Variational Tree Synthesiskucg.korea.ac.kr/new/seminar/2016/ppt/ppt-2016-11-24.pdf · Variational...

Variational Tree Synthesis

Rui-Wang et al.Computer Graphics Forum 2014

Copyright of figures and other materials in the paper belongs original authors.

Presented by Qi-Meng Zhang

2016. 11. 24

Computer Graphics @ Korea University

Qi-Meng Zhang | 2016. 11. 24 | # 2Computer Graphics @ Korea University

Abstract

• Generate realistic trees in specific shapes

• Formulate the tree modeling as an optimization process

• Applicable to generate trees with different shapes, from interactive design and complex polygonal meshes

1. Introduction


• Typical methods

L-system

• Modeling trees from symbolic rules

• Capable of generating various types of trees

• Limited at modelling trees under specific global constraints

ex: crown shape

Sketch-based modeling

• From the view angle of user interface

• A trade-off has to be made between the amount of user-involved sketching and the fidelity of resultant models

1. Introduction


• In this paper, we formulate the shape-guidance tree modelling problem in a multilevel variational optimization framework

Variational cost function is iteratively minimized at each level

• Measures the difference between the guidance shape and the target tree crown

First

∙ Generate initial tree branches

Second

∙ Generate shape sample points and cluster

Finally

∙ Optimize sub-trees to best fit these clustered sample points

1. Introduction


• Consider the botanical factors constrains in the optimization

Each sub-tree is parameterized in several botanical parameters and constructed

• Including the minimum total branches volume and spatial branches patterns

Why need volume minimization

• Most wildly applied model to depict the optimized structure of tree

1. Introduction


• Modeling system

Overview

Optimization process

Initialization&Partition Local optimization Global optimization

2. Related Work


• Extended L-systems

• Sketch-based plant modeling

2. Related work

MECH ˇ R.et al., ”Visual models of plants interacting with their environment” SIGGRAPH 1996

PRUSINKIEWICZ P.et al., ”Synthetic topiary”ACM SIGGRAPH 1994

Boudon F.et al., ”Structure from silhouettes: A new paradigm for fast sketch-based design of trees” Computer Graphics Forum 2009

Longay, S.et al., ”Treesketch: Interactive procedural modeling of trees on a tablet” Eurographics 2012


• Space colonization method

2. Related work

RUNIONS A.et al., ”Modeling trees with a space colonization algorithm” NPH’ 2007

· Proposed a space colonization methodbut it did not consider the botanicalconstraints

· Improve the problem of space coloniza-tion method, shape constraints optimizedby local branches growth and competition

PALUBICKI W.et al., ”Self-organizing tree models for image synthesis” ACM TOG 2009


• Tree reconstruction methods

2. Related work

Boris Neubert.et al., ”Approximate Image-Based Tree-Modeling using Particle Flows”ACM TOG 2007

Livny Y.et al., ”Automatic reconstruction of tree skeletal structures from point clouds”ACM TOG 2010

Livny Y.et al., ”Texture-lobes for tree modelling”ACM TOG 2011

·Model trees from acquired data such

as from images, video, scanned pointset .These method tend to accomplish a reconstruction mission rather than a modeling issue.


2. Related work

RUNIONS A.et al., ”Modeling and visualization of leaf venation patterns” ACM TOG 2005

HAHN H.et al., ”Fractal aspects of three-dimensional vascular constructive optimization”Fractals in Biology and Medicine2005

· Generate branch structure according to

biological factors, result patterns are applicable to texture synthesis

· Proposed a Global Constructive

Optimization method

3. Variational Tree Synthesis Model


• In a tree structure

Node: An insertion zone of a leaf on the stem

Internode: The stem portion between two successive nodes

Metamer: The basic structural unit of a plant body formed by a node

• An abstract branching model

•

3.1 Preliminaries

,defines N + 1 node ( is root node)

,corresponding spatial positions of the node set

,the diameters of the node set

①

②

③

,the topological relationship ④


• Pipe model

The diameter of a parent branch has a relationship with its child braches

is a branch transmission coefficient between (2.0,3.0)

• The structure of tree branches

3.2 Botanical Rules

Major morphological features


The major morphological features of a tree

A tree could represented as a hierarchical structure

• combine all parameter vectors of different levels to be a botanical arguments set

