Geometry Synthesis Ares Lagae Olivier Dumont Philip Dutré Department of Computer Science Katholieke Universiteit Leuven 10 August, 2004

IntroductionIntroduction (images by Wei & Levoy, SIGGRAPH 2000) example texture synthesized texture texture synthesis

IntroductionIntroduction Given an example of input geometry, synthesize new output geometry that is perceived similar to the input geometry. example geometry synthesized geometry geometry synthesis

Related Work Procedural modeling Texture synthesis –Pixel based –Patch based Bidirectional texture function synthesis

Texture Synthesis Pixel Based example texture synthesized texture Efros & Leung 1999, Wei & Levoy 2000,... find best match copy pixel

Texture Synthesis Patch Based Liang et al. 2001, Efros & Freeman 2001,... example texture synthesized texture find best match copy patch merge overlap

Design Decisions Geometry representation ?  triangle mesh ? Geometry representation ?  surfels ? Geometry representation ?  voxel grid ? Geometry representation ?  regularly sampled distance field (images by Frisken et al., SIGGRAPH 2000)

Design Decisions Geometry representation ?  regularly sampled distance field Unit of synthesis ?  block (~ patch in texture synthesis) Finding similar blocks ?  geometry matching algorithm

System Overview example geometrysynthesized geometry meshdistance fieldsynthesized distance field geometry matching algorithm find best match copy block

Geometry Matching Algorithm The Problem... texture synthesis geometry synthesis feature vector size ≈ ½ (neighbourhood size) ² size = (block size) ³ 9 x 9 9 x 9 x x 32 x

Geometry Matching Algorithm Key Idea similarity decreases similarity ?...

all possible blocks (includes overlapping blocks) Geometry Matching Algorithm Search Tree Construction...

Geometry Matching Algorithm Search Tree Construction...

Geometry Matching Algorithm Search Algorithm... priority queue similarity decreases

Geometry Matching Algorithm Performance Up to ≈ 5000 times faster than a brute force linear search Speedup is data dependent Works very good for distance fields

Geometry Construction distance field geometry examplesynthesized matching geometry construction ∕∕

Geometry Synthesis Results

Geometry Synthesis Conclusion Extended texture synthesis to geometry synthesis Fast geometry matching algorithm using distance fields

Geometry Synthesis Future Work Better mesh reconstruction Port applications of texture synthesis to geometry synthesis Synthesize geometry over a mesh

Thank You! Questions ? technical report available at

Some Numbers distance field resolution 64³128³256³ block size 8³16³32³ blocks in distance field 1.75 x 10^5 1.4 x 10^6 1.1 x 10^7 average matching time 0.025s0.5s10s speedup factor