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 Difficulties: various sizes, noises, distortions, complex environment Methods: vectorization-based methods, direct recognition methods

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

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

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)

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

Paradigm of Multi-resolution Arc Segmentation (MAS)

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

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

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

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

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

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

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

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

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

Various Line Thickness

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

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

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

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

Various Noise Types and Levels - Results

Various Contexts - Circle-circle intersection

Various Contexts - Arc-line intersection

Various Scan Resolutions

Complex Environment

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

Processing Time Distribution

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