Multi-resolution Arc Segmentation: Algorithms and Performance Evaluation

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
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)
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Parameter Derivation

• Number of layers
• Maximum radius
• Memory consumption
• lt 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.

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Arc Seed Detection (contd)

• 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
Arc Localization

• Layer-by-layer localization using backup images

Layer n
Layer i, i1..n-1
Layer 0
SP (x, y, r) x?2n ? x lt (x1)?2n y?2n ?
y lt (y1)?2n r?2n ? r lt (r1)?2n. The
dimension of SP is 2n?2n?2n
SP (x, y, r) 2x?x?2x1 2y?y?2y1
2r?r?2r1 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 (contd)

• 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?Dv0.5?(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

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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
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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
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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