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Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation

Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation. Jiqiang Song Jan. 12 th , 2004. Introduction. Arc segmentation: raster-to-graphics conversion Applications: automatic interpretation of engineering drawings, diagram recognition

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Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation

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  1. Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation Jiqiang Song Jan. 12th, 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. Arc fitting Circular HT Stepwise extension Vectorization-based Methods • Arc fitting methods • Circular Hough Transform methods • Stepwise extension methods

  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. P 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.

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

  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Dv+0.5(1-Fv) . Dv : correct detection rate, Fv : 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 = 3 Level = 5 Level = 7 Level = 9

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

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

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

  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

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