Approximate ImageBased TreeModeling using Particle Flows

1
Approximate Image-Based Tree-Modeling using
Particle Flows

• Boris Neubert, Thomas Franken, Oliver Deussen
• University of Konstanz
• SIGGRAPH 2007

2
Abstract

• A set of input photographs
• Result 3D tree models

3
Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

4
Introduction

• Image-based modeling methods
• qualified approximations
• avoid numerical problems
• Input
• a small set of photographs of a tree taken from
  different views

5
Introduction

• use particle simulation to generate tree skeleton
• create a 3D surface model from the given tree
• automatic image-based construction
• possible to interactively guide the method to a
  desired result
• paint densities
• change directions for particle simulation

6
Related Work

• Classical tree modeling
• rule-based
• L-system
• small changes of values might cause large changes
  in the overall shape
• a large set of parameters has to be defined

7
Related Work

• Classical tree modeling
• procedural approaches
• Real time design and animation of fractal
  plants and trees, SIGGRAPH 86
• Plant models faithful to botanical
  structure and development, SIGGRAPH 88
• Creation and rendering of realistic trees,
• SIGGRAPH 95
• limit the amount of adjustable parameters for the
  user

8
Related Work

• Classical tree modeling
• Xfrog system
• Interactive modeling of plants, IEEE
  Computer Graphics and Applications 1999
• procedural elements are combined using a simple
  rule system
• allows faster modeling
• the number of parameters is still large

9
Related Work

• Image-based modeling
• Volumetric reconstruction and interactive
  rendering of trees from photographs, SIGGRAPH
  2004
• visualization only , unable for animation or
  editing
• not easy to show the tree under various lighting
  conditions

10
Overview

• particle simulation
• external constraints from input images
• internal botanical restrictions
• Pre-processing
• separate the tree from the background
• compute a 2D attractor graph
• Creating of the voxel model
• fill a voxel-grid with density values

11
Overview

• Computation of direction field
• use the 2D attractor graphs to create direction
  fields
• Particle simulation
• obtain the main tree skeleton in form of a 3D
  graph
• Creating the Tree Geometry
• The tree skeleton is now converted into 3D
  geometry using allometric rules

12
Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

13
Pre-processing

• separate the tree from the background
• performing alpha matting
• Poisson matting, SIGGRAPH 2004
• not fully automatic
• user create an initial trimap
• the pixels of the object
• pixels of the background
• an uncertainty region

14
Pre-processing

• separate the tree from the background
• performing alpha matting
• Poisson matting, SIGGRAPH 2004
• selecting pixels with appropriate colors in the
  input images
• use the result as a density estimation of the
  tree for the corresponding view

15
Pre-processing

• find the underlying tree skeleton in the
  corresponding view
• Livewire approach
• Color lesion boundary detection using live
  wire,
• Proceedings of SPIE Medical Imaging 2005
• a target point
• the foot point of the tree
• seed points
• randomly selecting points on the tree silhouette
• starts at each seed point and finds a path to
  reach the target point

16
Pre-processing

• The attractor graph

17
Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

18
Creating of the voxel model

• construct an initial 3D estimation of the plant
  volume that encompasses a voxel grid
• Volumetric reconstruction and interactive
  rendering of trees from photographs, SIGGRAPH
  2004
• Initial density values for the voxels are
  estimated from the input photographs
• project the voxel back onto each input image to
  initialize the density ai for the i-th voxel Vi

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Creating of the voxel model

• reconstruct the density values of the volume grid
  V
• Optical models for direct volume rendering, IEEE
  
• TVCG 1995
• discrete form of the volume rendering equation

?j is the transparency of voxel j bk is the
light emittedfrom the k-th voxel
20
Creating of the voxel model

• reconstruct the density values of the volume grid
  V
• Optical models for direct volume rendering, IEEE
  
• TVCG 1995
• discrete form of the volume rendering equation

?j is the transparency of voxel j bk is the
light emittedfrom the k-th voxel
21
Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

22
Particle Tracing

• create initial particle positions for the main
  tree skeleton
• the particles are placed randomly in the voxels
  in proportion to their density
• for medium-sized trees use 5001000 particles
• introduce the attractor graphs to particle
  tracing
• Particle systems for plant modeling, Plant
  Growth
• Modeling and Applications 2003

• the positions of the particles are updated
• according to their mass and external forces

23
Particle Tracing

• particle attraction
• particles close to each other are forced to join
  and subsequently move forward together
• search the nearest neighbor for each particle and
  combine them if their distance is below a given
  threshold

• the particles are directed towards the tree
  basis
• and towards their respective nearest
  neighbors

24
Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

25
The Direction Field

• direct the particles moving towards the attractor
  graphs that correspond to these input images
• apply a distance transform to the attractor graph
• compute the tangential vector of the graph ti,j
  at position gi, j

for each position xi, j in the direction field
the closest point on the attractor graph gi, j is
computed
26
The Direction Field

• direct the particles moving towards the attractor
  graphs that correspond to these input images
• compute direction vector fij as external force on
  a particle close to xi,j
• particles far away from the graph are directed
  towards gi, j
• particles close to the graph into the tangential
  direction ti, j in gi, j

the blending function h(d) depends on the
distance d vi, j
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The Direction Field
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Outline

• Introduction
• Related Work
• Overview
• Pre-processing
• Creating of the voxel model
• Particle Tracing
• The Direction Field
• Creating the Tree Geometry
• Result and Discussion
• Conclusions and future work

29
Creating the Tree Geometry

• convert 3D graph that represents the main
  branching structure into 3D geometry
• assign each branch a thickness
• introduce appropriate geometry to the branchs
• store a number indicating how many particles were
  combined to form this segment
• Digital Design of Nature Computer
  Generated Plants and Organics, 2005

r is the radius of the main branch ri are the
radii of the branching twigs a is a constant
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Creating the Tree Geometry

• convert 3D graph that represents the main
  branching structure into 3D geometry
• connect discs of the required thickness that are
  positioned along the branch in certain distances
  and that are oriented perpendicular to the branch
• use photographs of natural leaves to create the
  foliage texture

31
Result and Discussion

• standard PC with 3 GHz
• The flow simulation needs about 510 seconds for
  10002000 particles and 200 iterations

32
Conclusions and future work

• a new image-based modeling method for 3D tree
  geometry runs at interactive rates
• capture branching patterns and density
  distributions
• adapt particle simulation with direction field
• with Level-of-Detail data structures