Density Measure for Line-Drawing Simplification

1
Density Measure for Line-Drawing Simplification
Stéphane Grabli Frédo Durand François X. Sillion
ARTIS/GRAVIR-IMAG-INRIA CSAILMIT ARTIS/GRAVIR-IMAG-INRIA
2
Motivation

• Many applications use 3D graphics to produce line
  drawings

3
Motivation

• Many applications use 3D graphics to produce line
  drawings

4
Motivation

• Many applications use 3D graphics to produce line
  drawings
• Scene complexity line clutter

5
Motivation

• Drawing can afford abstraction
• Artists have developed techniques to avoid
  clutter (e.g. using line omission)
• We borrow inspiration from real illustrations
• 2 main strategies
• Indications

6
Inspiration Indications
Les maitres de lorge, J. Van Hamme, F.
Valles, Glenat
Le petit spirou, Tome, Janry, Dupuis

• Non uniform simplification of repetitive
  structures
• Full details drawn in few small regions

7
Motivation

• Drawing can afford abstraction
• Artists have developed techniques to avoid
  clutter (e.g. using line omission)
• We borrow inspiration from real illustrations
• 2 main strategies
• Indications
• Uniform pruning

8
Inspiration Uniform pruning
Les maitres de lorge, J. Van Hamme, F. Valles,
Glenat

• Lines omitted nearly uniformly

9
Contributions

• Define numerical tools (causal density and a
  priori density) to quantify and qualify visual
  complexity in a line drawing.
• Drive automatic simplification strategies using
  these tools.

10
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

11
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

12
Related Work

• Winkenbach and Salesin, 1994
• Simplification using Indications
• Manually specified

13
Related Work

• Deussen et al. 2000
• Trees and foliage abstraction
• Complex geometry replaced by simpler primitives
• Powerful abstraction
• Approach dedicated to trees

14
Related Work

• Wilson et al. 2004
• Work closest to ours
• Simplification based on line omission
• Generate hatching
• Not appropriate to structured objects

15
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

16
Measuring visual complexity

• Input Set of 2D lines extracted from a 3D model
  (silhouettes)

17
Measuring visual complexity

• We want a tool to quantify the clutter of this
  set of lines

18
Measuring visual complexity

• Clutter depends on scale

19
Measuring visual complexity

• Clutter depends on scale

20
Measuring visual complexity

• Clutter depends on scale

21
Measuring visual complexity

• Clutter depends on scale

22
Measuring visual complexity

• ? Our estimator must be parameterized by scale
  it considers a region

23
Measuring visual complexity

• Measuring visual complexity Measuring a density
  of lines inside the region

24
Measuring visual complexity

• We choose to measure the density by
• Rendering the lines in an image
• Convolving a Gaussian function with this image

25
Measuring visual complexity

• We choose to measure the density by
• Rendering the lines in an image
• Convolving a Gaussian function with this image

26
Measuring visual complexity

• We choose to measure the density by
• Rendering the lines in an image
• Convolving a Gaussian function with this image

Intuitive definition.More mathematical
considerations in the paper
27
Using density

• How can this tool be used to drive simplification
  (e.g. line omission)?
• We propose two complementary strategies
• The causal density
• The a priori density

28
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

29
Causal density

• Here, the density tool is used on the output
  image, as it is rendered
• Can monitor the output image density

30
Causal density

• Most obvious strategy
• Previously used in various formsWinkenbach et
  al. 94Salisbury et al. 97Wilson et al. 04

31
Causal density
32
Causal density
33
Causal density

• Discard a line if the density is already too high

34
Causal density

• Discard a line if the density is already too high

View
Output Image
35
Causal density

• Discard a line if the density is already too high

View
Output Image
The order in which lines are processed matters
36
Ordering
1
2
3
4

View
Output Image
37
Ordering
1
2
3
4

View
Output Image
38
Ordering
1
2
3
4

View
Output Image

• Line ordering stage required (e.g. to draw most
  important lines first)

39
Ordering
40
Ordering
41
Ordering
Ordered View
Ordering
Output Image
1
2
3
4

• The ordering operator can use any information
  (depth, depth discontinuity, length, 3D or 2D
  curvatures)

42
Causal density
Ordered View
Output Image
1
2
3
4

• Ordered by depth discontinuity

43
Ordering
No ordering
Orderingwrt depth discontinuity
44
Causal density Limitations

• How to keep more lines at borders for high
  density regions of the view?

