilarity measure: : Gaussian-weighted SSD (sum of squared differences).Update schedule is purely causal and deterministic.International Symposium of Robotics and Automation, August 25-27, 2004Order 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 region = i + rInternational Symposium of Robotics and Automation, August 25-27, 2004Priority value computationConfidence value:Data term value:Normalization factorIsophote (direction and range)Unit vector orthogonal to Number of voxels having an edge in Nx,yInternational Symposium of Robotics and Automation, August 25-27, 2004Experimental EvaluationScharstein & Szeliskis Data Set Middlebury CollegeInput intensity imageIntensity edge mapGround truth rangeInput range image65% of range is unknownInput data given to our algorithm International Symposium of Robotics and Automation, August 25-27, 2004Isophotes vs. no Isophotes ConstraintCaseI: 65% of range is unknownCase II: 62% of range is unknownInitial range dataResults without isophotesResults using isophotesSynthesized range imagesGround truth rangeInternational Symposium of Robotics and Automation, August 25-27, 2004More examplesInitial range data. 79% of range is unknown.Synthesized result.MAR error: 5.94 cms.Input intensity imageIntensity edge mapInitial range dataGround truth rangeInternational Symposium of Robotics and Automation, August 25-27, 2004More examplesInput intensity imageIntensity edge mapInitial range dataGround truth rangeInitial range data. 70% of range is unknown.Synthesized result.MAR error: 5.44 cms.International Symposium of Robotics and Automation, August 25-27, 2004More examplesInput intensity imageIntensity edge mapInitial range dataGround truth rangeSynthesized result.MAR error: 7.54 cms.Initial range data. 62% of range is unknown.International Symposium of Robotics and Automation, August 25-27, 2004Adding 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 computed between surface normals instead of range values. International Symposium of Robotics and Automation, August 25-27, 2004Adding Surface NormalsGround truth rangePrevious synthesized resultInitial range data Synthesized result using surface normalsInternational Symposium of Robotics and Automation, August 25-27, 2004Initial range scansMore Experimental Results Synthesized range imageGround truth rangeEdge map Real intensity imageInitial range dataReal intensity imageEdge mapInternational Symposium of Robotics and Automation, August 25-27, 2004Initial range scans More Experimental Results Synthesized range imageGround truth rangeEdge map Real intensity imageInitial range dataReal intensity imageEdge mapInternational Symposium of Robotics and Automation, August 25-27, 2004ConclusionsWorks very well - is this consistent?Can be more robust 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.International Symposium of Robotics and Automation, August 25-27, 2004Discussion & Ongoing WorkSurface 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 viewpointsInternational Symposium of Robotics and Automation, August 25-27, 2004Questions ?