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 Line ThicknessVarious Line Thickness

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

Various Noise Types and LevelsVarious Noise Types and Levels- Results- Results

Various ContextsVarious Contexts- Circle-circle intersection- Circle-circle intersection

Various ContextsVarious Contexts- Arc-line intersection- Arc-line intersection

Various Scan ResolutionsVarious Scan Resolutions

Complex EnvironmentComplex Environment

Comparison with GREC Arc Segmentation Comparison with GREC Arc Segmentation Contest AlgorithmsContest Algorithms

Similar performance on synthesized imagesOutperform others on real scanned images

Processing Time DistributionProcessing Time Distribution

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