multi-resolution arc segmentation: algorithms and performance evaluation jiqiang song jan. 12 th,...
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Multi-resolution Arc Segmentation: Multi-resolution Arc Segmentation: Algorithms and Performance Algorithms and Performance
EvaluationEvaluation
Jiqiang Song
Jan. 12th, 2004
IntroductionIntroduction
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 WorkRelated Work
Two classes– Vectorization-based methods
raster raw vectors arcs/circles
– Direct recognition methods
raster arcs/circles
Vectorization-based MethodsVectorization-based Methods
Arc fitting methodsCircular Hough Transform methodsStepwise extension methods
Arc fitting Circular HT Stepwise extension
Direct Recognition MethodsDirect Recognition MethodsStatistical methods
– Circular HT using pixels– Symmetry-based methods
Pixel tracking methods– Center polygon constrained tracking– Distance constrained tracking– Seeded circular tracking (SCT)
Limitations of SCTLimitations of SCTIndependency
– 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 Paradigm of Multi-resolution Arc Segmentation (MAS)Segmentation (MAS)
Parameter DerivationParameter DerivationNumber of layers:
Maximum radius:
Memory consumption:– < 3S
– S(A0, 300dpi) = 12 MB
Arc Seed DetectionArc Seed DetectionA 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)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
Dynamic Circular TrackingDynamic Circular TrackingImproved from the SCT method:
– select the adjustment position: best-of-all – measure the extensibility of an adjustable
position – Half-pixel precision adjustment
Arc LocalizationArc LocalizationLayer-by-layer localization using backup images
O(8n) O(8n)
Layer n
Layer 0 Layer 0
Layer n
Layer i, i=1..n-1
SP = {(x’, y’, r’) | x2n x’ < (x+1)2n; y2n y’ < (y+1)2n; r2n r’ < (r+1)2n}.
The dimension of SP is 2n2n2n
SP = {(x’, y’, r’) | 2xx’2x+1; 2yy’2y+1; 2rr’2r+1 }
The dimension of SP is 222
Arc VerificationArc VerificationOnly 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)Arc Verification (cont’d)
Overall confidence
Segment confidence
Curvature confidence
Thickness confidence
Distance confidence
Performance EvaluationPerformance EvaluationVector Recovery Index (VRI)
– localization accuracy, endpoint precision, and line thickness accuracy
– VRI = 0.5Dv+0.5(1-Fv) . Dv : correct detect
ion 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
Various Angles and LengthsVarious Angles and Lengths
Handle all angles wellMiss too-short arcs and flat arcs
Various Noise Types and LevelsVarious Noise Types and Levels- Gaussian Noise- Gaussian Noise
Level = 3 Level = 5
Level = 7 Level = 9
Level = 3 Level = 4
Level = 5 Level = 6
Various Noise Types and LevelsVarious Noise Types and Levels- Hard Pencil Noise- Hard Pencil Noise
Level = 8 Level = 14
Level = 19 Level = 24
Various Noise Types and LevelsVarious Noise Types and Levels- High Frequency Noise- High Frequency Noise
Level = 2 Level = 7
Level = 11 Level = 14
Various Noise Types and LevelsVarious Noise Types and Levels- Geometry Noise- Geometry Noise
Comparison with GREC Arc Segmentation Comparison with GREC Arc Segmentation Contest AlgorithmsContest Algorithms
Similar performance on synthesized imagesOutperform others on real scanned images
ConclusionsConclusions
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