Spin image based on local shape similarity and its application

- 40 -

http://www.ivypub.org/cst

Transactions on Computer Science and Technology September 2013, Volume 2, Issue 3, PP.40-48

Spin Image Based on Local Shape Similarity and

Its Application Yongwei Miao

1, Linghong Bao 2, Minyan Chen

1, Xudong Zhang

1

1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China

2. College of Science, Zhejiang University of Technology, Hangzhou 310023, China

Email: [email protected]

Abstract

Local shape similarity, an indicator to measure how similar a region of 3D shape is or dissimilar to another region, has been widely

applied to computer graphics and computer vision. Different from traditional curvature map, a novel spin image based on local

shape similarity measure is presented in this paper and its application on visual enhancement of 3D models is also given. To

efficiently compare two different regions, the neighboring points for each surface vertex are firstly obtained by uniformly sampling

along evenly distributed directions on the tangent plane. The spin images are constructed for these uniformly distributed sampling

points and the local shape similarity measure can thus be calculated by comparing two spin images of different regions. Finally,

due to our proposed local shape similarity definition, an efficient visual enhancement scheme is provided by incorporating our

similarity measure into the color adjustment operation. Experimental results indicate that our spin image based on local shape

similarity definition is robust and also contributes to visual enhancement.

Keywords: Local Shape Similarity; Spin Image; Uniform Sampling; Visual Enhancement

Spin* 1 2 1 1

1. 310023

2. 310023

Spin

Spin

Spin

Spin

[1, 2, 3]

[4][5][6]

*( 61272309)( Y201017442)

- 41 -


Zerlinka Garland [6]

Chua

Jarvis[7]

Gatzke [8]

Gal Cohen-Or [9]

Cipriano [10]

Belongie[11]

Maximo [12]

Zernike

Spin [13,14] Spin

Spin

Spin

Spin

1 Spin

1.1

Spin

Spin

1) 16

2) Spin

3) Spin Spin

4)

1.2

Spin

16

p 8

p

1(a) 8 p x y zn n ,n ,n

- 42 -


nx 0 8

0

2 2

0n n / n ,n ,n

y z x y zm ,

0

1 0m n m ,

0

2 0 1m m m ,

0

3 1 0m m m ,

0

4 0 2m m m ,

0

5 1 2m m m ,

0

6 1 3m m m ,

0

7 6 0m m m

0

(a) (b)

1

0

0

0

m

0 0p p m 'p 0 p S p S p[15]

0

S

1(b)1 3

po o 2 1

po o 0

A

A S A1 2 4

o o o 0

Smax

L

max

L 3~5

0

1 3

po o 2 1

po o 1 3

po o

0

1

po 1' tp p o p 'p

0 t 1 'p 1

po 0

1 0t 0o p m t 0 p S

1 3o o t 0

1 3o o

0

0

3

o p p1 3

po o 0

2 1

po o 2

po 2tp p o p 0 t 0

0

2 1o o

2 1o o 2 1 2tp o o o

0

0 2 0 1 0 2 0t /p m o m o m o m A S

0

1

o p

0

S { , , , , , }A B C D E F

Smean

L

1(b)1 2 3 4 5 6 7 8 9

U { , , , , , , , , }q q q q q q q q q

1 2 1 2 3 8 7 8 9 mean... Lq p q q A q q A q q D q q D

2

- 43 -


2

Spin

1.3 Spin

Spin[13]

22

x,y ,i i i i

q q p n q p n q p

(1)

3(a) n pi

q xi

q p p

yi

q p

3(b)mean

L

1.5 , 0,0x y ,x y p ,i j

0 , 0,0i j 3(b) x i y j 3(b)

3(c) ,a b ,a b

Spin

20*20 I Spin 0 2(b)

3(c) I ,a b

meana x( ) L i

iq ,

meanb y( ) L j

iq (2)

i, j

mean

x ( )i

L

iq

, max

mean

y y( )j

L

iq

(3)

max

x max

y max

L max

x max

y max

x max

y

3(c) p Spin I

Spin

FOR q

{

Spinq

I 0

FORi

q 0 i

{

(1)i

q ,x y ,i ix q y q (3) ,i ix q y q ,i j (2) ,i j ,a b

i, j 1 a 1 bI q i 1, j a 1 bI q

i, j 1 1 a bI q

i 1, j 1 a bI q }

}

- 44 -


(a) (b) Spin (c)

3 Spin

1.4 Spin

Spin Spin

[13] C ,I J

Spin I J

2

C , artanh R , / N 3I J I J (4)

N Spin I J

[13] Spin

Spin 3 1/ N 3 0

0.5 (4) R ,I J Spin I J

2 22 2

NR ,

N N

i i i i

i i i i

p q p qI J

p p q q

2

artanh R ,I J 1/ N 3 (4) Spin Spin Spin

(4)

(4)

Spin

Spin Spin C ,i jI J

ip

jp

,D

i j

,D C( , ) C / S ( , )i j i j C i jI I I I

i

I j

I i

p j

p Spin C C , , ( i 1,2,..., N)i jI I S ( , )

