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1、Statistics in the Image Domain for Mobile Robot Environment Modeling,L. Abril Torres-Mndez and Gregory Dudek Centre for Intelligent Machines School of Computer Science McGill University,Our Application,Automatic generation of 3D maps. Robot navigation, localization - Ex. For rescue and inspection ta
2、sks. Robots 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 commonp
3、lace, but Volume 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,Problem Statement,From incomplete range data combined with intensity, perform scene recovery.,Overv
4、iew of the Method,Approximate 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 ima
5、ge Range image,What about Edges?,Edges often detect depth discontinuities Very useful in the reconstruction process!,Intensity Range,edges,Isophotes in Range Data,Linear structures from initial range data All normals forming same angle with direction to eye,Intensity Range,Range synthesis basis,Rang
6、e 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).,Mark
7、ov Random Fields,Related Work,Probabilistic 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 distribution can converge to
8、 inappropriate dynamic equilibria,MRFs for Range 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 image E is a binary matrix (1 if an edge exists and 0 otherwise).
9、R=Rx,y, (x,y) Zm: incomplete depth values We model V as an MRF. I and R are random variables.,R,I,vx,y,Augmented Range 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
10、 nxn centered at voxel Vx,y.,Computing the Markov Model,From observed 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,From what should an unknown range v
11、alue be? For an unknown range value with a known neighborhood, we can select 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). Simila
12、rity measure: Gaussian-weighted SSD (sum of squared differences). Update schedule 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, R
13、egion to be synthesized (target region) The contour of target region The source region = 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 ra
14、nge image 65% of range is unknown,Input data given to our algorithm,Isophotes vs. no Isophotes 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.,
15、More examples,Initial range data. 70% of range is unknown.,Synthesized result. MAR error: 5.44 cms.,More 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
16、pixels. Normal vector: Eigenvector with the smallest eigenvalue of the covariance matrix. Similarity is now computed 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
