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

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


completion

geometric edits

Motivation

compression

geometry synthesis

Text

Motivation


Compression


Completion


Geometry Synthesis


Transform

Analysis

Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

spatial

domain

transform

domain

Structure

Discovery


A similarity transformation T

Repetitive Structures


Repetitive Structures

1-parameter patterns


Repetitive Structures

2-parameter commutative patterns


Repetitive Structures


Repetitive Structures

regular structure

is a transformation group acting on

is a collection of n patches of a given surface S


Repetitive Structures

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

The elements of can be represented as


Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery


Transformation Analysis

Algorithm for analyzing transformations


Transformations

spatial domain

transformation space

pairwise transformations


Transformations

spatial domain

transformation space

pairwise transformations


Model Estimation

origin

density plot of

pair-wise transformations


Model Estimation

cluster centers


Transformation Analysis

Algorithm for analyzing transformations


Transformation


Model Estimation

Is there a Pattern?


Model Estimation

Yes, there is!


Model Estimation

Yes, there is!


Model Estimation

Global, non-linear optimization

– simultaneously detects outliers and

grid structure


grid location

generating vectors

Model Estimation

  • Grid fitting

    – input: cluster centers

– unknowns: grid generators


data confidence

cluster center

closest grid point

grid confidence

grid point

closest cluster center

Model Estimation

  • Fitting terms


Model Estimation

  • Fitting terms

  • Data and grid confidence terms

  • objective function


Model Estimation

Global, non-linear optimization

– simultaneously detects outliers and

grid structure


Input Model

Transform Clusters

Model

Estimation

Aggregation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery


Aggregation

  • Region-growing to extract repetitive elements

  • Simultaneous registration


Simultaneous Registration


Input Model

Transform Clusters

Model

Estimation

Regular Structures

Transform Generators

Structure Discovery

Transform

Analysis

Structure

Discovery

Aggregation


Results and Applications


Robustness


Geometry Synthesis


Geometry Synthesis


Scan Completion


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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