A COMPARISON AND EVALUATION OF MOTION INDEXING ...

Figure 3.2: Process of Indexing Document.
for similarity between some parts of a motion clip. Figure 3.3 shows the process of
finding exact hits.
The technique described here is based on an exact hit and tries to find the exact
match of a motion. The two motion clips are considered similar with respect to the
selected feature function if they exhibit the same feature sequence. Mathematically,
if w = (w0, w1, · · · , wM) and v = (v0, v1, · · · , vN) are the feature sequences of the
database and the query, respectively, then an exact hit is an element k ∈ [0, M] such
that v is a subsequence of consecutive feature vectors in w starting from index k. This
is denoted with the expression vkw. The set of all exact hits in the database Γ is
defined as: HΓ(v) := {k ∈ [0, M] |vkw}. In terms of inverted lists, which are shifted
and intersected, the set of all exact hits can be expressed as:
HΓ(v) =
n∈[0:N]
36
(L(vn) − n) . (3.1)
The input lists L(vn) are additively adjusted by −n. The more efficient way is to
adjust the lists appearing as intermediate results by +1 prior to each intersection
step. After the final iteration, an adjustment of the resulting set by −(N + 1) yields