C i jI I C ,i jI I ,Di j

4 Spin Spin

Chinese Lion Gargoyle 4j

p

i

p ,

Gi j

,

, , ,

,

1 D 1.9

G 10*D 18 / 37 1.9 D 1.8

0 D 1.8

i j

i j i j i j

i j

i

p j

p ,

Di j

ip

,G

i j

- 45 -


1.8-1.9

0 1

(a) Chinese Lion (b) Gargoyle

(max

L 4mean max

L L / 8 25max

L 5mean max

L L / 8 15

4 Spin

2

RGB 201.0,13.0,3.0 i i i( , , )R G Bp p p

i

i

i

201.0 G *255

13.0 G *255

3.0 G *255

R

i

G

i

B

i

p

p

p

(5)

255 255

(5)i

p

Gi 0

i i i( , , )R G Bp p p 201.0,13.0,3.0

i i i( , , )R G Bp p p

3

Microsoft Visual Studio 2005 Intel Core

i3-2300M, 2.20GHz CPU, 2.92GB

3.1

Spin

5 Dragon 16887

Spin Dragon

max

L 4mean max

L L / 8

25 5(a) Dragon

- 46 -


5(b) Dragon

(a) (b)

5 Dragon

6 Chinese Lion 152804

max

L 4mean max

L L / 8 25 6(a)

6(b)

Chinese Lion

6(a) 6(b) Chinese Lion

(a)

()(b)()

(a) (b)

6 Chinese Lion

3.2

7 Gargoyle

(5)()

Gargoylemax

L 5mean max

L L / 8 15

7(a)

7(b)

- 47 -


(a) (b)

7 Gargoyle

4

Spin

Spin

REFERENCES

[1] Michael Kazhdan, Thomas Funkhouser, Szymon Rusinkiewicz. Shape matching and anisotropy. ACM Transactions on Graphics,

2004, 23(3): 623-629

[2] Johan W. Tangelder, Remco C. Veltkamp. A survey of content based 3D shape retrieval methods. Multimedia Tools and

Applications, 2008, 39(3): 441-471

[3] Alexander Berner, Martin Bokeloh, Michael Wand, et al. A graph-based approach to symmetry detection. Proceedings of the

Eurographics / IEEE VGTC conference on Point-Based Graphics, Aire-la-Ville, Switzerland, 2008: 1-8

[4] Rong Liu, Hao Zhang, Ariel Shamir, et al. A part-aware surface metric for shape analysis. Computer Graphics Forum, 2009, 28(2):

397-406

[5] Michael Kazhdan, Thomas Funkhouser, Szymon Rusinkiewicz. Symmetry descriptors and 3D shape matching. Proceedings of the

Eurographics/ACM SIGGRAPH symposium on Geometry Processing, Nice, France, 2004: 115-123

[6] Steve Zelinka, Michael Garland. Similarity-based surface modelling using geodesic fans. Proceedings of the Eurographics/ACM

SIGGRAPH symposium on Geometry Processing, Nice, France, 2004: 204-213

[7] Chin Seng Chua, Ray Jarvis. Point Signatures: A new representation for 3D object recognition. International Journal of Computer

Vision, 1997, 25(1): 63-85

[8] Timothy Gatzke, Cindy Grimm, Michael Garland, et al. Curvature maps for local shape comparison. Proceedings of the

International Conference on Shape Modeling and Applications, Cambridge, MA, USA, 2005: 246-255

[9] Ran Gal, Daniel Cohen-Or. Salient geometric features for partial shape matching and similarity. ACM Transactions on Graphics,

2006, 25 (1): 130-150

[10] Gregory Cipriano, George N. Phillips Jr., Michael Gleicher. Multi-scale surface descriptors. Transactions on Visualization and

Computer Graphics, 2009, 15(6): 1201-1208

[11] Serge Belongie, Jitendra Malik, Jan Puzicha. Shape matching and object recognition using shape contexts. Pattern Analysis

- 48 -


Machine, 2002, 24(4): 509-522

[12] Andr Maximo, Robert Patro, Amitabh Varshney, et al. A robust and rotationally invariant local surface descriptor with

applications to non-local mesh processing. Graphical Models, 2011, 73(5): 231-242

[13] Andrew Johnson. Spin-Images: A representation for 3D surface matching. Ph.D. Dissertation. The Robotics Institute, Carnegie

Mellon University, August 1997

[14] Andrew Johnson, Martial Hebert. Using Spin images for efficient object recognition in cluttered 3D scenes. IEEE transactions on

Pattern Analysis and Machine Intelligence, 1999, 21(5): 433-449

[15] Yao Jin, Zhong Li, Jianfeng Shi, et al. Fast computing for the approximate straightest path on triangular mesh surfaces. Journal of

Computer-Aided Design and Computer Graphics, 2010, 22(4): 599-604(in Chinese)

11971-

2 1988-

3 1989-

4 1982-

Documents

Spin image based on local shape similarity and its application