Geometric clustering for line drawing simplification

Pascal Barla – Joëlle Thollot – François Sillion

ARTIS, GRAVIR/IMAG-INRIA

2Geometric clustering for line drawing simplification

Introduction

• Line drawings are useful– Convey shape, tone, style– Used in illustration, art– Created in many different ways

• Complexity issues– Artists know how to tune

complexity– Computers don’t

• Often too many lines…

3Geometric clustering for line drawing simplification

Problem statement

• Lines from various sources– Scanned drawing– Digital drawing– Image processing– Non-photorealistic rendering

• Simplification– Smaller set of lines– Keep drawing’s overall structure

Scanned drawing of a hand

Non-Photorealistic Rendering [Grabli]

4Geometric clustering for line drawing simplification

Outline

• Related Work• Methodology• Clustering algorithm• Geometric strategies• Results• Conclusions

5Geometric clustering for line drawing simplification

Related work

• Density reduction– trees in object-space [Deussen]– in image-space [Wilson][Grabli]

• Indication– for complex textures

[Winkenbach]

• Oversketching– smoothed [Baudel]– constrained [Igarashi]

Oversketching tool [Baudel]

Density reduction [Grabli]

Texture indication [Winkenbach]

6Geometric clustering for line drawing simplification

• levels of detail for NPR– In texture-space

• Tonal Art Maps [Praun]

– In object-space • WYSIWYG NPR [Kalnins]

• Overall limitations– Specific solutions– Simplify = remove– No perceptual consideration

NPR with hatching patternsExhibiting LOD behaviors [Kalnins]

Related work

7Geometric clustering for line drawing simplification

• Perceptual organization [Boyer&Sarkar]– Only group lines

• Based on human perception• Study criteria independently (e.g., parallelism)

Related work

A schematic sun figure and the two largest parallel groupings [Rosin]

8Geometric clustering for line drawing simplification

• Contributions– Identify common behavior

• Oversketching, Density reduction and Levels of detail

• Perceptually motivated

– Various simplification strategies• Not only deletion

• Limitations– Low-level – Static 2d drawings

Contributions / limitations

9Geometric clustering for line drawing simplification

Outline

• Related Work

• Methodology• Clustering algorithm• Geometric strategies• Results• Conclusions

10Geometric clustering for line drawing simplification

• Single control param – simplification scale

• 2 steps:– Automatic Clustering

• Common to envisioned applications

– Line creation• Geometric strategies• Application dependent

Methodology

Clustering

Line creation

11Geometric clustering for line drawing simplification

• Input – 2d Vectorized lines– Attributes: e.g., color– Static drawings

• Clustering output– Line clusters

• Final output– Vectorized lines

+ attributes

Methodology

Clustering

Line creation

12Geometric clustering for line drawing simplification

• Proximity is not enough– Forks

– Hatching groups

Methodology

Unnatural fork behavior

Unnatural hatching group behavior

Two simplifying lines keeping underlying fork structure

Three simplifying lines keeping underlyingstack structure and orientation

13Geometric clustering for line drawing simplification

• Perceptual grouping [Palmer]– Criteria: proximity, parallelism,

continuation,and color.

• Integrated in clustering constraints– Definition of an -group (see paper)

Methodology

14Geometric clustering for line drawing simplification

Outline

• Related Work• Methodology

• Clustering algorithm• Geometric Strategies• Results• Conclusion

15Geometric clustering for line drawing simplification

• Clustering = partition

• Greedy algorithm

Clustering algorithm

16Geometric clustering for line drawing simplification

• Clustering = partition

• Greedy algorithm– Clustering 2 lines/groups

• Do they form an -group ?

