Surface reconstruction of sea-ice through stereo - initial steps

Rohith MVGowri Somanath

VIMS Lab

Sea iceIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

Overview

• Introduction• Need for reconstruction• Previous approaches• Camera system and field trip

• Stereo on ice images• Our algorithm• Results• Conclusion

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Need for reconstruction• “The feasibility of using snow

surface roughness to infer ice thickness and ice bottom roughness is promising….”

• “…the goal of a circumpolar high resolution data set of Antarctic sea ice and snow thickness distributions has not yet been achieved …”

• “…crucial for future validation of satellite observations, climate models, and for assimilation into forecast models…”

Ref: Workshop on Antarctic Sea Ice Thickness, 2006; Annals of Glaciology

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Previous methods – LIDAR

Echelmeyer, K.A., V.B. Valentine, and S.L. Zirnheld, (2002, updated 2004): Airborne surface profiling of Alaskan glaciers. Boulder, CO: National Snow and Ice Data Center. Digital media.

 Dalå, N. S., R. Forsberg, K. Keller, H.

Skourup, L. Stenseng, S. M.Hvidegaard, (2004): Airborne LIDAR measurements of sea ice north of Greenland and Ellesmere Island 2004, GreenICe/SITHOS/CryoGreen/A76 Projects, Final Report, pp 73.

 

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Camera systemIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

Field tripIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

SamplesIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Features in data

Smoothly changing disparityNo edge Low color variation

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Features in data

Specular Highlights

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Stereo Disparity

(d) Edge based matching(c) Non-Linear Diffusion(b) Membrane Diffusion

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

1

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

10

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

20

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

50

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

80

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

120

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

150

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

200

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

250

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Diffusion

300

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Classification

Unambiguous Low Variance

Occluded

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Algorithm for ClassificationIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

How to fill Low Variance areas?

• Don’t have any unambiguous information about the depth at those pixels

• Interpolate from Boundary

True MapSurface

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Interpolation

63 Sampled Vertices True Map

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

How to Interpolate?

• Given n points on the boundary• Triangulate…

• Which Triangulation?• Delaunay Triangulation

True Map

61 faces

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Subdivide

• Loop SubdivisionTrue Map

244 faces

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Subdivide

True Map

3904 faces

976 faces

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

What if…?

True Map

104 faces

225 faces

425 faces

244 facessubdivision

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Towards Algorithm

• Don’t know vertices…Don’t know edges• Given Vertices…What are the best

edges?• Delaunay Triangulation

• Outline• Scatter Points• Triangulate• Move Points • Repeat…

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Unstructured Triangulation Algorithm

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Advantages

• Very simple• Quality of Triangles is high

• Errors in Interpolation are low• Can handle concave shapes

and regions with holes

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Negatives

• Uses Delaunay to triangulate every iteration

• May become unstable with wrong choice of parameters (very rare)

• May not converge

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Finite Element Method

Courtesy : A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis, Petr Krysl

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Finite Element Method

Courtesy : A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis, Petr Krysl

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Finite Element Method

Courtesy :http://cfdlab.ae.utexas.edu/~roystgnr/libmesh_intro.pdf

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

True surface True map 63 samples on boundary

Interpolation with Delaunay

Delaunay Triangulation (61 faces) Delaunay + Loop Subdivision (244 faces)

Interpolation of Delaunay + Loop Subdivision

Unstructured triangulationFrom [1]

Interpolation with Unstructured triangulation

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Result

Ambiguous Unambiguous disparity

Triangulation Final disparity

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Comparison

(c) Non-Linear Diffusion

(b) Membrane Diffusion

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

(e) Ground Truth

More resultsIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

More resultsIntroduction Stereo on Ice Images Our Algorithm Results Conclusion

Conclusions

• In areas containing very low color variation, interpolation gives better results than image matching

• Heuristic for classifying image regions• Efficient methods for interpolation using

triangulation and FEM

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Future Directions

• Include disparity variance in factors for classification

• Change the differential equation to model developable surfaces

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Publications• Towards Estimation of Dense Disparities from Stereo

Images Containing Large Textureless Regions. Rohith MV, Gowri Somanath, Chandra Kambhamettu, Cathleen Geiger. 19th International Conference on Pattern Recognition. December 2008. Tampa, USA

• Reconstruction Of Snow And Ice Surfaces Using Multiple View Vision Techniques. Gowri Somanath, Rohith MV, Cathleen Geiger, Chandra Kambhamettu. 65th Eastern Snow Conference, May 2008, Vermont, USA.

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Bibliography

• Daniel Scharstein, Richard Szeliski. A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms. IJCV 2001.

• D. Scharstein, R. Szeliski, Stereo matching with Non-linear Diffusion. Computer Science TR 96-1575, Cornell University, Mar 1996.

• D. Scharstein, R. Szeliski. Stereo Matching with Non-linear diffusion. CVPR. June 1996.

• Jochen Alberty, Carsten Carstensen, Stefan Funken, Remarks Around 50 Lines of MATLAB:Short Finite Element Implementation, Numerical Algorithms,Volume 20, 1999.

• P. Persson, G.Strang. A simple mesh generator in Matlab. SIAM Review, Volume 46 (2), June 2004..

Introduction Stereo on Ice Images Our Algorithm Results Conclusion

Acknowledgements

• Dr. Chandra Kambhamettu• Dr. Cathleen GeigerThis work was made possible by National

Science Foundation (NSF) Office of Polar Program grants, ANT0636726 and ARC0612105.

Introduction Stereo on Ice Images Our Algorithm Results Conclusion