Discovering structural regularity in 3d geometry
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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

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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


Regular structures

Regular Structures


Regular structures1

Regular Structures


Motivation

completion

geometric edits

Motivation

compression

geometry synthesis

Text

Motivation


Compression

Compression


Completion

Completion


G eometry s ynthesis

Geometry Synthesis


Structure discovery

Transform

Analysis

Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

spatial

domain

transform

domain

Structure

Discovery


Repetitive structures

A similarity transformation T

Repetitive Structures


Repetitive structures1

Repetitive Structures

1-parameter patterns


Repetitive structures2

Repetitive Structures

2-parameter commutative patterns


Repetitive structures3

Repetitive Structures


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


Transformation

Transformation


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


Simultaneous registration

Simultaneous Registration


Structure discovery3

Input Model

Transform Clusters

Model

Estimation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery

Aggregation


Results and applications

Results and Applications


Robustness

Robustness


Geometry synthesis

Geometry Synthesis


Geometry synthesis1

Geometry Synthesis


Scan completion

Scan Completion


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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