– Error measure• Using attributes

Clustering algorithm

17Geometric clustering for line drawing simplification

• Clustering a pair of lines– Example of an invalid pair

(pb. with parallelism)

Clustering algorithm

18Geometric clustering for line drawing simplification

• Clustering a pair of lines– Example of an invalid pair

(pb. with parallelism)

– Five valid configurations (see paper)• Correspond to -groups on a pair of lines• Favor parallelism, continuation and proximity

Clustering algorithm

19Geometric clustering for line drawing simplification

• Error measure– Based on proximity

• Normalized between 0 and 1

Clustering algorithm

20Geometric clustering for line drawing simplification

Clustering algorithm

• Error measure– Based on proximity

• Normalized between 0 and 1

– Can take attributes intoaccount (e.g. color)• Normalized between 0 and 1• Combined in a multiplicative

way

21Geometric clustering for line drawing simplification

• Implementation– Clustering graph

• Graph node = line• Graph edge = valid pair• Error stored on edges

Clustering algorithm

22Geometric clustering for line drawing simplification

• Implementation– Clustering graph

• Graph node = line• Graph edge = valid pair• Error stored on edges

– Greedy algo = edge collapse• Collapse min error edge• Delete degenerated edges• Update graph locally

Clustering algorithm

23Geometric clustering for line drawing simplification

Outline

• Related Work• Methodology• Clustering algorithm

• Geometric Strategies• Results• Conclusion

24Geometric clustering for line drawing simplification

• Geometric strategies– Work on clustering output

• May use clustering history

– Many possibilities– Application dependent

Geometric strategies

Clusters

25Geometric clustering for line drawing simplification

• Geometric strategies– Work on clustering output

• May use clustering history

– Many possibilities– Application dependent

• 2 basic strategies– Average line– Most significant line

Average line strategy

Longest line strategy

Clusters

Geometric strategies

26Geometric clustering for line drawing simplification

Outline

• Related Work• Methodology• Clustering algorithm• Geometric Strategies

• Results• Conclusion

27Geometric clustering for line drawing simplification

• Density reduction (scanned drawing)– A single strategy– Average line

Results

357 input lines 87 output clusters

28Geometric clustering for line drawing simplification

• Density reduction(3D model)– Two different strategies

• Average line for the leaves

• Longest line for the inner part

Results

531 input lines

294 clusters

256 clusters

29Geometric clustering for line drawing simplification

Results

• Density reduction(scanned drawing)– Taking attributes

into account– Lab color threshold

30Geometric clustering for line drawing simplification

• Oversketching– Apply simplification iteratively

– Drawing sensitivity = • Each new a sketch has its own sensitivity

– Specific average line strategy• Give higher priority to last drawn line

– See video…

Results

31Geometric clustering for line drawing simplification

• Levels of detail

Results

32Geometric clustering for line drawing simplification

• Levels of detail– Increasing

• Simplify output of finer level

– Two different strategies• Average line for contour• Longest line for hatching

– See video…

Results

33Geometric clustering for line drawing simplification

Conclusions

34Geometric clustering for line drawing simplification

Conclusions

• 2-step approach is valuable– Analysis of common behavior– Adaptation to application goals– 3 application examples

35Geometric clustering for line drawing simplification

Conclusions

• 2-step approach is valuable– Analysis of common behavior– Adaptation to application goals– 3 application examples

• Perceptual grouping– Incorporate a human vision model in NPR– Perception of a drawing

36Geometric clustering for line drawing simplification

Conclusions

• Future work

37Geometric clustering for line drawing simplification

Conclusions

• Future work– Improve clustering

• More perceptual criteria (e.g closeness)• Individual control for each criterion• Medium- and high-level processing (i.e drawing

structure)

38Geometric clustering for line drawing simplification

Conclusions

• Future works– Create new applications

• Automatic creation of Tonal Art Maps• Morph transitions for LODs• Clustering of 2d lines for animation• Simplification of lines lying on surfaces

39Geometric clustering for line drawing simplification

Acknowledgements

• Gilles Debunne for the video• ARTIS team’s many reviewers• Lee Markosian and Chuck Hansen for

“english cleanup”.