Terrain reconstruction through the contour lines of the scanned topographic maps

1. Terrain reconstruction through the contour linesof the scanned topographic maps Meir Tseitlin 2007

2. Overview • Motivation • Background • Phase 1 – Extracting contour information • Phase 2 – Reconstructing sparse contour lines • Phase 3 – Estimating contour lines heights • Phase 4 – 3D terrain interpolation • Eliminating phase 2 (an attempt) • Results and conclusions • Bibliography

3. Motivation • The growing need of 3D terrain simulations • The cost of height measurements from airplanes or satellites • GBs of precise height measurements are not required • Wide spread of topographic maps

4. Contour lines properties (restrictions) • Distance between lines maintains elevation information • The height difference between two neighbor lines is constant • Continuation • Closed (circular) lines • Ends at the map boundaries • Intersection is not common • May appear as a result of typographic error • Smoothness • Continuously differentiable (gradient extraction) Background

5. Major problems • Contour lines are the lowest layer • Other information (grid, text, topographic symbols), split the lines into small sections • The same color used for different purposes • Height stamps • Low quality scans • Color instability (Additive noise) • Low resolution • As a result – contour lines are sparse with both salt’n’pepper and additive noises Background

6. Phase 1 - Extracting contour info Phase 1 overview: • Color filtering (exp. next slide) • Thresholding (Otsu's method) + noise removal (2D Median) • Thinning (8-connected lines) • Smoothing (not implemented) Phase 1

7. Color filtering • Converting from RGB to HSV mode (Hue Saturation Value) • Leaving only brown color Phase 1

8. Contour line reconstruction • How to sort the points to imitate the natural trace of the contour line, as perceived by a human? • Very problematic task: • Contour line restrictions should be preserved • Only local (window based) continuation is not practical (due to mentioned contour line restrictions) • Earlier noise removal may expand the problem ? Phase 2

9. Curve reconstruction techniques ? • Image based approaches • Euclidean distances between extreme points of curve segments • Line tracing techniques(good continuation) • Geometric based approaches • Computing Delaunay Triangulation and filtering it according to crust to find the reconstruction • Converting to Traveling Salesman Problem (TSP) • Post-processing • Pruning and disconnected pixels remove Phase 2

10. Curve reconstruction techniques (cont.) My approaches • Basic Euclidian distance algorithm, may be good enough for obvious continuity (1-2 pixels missing) • Using global relaxation labeling algorithm was not effective • Another approach was transforming the problem into Linear Programming transportation with costs problem and solving using Simplex method. (No results, but this approach may be useful, depending on well defined restricions) Phase 2

11. Phase 3 - Estimating contour lines heights Theoretical approach • Ex: h1< h2 = h4< h3 = h5 • (Based on K. Hormann) Phase 3

12. Practical approach Estimates the direction of elevation Handles unclosed contours Uses unique contour lines properties to achieve better results Method: Pass over open lines on the border Pass over sorted (starting from large) closed lines Good (linear) performance – ~O(P(image))!!! Estimating contour lines heights (cont.) Phase 3

13. Phase 4 - Going 3D… • C1-continuation • Hermite interpolation Phase 4

14. Estimate heights without reconstructing lines • Reconstructing lines is hard, but is not our main goal and we does NOT introduce any new info to the next phase! • Alternative technique • Reconnect obviously complement segments • Convert curves into lines using polyline approximation(for the ease of finding normal vectors) • Use curve extreme points and neighbor curves to calculate relational height • Many cases should be considered… 0 0 1 2 Eliminating Phase 2

15. Results and Conclusions • Selected conclusions • Better scans can improve the computer results, even the the human can have the same result with poor conditions • “Smarter” algorithms which can handle complicated input can have better results (for example: eliminating threshold step and letting reconstruction alg. handle not binary data) • Results • Proposal of practical and efficient method for estimation of complete contour lines relative heights • Proposal of an alternative method for finding heights of sparse contour lines • MATLAB code for 70% of the processing pipeline Thank you!

16. Bibliography • Articles • S. Salvatore, P. Guitton – Contour line recognition from scanned topographic maps (2003) • K. Hormann, S. Spinello, P. Schroder - C1-continuous terrain reconstruction from sparse contours • N. Amenta, M. Bern, D. Eppstein - The Crust and the -Skeleton combinatorial curve reconstruction (1997) • T. Tversky, W. Geisler, J. Perry - Contour grouping: closure effects are explained by good continuation and proximity (2004) • Books • G. Ritter, J. Wilson – Handbook of Computer Vision Algorithms in Image Algebra. Second Edition (2001) • Web • Wikipedia.org • Peter’s functions for Computer Vision - www.csse.uwa.edu.au/~pk/research/matlabfns/ • Nina Amenta’s publications - www.cs.utexas.edu/users/amenta/pubs/pubs.html • Geometric Calculations for MATLABhttp://www.scs.fsu.edu/~burkardt/m_src/geometry/geometry.html