45
Causal density Limitations

• Lacks knowledge about the full set of lines
• ?The a priori density gives this knowledge

46
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

47
A priori density

• Here, the density tool is used on the full set of
  lines (the view)

48
A priori density

• We want this metric to give as much information
  as possible about dense areas structure
• ?We enhance the base density tool for the a
  priori density

49
A priori density An estimator

• Base parameter scale
• New parameter direction

50
A priori density An estimator

• Base parameter scale
• New parameter direction

51
A priori density An estimator

• Base parameter scale
• New parameter direction
• Each line contribution is weighted wrt its angle
  with the direction

density
52
A priori density maps

• Density maps precomputed for a sampling of the
  parameters space
• 4 directions 0, 45, 90, 135
• Dyadic scales

53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
Properties of the a priori density

• Quantifies the potential drawing complexity
• Qualifies this complexity
• Directionality

57
(No Transcript)
58
(No Transcript)
59
Properties of the a priori density

• Quantifies the potential drawing complexity
• Qualifies this complexity
• Directionality
• Scale

60
(No Transcript)
61
Scale
62
Properties of the a priori density

• Quantifies the view complexity
• Qualifies this complexity
• Directionality
• Scale
• Geometry

63
(No Transcript)
64
Properties of the a priori density Geometry
65
Properties of the a priori density

• Quantifies the potential drawing complexity
• Qualifies this complexity
• Geometry
• Directionality
• Scale

Base components
66
A priori and causal densities

• The a priori density can drive the causal
  density
• By defining the ordering
• By modulating the threshold

67
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

68
Uniform Pruning
original

• Scale profile ? pattern size

69
Uniform Pruning
simplified
scale

• Scale profile ? pattern size

70
Uniform Pruning
simplified
scale

• Scale profile ? pattern size

71
Uniform Pruning
original

• Directional profile ? lines of high anisotropic
  density

72
Uniform Pruning
simplified

• Directional profile ? lines of high anisotropic
  density

73
Uniform Pruning
Omitted lines
74
Uniform Pruning
original

• Varying scale ? 3D uniform simplification

75
Uniform Pruning
simplified

• Varying scale ? 3D uniform simplification

76
Automatic Indications
original

• Gradient on the a priori density map ?
  indications locations

77
Automatic Indications
simplified

• Gradient on the a priori density map ?
  indications locations

78
Automatic Indications
original

• Gradient on the a priori density map ? indicates
  locations

79
Automatic Indications
simplified
threshold

• Gradient on the a priori density map ? indicates
  locations

80
Outline

• Related Work
• Density
• Causal Density
• A-priori Density
• Results
• Conclusions

81
Summary

• Complexity measures
• On the initial set of lines a priori density
• On the ongoing drawing causal density
• Successfully drive simplification strategies
• Uniform pruning
• Indication

82
Limitations

• Computation time 1mn ? readback cost in
  causal density queries
• Temporal coherence

83
Future Work

• Experiment with more simplification strategies
• Exploit graphics hardware new capabilities to
  speed up causal density queries
• Add directionality to causal density

84
Thank you !
85
Thank you !
Im still looking for a postdoc
86
Line Density Query

• The line density query process
• The line is sampled (user specified sampling)
• The density is evaluated at each sample location
• A single value is computed for the line using
  mean, max

View
Output Image
87
Uniform Pruning
original
simplified
s1
simplified
s2
88
Regularity
Drawing

• s and t influence the final drawing mean density
  and the regularity in the line distribution

89
A Line Density Estimator