Selection of Visual Descriptors for the Purpose of Multi-camera Object Re-identification - Feature Selection for Data and Pattern Recognition - page 272

SD

= (

1

+

Scat

) ·

Dis

,

(12.18)

where Scat represents cluster compactness and Dis indicates the separation between
different classes. Both of these components are calculated according to the following
formulas:

v i

⊛ ⊞

− 1

max v j −

n c n c

i , j = 1 ,..., n c

⊝ ⊠

,..., n c

v i ·

Dis =

j

v j − v i , (12.19)

min
i , j =

v j −

i = 1 j = 1 , i =

1

i = 1 σ(

n c

v i )

Scat = , (12.20)

n c σ( x )

where n c is the class count, v i and v j are the corresponding class mean vectors, σ( v i )

denotes i th cluster standard deviation and is the deviation of the whole dataset.

Low Scat factor value means that clusters are more compact. Dis parameter is
related to the clusters distribution and its value increases with the cluster number.
To ensure the best dataset cluster separation and compactness, the SD index value
should be minimum.
This validity measure, similarly to the RS index, is calculated for two separate
cases and aggregated afterwards (Eq. 12.16 ). From the obtained results, SD A term is
determined as the inverted relation from Eq. 12.17 :

σ( x )

SNR O
SNR C .

SD A = (12.21)

12.5.3 Dissimilarity Measure

A new method of descriptor evaluation is proposed. It is based on direct comparison of
dissimilarity of all image pairs in the dataset according to a chosen visual descriptor.
The goal of the dissimilarity measure is to compare descriptors according to their
behaviour in a multi-camera, multi-object environment. The measure highlights the
fact that similarity of two images of the same object should be greater than similarity
of different objects, regardless of the cameras used to acquire both images. The
measure has also one additional advantage: in contrast to SD and RS indexes, the
dissimilarity measure may be obtained for local image features, because it does not
utilize mean and standard deviation values that are not defined for set-of-vectors
descriptors.
Given two images I 1 and I 2 and their descriptors V 1 and V 2 , the dissimilarity d
for standard (non-local-based) descriptors is calculated as the Euclidean distance:

d = V 1 − V 2 . (12.22)