Selection of Visual Descriptors for the Purpose of Multi-camera Object Re-identification - Feature Selection for Data and Pattern Recognition - page 273

In case of local image feature-based descriptors, V 1 and V 2 are matrices m 1 × n

and m 2 ×

n , accordingly. Therefore, a matching procedure is used in order to find the
best matching vector in matrix V 2 for each vector in V 1 and vice versa [ 50 ]. For k th
vector (row) of matrix V i , the best matching vector in the matrix V j is the one having
the smallest Euclidean distance; this distance is denoted as e ij . The dissimilarity of
V 1 and V 2 is calculated according to the equation:

k = 1

m 1

k = 1

m 2

e 21 e 21

d = 0 . 5 · + 0 . 5 · . (12.23)

m 1 m 2

The smaller the value of d , the smaller the dissimilarity and thus the greater
similarity of the compared images.
Dissimilarity values d of image pairs are divided into 4 sets depending on the
objects that are depicted in the images and on cameras that were used to capture
images. The sets are as follows: the same object in the same camera (SOSC), the same
object in different cameras (SODC), different objects in the same camera (DOSC) and
different objects in different cameras (DODC). In each set, SNR measure is calculated
as the ratio of the mean value to the standard deviation. This normalizes results
and makes it possible to compare visual descriptors according to the dissimilarity
measure. Final dissimilarity measure DSIM for the given visual descriptor is derived
from the following equation:

SNR SOSC · SNR SODC

DSIM =

SNR DODC .

(12.24)

SNR DOSC ·

The numerator is related to similarity of image pairs belonging to the same object
while the denominator reflects similarity of images of different objects. Therefore,
the smaller dissimilarity measure DSIM for the given visual descriptor, the better the
descriptor is suited to identify objects in a multi-camera environment.

12.5.4 Result Aggregation

Descriptor evaluation measures (DEMs) discussed in Sects. 12.5.1 - 12.5.3 are calcu-
lated for one set of objects' images only. In order to perform a thorough evaluation
of various visual descriptors, they need to be verified using several test datasets. This
subsection presents methodology for aggregation of results from such an analysis.
Let U

N U be the set of N U datasets used for visual descriptors
evaluation. Each set contains images of different objects recorded in different loca-
tions. Each dataset u i is divided into N i subsets u ij ∈

= u i , i = 1 ,...,

u i containing objects from the
dataset u i . DEMs are calculated for each subset u ij , independently. The aim of the
approach is to make results of analysis robust against selection of particular objects
in the dataset.