Mobile Landmark Recognition - Multimedia Database Retrieval: Technology and Applications - page 134

- Centroid update : When a new vector s i is added to a cluster, C h , the old

centroid of that cluster (denoted by v l , h ( old ) ) will be updated as follows:

C h w i s i

∑

s i ∈

v l , h ( old ) ₒ v l , h = (5.7)

( N h ) ∑ s i ∈ C h w i

where N h is the total number of vectors in the cluster C h .
These two substeps are repeated until there is no decrease of the following
weighted cost function,

w i s i v l , h

2

( S,V )= ∑

v l , h ∈V ∑

E SSD − (5.8)

s i ∈ C h

V = v l − 1 , ( h − 1 ) B + k ,

where E SSD is the sum-of-squared-distance criterion, and

k ∈{ 1 , 2 ,..., B }

￿ Step III. The current level is assigned with a new value, l ₐ l − 1, and Step II is

repeated until l = 0.

5.4.2 Saliency-Aware Bag-of-Word Representation

For a query landmark image, I q , its local descriptors can be described by S q =

s 1 ,...,

s J . These descriptors can be used for image matching, involving pairwise
comparison between the descriptors [ 144 ],

s j , s j

J
j = 1

s i , i = s i , D d ( I x , I q )= s . t . arg min

i

(5.9)

where I x is an input image in the database being compared, and has the descriptors
S x = { s 1 ,..., s J } . For the database of size N , an optimized ranking using S q is the

one that minimizes the following ranking loss:

N
x = 1 R ( x ) D d ( I x , I q )

L = (5.10)

R ( x )= exp ( − rank ( x )) (5.11)

where R is the ranking position weight of I x with respect to I q . Apparently,

minimizing the loss

( x )

with respect to D d in Eq. ( 5.10 ), does not scale well due to
the linear complexity to the image volume N . In comparison, the transformation of
S x to the BoW representation h x =[

L

h 1 ,..., h q M ]

t , can address the scalability [ 149 ].
The matching of I x and I q can be obtained by comparing the BoW component h i for
the given query I q :