Embedded mesh colors

Embedded Mesh ColorsEmbedded Mesh Colors 內嵌式網格色彩內嵌式網格色彩

Chung-Yuan Lee (李仲元 ), Ran-Zan Wang (王任瓚 )

Department of Computer Science and Engineering,

Yuan Ze University, Taiwan

2013/01/25

元智大學資訊工程所碩士論文口試

Outline

IntroductionRelated workProposed method

• Concept• Embedding phase• Reconstruction phase

Experimental resultsConclusion

Embedded mesh colors is a new way to 3D color models drawing.

without any texture atlas or additional color data

Introduction

Texture atlas

2D texture image textured bunny3D mesh

texture charts

Introduction

IntroductionDisadvantages of texture atlasseamsa triangle cannot span multiple chartsmesh dependencychart packing: wasted texels

Introduction

texturefrom

chart A

texturefrom

chart B

Disadvantages of texture atlasseamsa triangle cannot span multiple chartsmesh dependencychart packing: wasted texels

IntroductionDisadvantages of texture atlasseamsa triangle cannot span multiple chartsmesh dependencychart packing: wasted texels

Introduction• Texture data and mesh data are saved as separate files.

Related workTo make texture mapping high efficiency.

• Marco Tarini , Kai Hormann , Paolo Cignoni , Claudio Montani “Polycube-Maps”, in 2004.

mesh polycube

texture spaceworld space

Polycube roughly resemble the mesh.

Related works

Polycube-maps

Related works

Polycube-maps

polycube

case A

case B

Related works

Polycube-maps

object space

And a tiny structure to store polycube layout mesh

(with vertex texture coord)

If the geometry or topology of a mesh is too complex.

A polycube would consist of so many cubes.

The texture memory will be soon exceed!!

Related work

A concept of 3D models using one-to-one correspondence with model surface and color data.

Cem Yuksel, John Keyser and Donald H. House

“Mesh Colors”

ACM Transactions on Graphics, Vol. 29, No. 2, Article 15,in 2010.

Related works

Mesh colors Conception of mesh colors

Related works

Mesh colors• Texture mapping

• Mesh colors

Related works

Mesh colors

Related works

Mesh colors Features of mesh colors

There are no mapping discontinuities.No mapping function is necessary.Models can be edited after coloring, without

resampling.

Related works

Mesh colors Features of mesh colors

The procedure is compatible with the current real-time graphics pipeline.

Support for non-triangular Meshes.

Related works

Mesh colors Advantages of Mesh colors

Solve many texture mapping problem for 3D color model.

Disadvantages of Mesh colorsStill need some additional data space to save

color data, and has no integration with operating data architecture.

Embedded mesh colors

Proposed method

Goal• Bind color data and mesh data together, improve the safety of model files.

• Fast executing speed for color model drawing.

• High performance with low computing power requirement.

Proposed method

Model construction using embedded mesh

colors files

Color hiding in 3D model mesh

Embedded mesh colorsProposed method

Proposed method

{ }{ }{ }

,...,,

( ){ }

=≠≠===

nifififivvvf

mizyxv

fififii

,...,2,1,:,,

,...,2,1,,,

321321

Proposed method

Embedded mesh colorsProposed method

Proposed method

+−=+=

eInterpolati

eInterpolat

×+×=

Mesh interpolationProposed method

3'iv 4'iv

6'iv7'iv

• Disadvantage of linear mesh interpolation

Mesh interpolationProposed method

• Better method for mesh interpolation

Mesh interpolation - method 2

Proposed method

3'iv 4'iv

6'iv7'iv

3'iv 4'iv

• Considerations of interpolation

Proposed method

2Nei 1Nei

−−

Proposed method

Case 1

Case 2

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

16' 211

2111 ×+×

−×−

+= VNeiVNeiV

VVVv i

3'iv 4'iv

rqpniVN

VNNNei n

i ,,,3,2,1,1

1 ==−

−×=

∑∑

1Nei2Nei

Proposed method

3'iv 4'iv

( ) ( )

−×−×

÷−+−+−+=

−×−

321321

1322217

VVVvand

NNNNwhere

VVVVVVvv

VNeiVNeiV

avgtotal

totalavg

Proposed method

TvSamplec

',...,','' 21

Color samplingProposed method

( )kkk tsvt ,=

( )htwscolorc kkk ××= ,

Proposed method

( )kkck cvEmbv ,'' =

Color embeddingProposed method

• Embedding color into vertex data by using characteristic of IEEE−754 standard floating-point format

• Composition of IEEE754 standard floating-point encoded with 32 bits• 1 sign bit• 8 exponent bits• 23 mantissa bits

s e e e e e e e e m m m m m … m m m m m m m

31 30 29 28 27 26 25 24 23 22 5 4 3 2 1 0

(s = sign bit ； e = exponent bits ； m = mantissa bits)

)127(2.]1[ +××= emsn

numberoriginalastimesdistortion 103 5 　　−×<

(x, y, z)

X-axisRED Y-axisGREEN Z-axisBLUE

( )( )( )

+−=+−=+−=

kkzkzkz

kkykyky

kkxkxkx

bModfff

gModfff

rModfff

2'( )( )( )

kzkzkzk

kykykyk

kxkxkxk

The embedding method will let ALL vertices have distortion.

In model reconstruction phase, we want vertices in original model can be recover lossless.

Interpolated vertices can help to hide the color data in original vertices.

Original vertices• Keep vertex coordinate and color the same as

original 3D model in reconstruction phase.• Every each of neighbor is interpolated vertex.

Interpolated vertices• Only one neighbor is original vertex.• Provide data space for color data in original

vertex and itself.

Color embedding – improvement method

Proposed method

original

interpolate

original interpolate

(127, 30, 79) (217, 182, 56)

Proposed method

original

interpolate

(127, 30, 79) (217, 182, 56)

Proposed method

original

interpolate

Bit2 Bit 3

0 Have no color Green

1 Red Blue

(127, 30, 79) (217, 182, 56)

Proposed method

interpolate

original

interpolate

(127, 30, 79) (217, 182, 56)

0 1 1 1 1 1 1 1

7 6 5 4 3 2 1 0

Proposed method

interpolate

(127, 30, 79) (217, 182, 56)

(217, 182, 56)

(26, 22, 7)

Proposed method

original

interpolate

original

interpolate

Proposed method

( )( ) ( )

( ) ( )

×+×+−=

×+×÷+−=

+×+×+××+−=

31222'

1222255

kkzkzkz

kkykyky

kkxkxkx

bModcModfff

gcModfff

slrModfff

Proposed method

{ }{ }

',...,','' 21

Proposed method

v -67.87744904 56.95598221 17.50121880v -87.78181458 59.63884354 11.98297787v -165.97395325 132.04194641 124.09216309v 44.16437149 63.88375854 79.08065796v -21.16270256 51.64666367 24.10216522

.f 10116 17655 17645f 10117 17656 17475f 10189 17474 17646f 17655 17656 17657

Proposed method

Color extracting – basic embedding method

• Improvement embedding method

original

interpolate

Proposed method

Color extracting – Improvement method

original

interpolate

Proposed method

interpolate

original

interpolate

interpolate(217, 182, 56)

(214, 181, 58)

(26, 22, 7)

(214, 181, 58)Color distortion in each color channel will less than 2% !

Proposed method

Experimental results• Comparison of different mesh interpolation methods

Experimental results

Linear interpolation method Improvement interpolation method

Experimental resultsMesh of Original model Mesh after interpolation

Vertices of Original model Vertices after interpolation

Model Vertex

Vertex count after

interpolation

Face count after

interpolation

Vertex count after

interpolation

Face count after

interpolation

Feline 20,531 41,066 184,806 369,593 2,771,964 3,326,345

Bunny 15,258 30,338 136,810 273,055 2,048,202 2,457,503

Buddha 15,138 30,272 136,227 272,447 2,043,363 2,452,031

Zebra 20,157 40,310 181,398 362,789 2,720,928 3,265,109

• Data of experimental model

Model OBJ file size

(MByte)

BMP file

size (MByte)

(MByte)

Feline 3.21 3.00 15.00 11.60 189.77 132.93

Bunny 2.32 3.00 11.10 8.63 141.24 98.86

Buddha 2.30 3.00 11.00 8.55 140.60 98.42

Zebra 3.12 3.00 14.70 11.43 186.27 130.39

Experimental results• File size of experimental model

Embedded mesh color file size with interpolation once. (1) text file / (2) binary fileEmbedded mesh color file size with interpolation twice. (3) text file / (4) binary file

(Estimate)

Texture mapping Embedded vertex colors

Texture mapping Embedded mesh colors with mesh interpolation once

Texture mapping Embedded mesh colors with mesh interpolation twice

Embedded mesh colors with mesh interpolation twice

Embedded mesh colors with mesh interpolation once

Texture mapping Embedded mesh colors with mesh interpolation once

Texture mapping Embedded mesh colors with mesh interpolation twice

• Point-Sampled Model

ConclusionPresent a fast 3D drawing method, and Inherit the advantages of mesh colors.

Combine mesh and color data for easy management.The vertices and color in original model can be reconstructed lossless.

Can provide authorization for different user-level.Low computing requirements. (e.g. mobile devices)

Thanks for listening

Embedded mesh colors

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