Selection of Visual Descriptors for the Purpose of Multi-camera Object Re-identification - Feature Selection for Data and Pattern Recognition - page 271

SS t − SS w

SS t

RS = , (12.13)

where SS t and SS w are the sum of squared distances for the whole dataset and for
each of the clusters, respectively. These parameters are defined as follows:

2

SS t =

C

v − v , (12.14)

v ∈

2

SS w =

C i

v − v i , (12.15)

i v ∈

where v is the mean of the whole dataset, described as C , and v i represents the mean
vector for the i th cluster. RS parameter ranges from 0, for poorly clustered data, to 1
for the classes which can be characterized as compact and separable. Thus, this term
should be maximized.
For the purpose of visual descriptors assessment this measure is calculated in two
variants:
• C —for each camera independently, where clusters represent objects,

• O —for each object independently, where clusters represent cameras.

The C variant is utilized to depict descriptor capabilities to distinguish between
objects in the same camera. On the other hand, O variant is utilized to represent
the compactness of object description between different system cameras. Stability
of these results, for each of the variants, is calculated as:

= μ i SNR i

σ i ,

(12.16)

where σ i are mean and standard deviation calculated for i th variant.

Afterwards, the aggregated results are utilized to determine the parameter RS A which
can be used to compare different descriptors quality:

μ i and

SNR C
SNR O .

RS A = (12.17)

For the optimal feature extractor, object description between cameras should be as
compact as possible and, at the same time, its description within a particular camera
should be distant from other objects descriptions. Hence, for a good parametrization
technique, RS A term should be maximized.

12.5.2 SD Index

SD validity index is another measure utilized to verify data clustering [ 22 ]. This
parameter is calculated as a relation of two components: