Statistical Inference and Synthesis in the Image Domain for Mobile Robot Environment Modeling

1. Statistical Inference and Synthesis in the Image Domain for Mobile Robot Environment Modeling L. Abril Torres-Méndez and Gregory Dudek Centre for Intelligent Machines School of Computer Science McGill University

2. Our Application • Automatic 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 data

3. Problem Context • Pure vision-based methods • Shape-from-X remains challenging, especially in unconstrained environments. • Laser line scanners are commonplace, 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

4. From range scans like this infer the rest of the map Problem Statement From incomplete range data combined with intensity, perform scene recovery.

5. Overview 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.

6. far surface smoothness surface smoothness variations in depth close What knowledge does Intensity provide about Surfaces? • Two examples of kind of inferences: Intensity image Range image

7. edges edges What about Edges? • Edges often detect depth discontinuities • Very useful in the reconstruction process! Intensity Range

8. Range 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 Fields

9. 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 inappropriate dynamic equilibria

10. Augmented Range Map R I MRFs for Range Synthesis States are described as augmented voxels V=(I,R,E). Zm=(x,y):1≤x,y≤m: 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). R={Rx,y}, (x,y) Zm: incomplete depth values We model V as an MRF. I and R are random variables. R vx,y I

11. 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.

12. intensity intensity & range Computing the Markov Model • From observed data, we can explicitly compute Nx,y Vx,y • This can be represented parametrically or via a table. • To make it efficient, we use the sample data itself as a table.

13. intensity intensity & range • Further, we can do this even with partial neighborhood information. • Even further, if both intensity and range are missing we can marginalize out the unknown neighbors. Estimation using the Markov Model • Fromwhat 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.

14. 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 is purely causal and deterministic.

15. With the spiral-ordering Correct result Order of Reconstruction • Dramatically reflects the quality of the result. • Our reconstruction sequence is based on the amount of reliable information surrounding each of the voxels to be synthesized. • Edge information used to defer reconstruction of voxels with edges as much as possible. Info-edge-driven ordering

16. Experimental Evaluation • Obtain full range and intensity maps of the same environment. • Remove most of the range data, then try and estimate what it is. • Use the original ground truth data to estimate accuracy of the reconstruction.

17. Input Intensity Ground truth range Synthesized result Input range image Ground truth range Arbitrary shape of unknown range data Compactcase Synthesized result Scharstein & Szeliski’s Data Set Middlebury College

18. Input range image Input Intensity Ground truth range Arbitrary shape of unknown range data Less compactcase Synthesized result Scharstein & Szeliski’s Data Set Middlebury College

19. Compact Distributed Synthesized results Ground truthrange Arbitrary shape of unknown range data • Expected quality of reconstruction degrades with • distance from known boundaries • Need broader distribution of range-intensity • combinations in the sampling

20. xw rw Case 1: rw=10, xw=20. 39% of missing range Ground truth range Ground truth range Approximated scene size: 550cms. Approximated scene size: 550cms. Type I: Stripes along the x- and y-axis Synthesized Result Mean Absolute Residual (MAR) Error: 5.76 cms. Input Intensity Data courtesy of Oak Ridge National Labs & Univ. of Florida

21. Initial range 61% missing range Ground truth range (approx. scene size: 550 cms.) Initial range (rw=5, xw=25). 61% of missing range Case 2 Result Input intensity Mean Absolute Residual (MAR) Error: 8.86 cms.

22. Initial range 76% missing range Ground truth range (approx. scene size: 550 cms.) Initial range data (rw=3, xw=28). 76% missing range Case 3 Result Input intensity Mean Absolute Residual (MAR) Error: 9.99 cms.

23. Ground truth range Input intensity and range data Synthesized results

24. Ground truth range Input range data. 66% of missing range Achromatic vs. Color Results Color image Greyscale image Using achromatic image Using color image Synthesized range images

25. xw xw rw rw Ground truth range Ground truth range Case 1: rw=10, xw=20. 62.5% of missing range Approx. scene size: 600cms. Approximated scene size: 600cms. Type II: Stripes along the x-axis (like those obtained by our robot) Input Intensity Synthesized Result MAR Error: 20.72 cms.

26. Case 2 Result Input intensity 75% missing range Mean Absolute Residual (MAR) Error: 18.98 cms.

27. Case 3 Result Input intensity 78% missing range Mean Absolute Residual (MAR) Error: 20.23 cms.

28. Mike, just in case somebody ask The picture on the top appears on the paper and the bottom one on this presentation. The only difference is in the region indicated by the red ellipse in the ground truth range image (right).This regioncorresponds to the glass window of the intensityimage(left).Because it is a reflective surface, our laser range finder cannot measure it correctly.We decided to inter-polate all the incorrect measure-ments to get a new ground truth range image (bottom). Thus, the synthesized images also differ.

29. More Experimental Results

30. Conclusions • Works 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.

31. Discussion & Ongoing Work • Surface normals are needed when the input range data do not capture the underlying structure • Data from real robot • Issues: non-uniform scale, registration, correlation on different type of data • Integration of data from different viewpoints

32. Questions ?

33. Not in the paper Adding Surface Normals • We compute the normals by fitting a plane • (smooth surface) in windows of nxn pixels. • Normal vector: Eigenvector with the smallest eigenvalue of the covariance matrix. • Similarity is now computed between surface • normals instead of range values.

34. Real intensity image Initial range data Real intensity image Edge map Edge map Ground truth range Initial range scans Not in the paper Preliminary Results Synthesized range image

35. N{x,y} v(x,y) I Neighborhood of v(x,y) R The Neighborhood • The neighborhood N{x,y} is a square mask of size nxn centered at the augmented voxel. • Observations: • The neighborhood is causal • The size is important to capture relevant characteristics

37. Initial range (none) Ground truth range Known intensity image Novel View Synthesis (ongoing work) • Infer range map from intensity of current view and • from range and intensity of other views. Other view Intensity image Range image Current view to estimate range map Synthesized range

38. Results using EDGES Ground truth range Previous results MAR Errors (cms.) 10.40 8.58 16.58 13.48 12.16 11.39 19.17 7.12

39. More examples The input intensity and range data Ground truth range Synthesized results

40. Not in the paper Adding Surface Normals • We compute the normals by fitting a plane (smooth surface) in windows of nxn pixels. • The eigenvector with the smallest eigenvalue of the covariance matrix is the normal vector. • The smallest eigenvalue measures the quality of the fit. • In the range synthesis, the similarity is now computed between surface normals instead of range values.