1. Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation Jiqiang Song Jan. 12 th, 2004

2. Introduction Arc segmentation: raster-to-graphics conversion Applications: automatic interpretation of engineering drawings, diagram recognition Difficulties: various sizes, noises, distortions, complex environment Methods: vectorization-based methods, direct recognition methods

3. Related Work Two classes – Vectorization-based methods raster  raw vectors  arcs/circles – Direct recognition methods raster  arcs/circles

4. Vectorization-based Methods Arc fitting methods Circular Hough Transform methods Stepwise extension methods Arc fitting Circular HT Stepwise extension

5. Direct Recognition Methods Statistical methods – Circular HT using pixels – Symmetry-based methods Pixel tracking methods – Center polygon constrained tracking – Distance constrained tracking – Seeded circular tracking (SCT)

6. Limitations of SCT Independency – Depends on straight line recognition to get seeds – Depends on the OOPSV model to remove false alarms Incapable of detecting too-small or too-large arcs – Too small: cannot find straight line seeds – Too large: cannot find curvature from three line seeds

7. Paradigm of Multi-resolution Arc Segmentation (MAS)

8. Parameter Derivation Number of layers: Maximum radius: Memory consumption: – < 3S – S(A0, 300dpi) = 12 MB

9. Arc Seed Detection A pixel-level arc seed is a segment of raster shape showing the circular curvature. Linear shape checking detects whether the neighborhood of p appears a linear shape. P

10. Arc Seed Detection (cont ’ d) Use two concentric circle windows centered at p’ to detect arc seeds – make the detection more efficient – make the detection more sensitive – make the accepted arc seed more reliable R inner = 8 pixels R outer = 15 pixels

11. Dynamic Circular Tracking Improved from the SCT method: – select the adjustment position: best-of-all – measure the extensibility of an adjustable position – Half-pixel precision adjustment

12. Arc Localization Layer-by-layer localization using backup images O(8 n ) O(8n) Layer n Layer 0 Layer n Layer i, i=1..n-1 SP = {(x’, y’, r’) | x  2 n  x’ < (x+1)  2 n ; y  2 n  y’ < (y+1)  2 n ; r  2 n  r’ < (r+1)  2 n }. The dimension of SP is 2 n  2 n  2 n SP = {(x’, y’, r’) | 2x  x’  2x+1; 2y  y’  2y+1; 2r  r’  2r+1 } The dimension of SP is 2  2  2

13. Arc Verification Only small or short arcs should be verified – “small” means the radius is small – “short” means the length of arc is short Difficulty: how to distinguish mis-detected arcs from true arcs in complex environment

14. Arc Verification (cont ’ d) Overall confidence Segment confidence Curvature confidence Thickness confidence Distance confidence

15. Performance Evaluation Vector Recovery Index (VRI) – localization accuracy, endpoint precision, and line thickness accuracy – VRI = 0.5  D v +0.5  (1-F v ). D v : correct detection rate, F v : false detection rate Synthetic images: various angles, arc lengths, line thickness, noise level, contexts Real scanned images: performance in complex environment, time complexity Comparison with others

16. Various Angles and Lengths Handle all angles well Miss too-short arcs and flat arcs

17. Various Line Thickness

18. Various Noise Types and Levels - Gaussian Noise Level = 3Level = 5 Level = 7Level = 9

19. Level = 3Level = 4 Level = 5Level = 6 Various Noise Types and Levels - Hard Pencil Noise

20. Level = 8Level = 14 Level = 19Level = 24 Various Noise Types and Levels - High Frequency Noise

21. Level = 2Level = 7 Level = 11Level = 14 Various Noise Types and Levels - Geometry Noise

22. Various Noise Types and Levels - Results

23. Various Contexts - Circle-circle intersection

24. Various Contexts - Arc-line intersection

25. Various Scan Resolutions

26. Complex Environment

27. Comparison with GREC Arc Segmentation Contest Algorithms Similar performance on synthesized images Outperform others on real scanned images

28. Processing Time Distribution

29. Conclusions Multi-resolution arc segmentation method – Self-contained & robust – Handles a wide range of arc radius – Improves the dynamic adjustment in tracking – Verifies arcs using confidence-based protocol Future work – Simplification of time complexity – Capability in handling dashed arcs