A COMPARISON AND EVALUATION OF MOTION INDEXING ...

F -equivalent if the corresponding feature vectors F (P1) and F (P2) are the same. An
F -run of Γ is defined to be a subsequence of Γ consisting of consecutive F -equivalent
poses, whereas F -segments of Γ are defined to be the maximal F -runs.
The segments of a given motion stream are runs of maximal length. Each
of these segments corresponds to a unique feature vector. A document has many
segments and becomes a sequence of feature vectors. This sequence is referred as the
F -feature sequence of document Γ and denoted by F [Γ].
For example, consider the segmentation of the motion consisting of a right foot
kick followed by a left hand punch. The first step is to create a feature function which
is a combination of any number of available boolean generic functions. To describe
this motion we use, a feature function F 4 : ℜ 3J → {0, 1} 4 consisting of the following
four boolean functions:
1. Angle-based function which checks whether the right knee is bent or stretched.
2. Angle-based function which checks whether the left elbow is bent or stretched.
3. Plane-based function to check whether the right foot is raised or not.
4. Plane-based function to check whether the left hand is reaching out to the front
of the body or not.
The total number of different feature vectors possible for a feature function is equal
to 2 f , where f is the number of boolean functions in the feature function. Hence,
for the above feature function F 4 there are 16 different feature combinations possible
and hence 16 feature vectors possible.
This type of feature-dependent segmentation provides for temporal invariance
because the motion capture data streams are compared at the segment level rather
than at the frame level. So the time factor denoted by frames is not considered. Math-
ematically stated: The sequence of F -segments of a motion stream Γ is segmented
and each segment corresponds to a unique feature vector. These feature vectors are
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