Shape Matching Using Thin-Plate Splines Incorporated to Extended Weighted-Tree Similarity Algorithm for Agent Matching in Virtual Market – Budianto Riyanarto
Sarno
ISSN 1858-1633 2005 ICTS 59
measure the context distance DP,Q between shapes P and Q as the sum of shape context matching costs
over the best matching points and , as follows [2, 3]:
be P
p Q
q P
p Q
q
D q
T p
C n
q T
p C
n Q
P D
+ +
=
∑ ∑
∈ ∈
∈ ∈
, min
arg 1
, min
arg 1
8 .
,
6 where
, Q
P D
be
is the effort of transformation done to adjust the shapes. For finding the similarity
between two shapes, we modify the equation 6 by subtract one with the context distance D P, Q such
that the result will reflect the similarity, as follows:
, 1
, Q
P D
Q P
Sim −
=
7 After we have found the similarity between pair-
node shapes in the trees, the result will be used to compute the similarity of the tree.
5. RESULTS
Here, we present results on the cloth shape data set
from http:www.loeshinsedesign.com. In our
experiments, we use 7 shapes of cloths. We also defined the similarity of node shapes based on
equation 7 and used three iterations of TSP transformation on each shape. Figure 9 shows all cloth
shape used in this experiment. For each cloth, we provide the back and the front of the cloth
respectively.
Figure 9. Examples of edge pixels generated from cloth
Figure 10 and figure 11 depict the form of arc- labeled arc-weighted tree which bring information of
shape a and shape g in figure 7 respectively. The whole information for each shape brought by each
agent is summarized in the Table 1. Each column on the table corresponds with each image on the figure 9
and each row presents the properties of arc-labeled arc weighted tree such as age, availability, fabric, gender,
etc.
Table 1. The dataset used for the experiments.
A B
C D
E F
G age
Adult Adult
Adult Adult
Adult Adult
Adult
avail 1day
1day 1day
1day 1day
1day 1day
major polyester
wol polyester
cotton polyester
polyester polyester
minor cotton
cotton cotton
polyester polyester
cotton cotton
gender
F F
F F
M F
M
occasion Formal
Casual Formal
Party Casual
Casual Formal
price Normal
Normal Expensive Expensive Cheap
Normal Normal
type Coat
Sweater Coat
Long dress Trouser Skirt
Trouser
button Sty Circle None
Strap None
None None
None
Back Shp
Figa Figb
Figc Figd
Fige Figf
Figg
Collar V-Style
Circle V-Style
Circle None
None None
Front Shp Figa
Figb Figc
Figd Fige
Figf Figg
Sleeve Long
Long Long
Long Short
Long Long
Using shape matching, we can compute the similarity between node shapes of the tree. After
finding the similarity between two node shapes, the overall similarity between two trees can be defined
using weighted-tree similarity algorithms.
Figure 10. The form of arc-labeled arc weighted tree with node shape for shape a in figure 9. Given
arc-labeled arc weighted trees summarized in Table 1, first we compute the similarity of each node shapes
exists in each tree. The result of similarity of node shape is shown in Table 2 and Table 3
Age Avail-
ability Fabric
Gender Occasion
Price Type
Adult 1 day
Polyester Cotton
Major Minor
F Formal
Coat
Garment
Button Style
Front Shape
Back Shape
Sleeve Collar
Normal
None V-Style
Long
Information and Communication Technology Seminar, Vol. 1 No. 1, August 2005
ISSN 1858-1633 2005 ICTS 60
Figure 11. The form of arc-labeled arc weighted tree with node shape for shape g in figure 9.
Table 2 and Table 3 summarized the similarity between two node shape of the front and the back of
each cloth in figure 9. The similarity of each tree in Table 1 along with the similarity between node shapes
in Table 2 and table 3 can be computed using equation 2 and the result is summarized in Table 4.
Table 2. The shape similarity of the front of the cloth
A B
C D
E F
G A
1.00 0.87
0.94 0.72
0.81 0.74
0.72
B 0.87
1.00 0.78
0.38 0.56
0.72 0.41
C 0.94
0.78 1.00
0.77 0.86
0.83 0.82
D 0.72
0.38 0.77
1.00 0.69
0.65 0.78
E 0.81
0.56 0.86
0.69 1.00
0.66 0.92
F 0.74
0.72 0.83
0.65 0.66
1.00 0.70
G 0.72
0.41 0.82
0.78 0.92
0.70 1.00
Table 3. The shape similarity of the back of the cloth
A B
C D
E F
G A
1.00 0.75
0.60 0.64
0.60 0.64
0.66
B 0.75
1.00 0.27
0.00 0.36
0.65 0.45
C 0.60
0.27 1.00
0.37 0.53
0.05 0.50
D 0.64
0.00 0.37
1.00 0.76
0.67 0.71
E 0.60
0.36 0.53
0.76 1.00
0.54 0.87
F 0.64
0.65 0.05
0.67 0.54
1.00 0.67
G 0.66
0.45 0.50
0.71 0.87
0.67 1.00
Cloth Total
A-B 0.2
1 0.05
1 0.05
0.2 0.1
1 0.1
0.2 1
0.3 0.56
A-C 0.2
1 0.05
1 0.05
1 0.1
1 0.1
1 0.2
0.3 0.852 0.7556
A-D 0.2
1 0.05
1 0.05
0.1 1
0.1 0.2
0.3 0.35
A-E 0.2
1 0.05
1 0.05
0.04 0.1
0.1 0.2
0.3 0.252
A-F 0.2
1 0.05
1 0.05
0.05 0.1
1 0.1
0.2 1
0.3 0.5525
A-G 0.2
1 0.05
1 0.05
0.05 0.1
0.1 1
0.2 1
0.3 0.5525
B-C 0.2
1 0.05
1 0.05
0.01 0.1
1 0.1
0.2 0.3
0.3505 B-D
0.2 1
0.05 1
0.05 0.1
1 0.1
0.2 0.3
0.35 B-E
0.2 1
0.05 1
0.05 0.1
0.1 1
0.2 0.3
0.35 B-F
0.2 1
0.05 1
0.05 0.01
0.1 1
0.1 1
0.2 1
0.3 0.6505
B-G 0.2
1 0.05
1 0.05
0.01 0.1
0.1 0.2
1 0.3
0.4505 C-D
0.2 1
0.05 1
0.05 0.1
1 0.1
0.2 1
0.3 0.55
C-E 0.2
1 0.05
1 0.05
0.04 0.1
0.1 0.2
0.3 0.252
C-F 0.2
1 0.05
1 0.05
0.05 0.1
1 0.1
0.2 0.3
0.3525 C-G
0.2 1
0.05 1
0.05 0.05
0.1 0.1
1 0.2
0.3 0.3525
D-E 0.2
1 0.05
1 0.05
0.01 0.1
0.1 0.2
0.3 0.2505
D-F 0.2
1 0.05
1 0.05
0.1 1
0.1 0.2
0.3 0.35
D-G
0.2 1
0.05 1
0.05 0.1
0.1 0.2
0.3
0.25 E-F
0.2 1
0.05 1
0.05 0.04
0.1 0.1
1 0.2
0.3 0.352
E-G
0.2 1
0.05 1
0.05 0.04
0.1 1
0.1 0.2
0.3 0.7
0.562 F-G
0.2 1
0.05 1
0.05 0.05
0.1 0.1
0.2 1
0.3 0.4525
TYPE ACCATION
PRICE AGE
AVAIL FABRIC
GENDER
Table 4. The similarity tree algorithm result
6. CONCLUSION