3.2 Botanical Rules


• The guidance shape

Collect shape nodes to form the constraint set

• Our goal is to approximate the input guidance shape, so there has a

optimization problem

3.3 Variational Model

,defines M+1 nodes

,represent spatial positions

,represent the diameters of corresponding nodes


• Branch model optimization

• is an object function to present modeling cost


① ② ③

①

②

③

: the intrinsic structure energy

: the exterior shape-guidance energy

: the parameter control penalty form the botanical parameter set


• The intrinsic structure energy

Minimize the total volume of branches

• The volume function for a given internode :

is the diameter computed by Equation(2)

is shape coefficient

∙ In general =2.0



• The shape-guidance energy

Compute the similarity between the target structure and the shape constraint set

• Distance-aware measurement

• The botanical parameter control penalty energy


Angle Rotation angle Length of

4. Optimization Algorithm


• First:

Structure initialization, generated by

• Second:

Shape partition

• Find best guidance shape for each subtree

• Final:

Structure update

4.1 Algorithm Overview

Three-step optimization

Shape partition

Local minima Global optimization

Structure update


• Recall these botanical parameters are used to create the initial topology and nodes’ positions of branches in the current level of the tree.

4.2 Iterative Optimization at One Level

Structure initialization

Input guidance shape

Structure initialization

Initial topology


• Recall , and are determined

by branch structure ,so the object function could become

According to the Equation(9), we form an initial partitionof the shape by clustering the shape nodes


Shape partition

Using K-Means, clustering sub-tree in k regions, in therecalled k-partition

Has 2 partitions


• The optimization of internodes will not break the shape-guidance so,

update the branch structure of sub-trees

Minimizes Equation(10) ,use a gradient descent method with numerically gradient evaluations


Structure update


• Given initial K subtrees

• Iteratively taken

Shape partition

• First, all the shape nodes are partitioned into K clusters

Structure update

• Then the resultant branch node position pj is update


Major procedure

Two level


• Jump out local minima

A given node to be the maximal steps connecting shape nodes in

• Branches in smaller order are pruned away from the structure

The corresponding shape sample nodes are reconnected to their nearest branch nodes in the remaining skeletal structure

4.3 Topology refinement

Local minima Global optimization

5. System and Modeling Interface


• Sketching guidance shape

Sketch silhouettes, the shape of crown is

automatically generated

• Importing mesh

Constrained points(shape nodes)are sampled

from this guidance shape


Input guidance shapes

Importing mesh


• Shape represented in triangles

Distribute uniform sample nodes on these triangles

• A is the averaged area

• Distribute uniform sample nodes in the shape volume

With same

• Replicate leaves and place them on branches based on botanicallaws governing leaf arrangement


Generation of shape sample nodes & Leaf population

6. Result


6. results

Modelling abilities

Lateral density Apical growth

Sub-branch Angle

N=5 N=7 N=9 P=0.2 P=0.6 P=1.0

n=1 n=2 n=3 θ=25◦ θ=45◦ θ=65◦


6. results

Apical and lateral control

P=1.0The apical control be limitedto the main stem

Level 0: P=0.3 N=3Level 1: P=0.5 N=3

Level 0: P=0.2Level 1: P=1.0


6. results

Alternate vs. opposite lateral

n=1 n=2


• The topology update can not always guarantee the global decrease of total energy

choose lowest energy

6. results

Local minima and topology refinement


• Under a same guidance shape

6. results

Comparison & Performance

PRUSINKIEWICZ P.et al., ”Synthetictopiary” ACM SIGGRAPH 1994

PALUBICKI W.et al., ”Self-organizingtree models for image synthesis”ACM TOG 2009

Our method

7. Conclusions and Discussion


• First

Only consider a small set of hierarchical botanical rules

• Limits our method to model like flowers and vine

• Second

Does not consider the environmental factors

• Ex: gravity or sunshine

• Third

All botanical rules are counted in the optimization by soft constraints

• Some unnatural result

• Finally

Uniformly generate shape sample nodes on triangles

• Final distribution of branches not wanted by users


Limitations


• First

Distribute sample nodes according to some botanical patterns with andwithin the shape

• Second

Tree geometry reconstruction

• Integrate with other image based techniques

• Finally

User interface


Future work

Variational Tree Synthesiskucg.korea.ac.kr/new/seminar/2016/ppt/ppt-2016-11-24.pdf · Variational...

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