Human Detection in Video over Large Viewpoint Changes

1250 G. Duan, H. Ai, and S. Lao
g(x, y, s), where (x, y) is the position and s is the scale. For instance, g(x, y, s)
indicates that the size of this granule is 2 s × 2 s and its left-top corner is at
position (x, y) of an image. In an image I, it can be calculated as
g(x, y, s) =
2
1 ∑
s −1
2 s × 2 s
j=0
2∑
s −1
k=0
I(x + k, y + j). (1)
s is set to 0,1,2 or 3 in this paper and the four typical granules are shown in
Fig. 2 (a).
In order to calculate the distance between two granules, Granular space G is
mapped into 3D space I, where for each element g ∈ G and γ ∈ I, g(x, y, s) →
γ(x + 2 s , y + 2 s , 2 s ). The distance between two granules in G is defined to be the
Euclidean distance between two corresponding points in I, d(g 1 , g 2 ) = d(γ 1 , γ 2 )
where g 1 , g 2 ∈ G, γ 1 , γ 2 ∈ I and γ 1 , γ 2 correspond to g 1 , g 2 respectively.
d(γ 1 (x 1 , y 1 , z 1 ), γ 2 (x 2 , y 2 , z 2 )) = √ (x 1 − x 2 ) 2 + (y 1 − y 2 ) 2 + (z 1 − z 2 ) 2 . (2)
3.2 Intra-frame and Inter-frame Comparison Features (I 2 CF s)
Similar to the approach in [1], we consider two frames each time, the previous
one and the latter one, from which two pairs of granules are extracted to fully
capture the appearance and motion features of an object. An I 2 CF can be
represented as a five-tuple c = (mode, g1, i g j 1 , gi 2, g j 2 ), which is also called a cell
according to [5]. The mode is Appearance mode, Difference mode or Consistent
mode. g1, i g j 1 , gi 2 and g j 2 are four granules. The first pair of granules, gi 1 and g j 1
are from the previous frame to describe the appearance of an object. The second
pair of granules, g2 i and g j 2 comes from the previous or latter frame to describe
either appearance or motion information. When the second pair are from the
previous frame, which means that both pairs are from the previous frame, this
kind of feature is Intra-frame Comparison Feature (Intra-frame CF); when
the second pair come from the latter one, the feature becomes Inter-frame
Comparison Feature (Inter-frame CF). Both of these two kinds of comparison
features are combined to be Intra-frame and Inter-frame Comparison Feature
(I 2 CF ).
Appearance mode (A-mode). Pairing Comparison of Color feature (PCC)
is proved to be simple, fast and efficient in [5] . As PCC can describe the invariance
of color to some extent, we extend this idea to 3D space. A-mode compares
two pairs of granules simultaneously:
f A (g i 1, g j 1 , gi 2, g j 2 ) = gi 1 ≥ g j 1 &&gi 2 ≥ g j 2 . (3)
PCC feature is a special case of A-mode. f A (g i 1, g j 1 , gi 2, g j 2 ) = gi 1 ≥ g j 1 , when
g i 1 == g i 2 and g j 1 == gj 2 .
Difference mode (D-mode). D-mode computes the absolute subtractions
of two pairs of granules, defined as:
f D (g1, i g j 1 , gi 2, g j 2 ) = |gi 1 − g2| i ≥ |g j 1 − gj 2 |. (4)