<s>
Histogram	B-General_Concept
of	I-General_Concept
Oriented	I-General_Concept
Displacements	I-General_Concept
(	O
HOD	O
)	O
is	O
a	O
2D	O
trajectory	B-Application
descriptor	O
.	O
</s>
<s>
The	O
trajectory	B-Application
is	O
described	O
using	O
a	O
histogram	B-Algorithm
of	O
the	O
directions	O
between	O
each	O
two	O
consecutive	O
points	O
.	O
</s>
<s>
Given	O
a	O
trajectory	B-Application
T	O
=	O
{	O
P1	O
,	O
P2	O
,	O
P3	O
,	O
...	O
,	O
Pn}	O
,	O
where	O
Pt	O
is	O
the	O
2D	O
position	O
at	O
time	O
t	O
.	O
For	O
each	O
pair	O
of	O
positions	O
Pt	O
and	O
Pt+1	O
,	O
calculate	O
the	O
direction	O
angle	O
θ( t	O
,	O
t+1	O
)	O
.	O
</s>
<s>
A	O
histogram	B-Algorithm
of	O
the	O
quantized	O
values	O
of	O
θ	O
is	O
created	O
.	O
</s>
<s>
If	O
the	O
histogram	B-Algorithm
is	O
of	O
8	O
bins	O
,	O
the	O
first	O
bin	O
represents	O
all	O
θs	O
between	O
0	O
and	O
45	O
.	O
</s>
<s>
The	O
histogram	B-Algorithm
accumulates	O
the	O
lengths	O
of	O
the	O
consecutive	O
moves	O
.	O
</s>
<s>
For	O
each	O
θ	O
,	O
a	O
specific	O
histogram	B-Algorithm
bin	O
is	O
determined	O
.	O
</s>
<s>
The	O
length	O
of	O
the	O
line	O
between	O
Pt	O
and	O
Pt+1	O
is	O
then	O
added	O
to	O
the	O
specific	O
histogram	B-Algorithm
bin	O
.	O
</s>
<s>
This	O
fall	O
will	O
affect	O
the	O
histogram	B-Algorithm
with	O
the	O
appropriate	O
angles	O
and	O
lengths	O
,	O
regardless	O
of	O
the	O
position	O
where	O
the	O
hand	O
started	O
to	O
fall	O
.	O
</s>
<s>
However	O
,	O
the	O
temporal	O
information	O
will	O
be	O
lost	O
,	O
as	O
the	O
order	O
of	O
movements	O
is	O
not	O
stored-this	O
is	O
what	O
we	O
solve	O
by	O
applying	O
the	O
temporal	O
pyramid	B-Algorithm
,	O
as	O
shown	O
in	O
section	O
\ref{sec:temp-pyramid}	O
.	O
</s>
