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Discovering Structural Regularity in 3D Geometry. Speaker: JinliangWu Date: 25 / 9 /2008. Authors. Mark Pauly ETH Zurich Niloy J. Mitra IIT Delhi Johannes Wallner TU Graz Helmut Pottmann TU Vienna Leonidas Guibas Stanford University. Regular Structures. Regular Structures.

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discovering structural regularity in 3d geometry

Discovering Structural Regularity in 3D Geometry

Speaker: JinliangWu

Date: 25 / 9 /2008

authors
Authors
  • Mark Pauly

ETH Zurich

  • Niloy J. Mitra

IIT Delhi

  • Johannes Wallner

TU Graz

  • Helmut Pottmann

TU Vienna

  • Leonidas Guibas

Stanford University

motivation

completion

geometric edits

Motivation

compression

geometry synthesis

Text

Motivation
structure discovery

Transform

Analysis

Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

spatial

domain

transform

domain

Structure

Discovery

repetitive structures1
Repetitive Structures

1-parameter patterns

repetitive structures2
Repetitive Structures

2-parameter commutative patterns

repetitive structures4
Repetitive Structures

regular structure

is a transformation group acting on

is a collection of n patches of a given surface S

repetitive structures5
Repetitive Structures

In the simplest setting, is a 1-parameter group with generating similarity transformation T .

The elements of can be represented as

structure discovery1

Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery

transformation analysis
Transformation Analysis

Algorithm for analyzing transformations

transformations
Transformations

spatial domain

transformation space

pairwise transformations

transformations1
Transformations

spatial domain

transformation space

pairwise transformations

model estimation
Model Estimation

origin

density plot of

pair-wise transformations

model estimation1
Model Estimation

cluster centers

transformation analysis1
Transformation Analysis

Algorithm for analyzing transformations

model estimation2
Model Estimation

Is there a Pattern?

model estimation3
Model Estimation

Yes, there is!

model estimation4
Model Estimation

Yes, there is!

model estimation5
Model Estimation

Global, non-linear optimization

– simultaneously detects outliers and

grid structure

model estimation6

grid location

generating vectors

Model Estimation
  • Grid fitting

– input: cluster centers

– unknowns: grid generators

model estimation7

data confidence

cluster center

closest grid point

grid confidence

grid point

closest cluster center

Model Estimation
  • Fitting terms
model estimation8
Model Estimation
  • Fitting terms
  • Data and grid confidence terms
  • objective function
model estimation9
Model Estimation

Global, non-linear optimization

– simultaneously detects outliers and

grid structure

structure discovery2

Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery

aggregation
Aggregation
  • Region-growing to extract repetitive elements
  • Simultaneous registration
structure discovery3

Input Model

Transform Clusters

Model

Estimation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery

Aggregation

conclusions
Conclusions
  • Algorithm is fully automatic
  • Requires no prior information on size, shape, or location of repetitive elements
  • Robust, efficient, independent of dimension

general tool for scientific data analysis

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