A COMPARISON AND EVALUATION OF MOTION INDEXING ...

oundary when a valley in H is followed by a peak. We also take into account the
difference between the valley and the peak to avoid false segments. This difference
should be greater than some threshold R. The value of the threshold is chosen by the
following equation (2.9):
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R = Hmax − Hmin
, (2.9)
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where Hmax and Hmin are the maximum and minimum possible values of H. If the
value of R is increased, it results in fewer segments that correspond to more distinct
behaviors. Whereas if R is decreased, finer segmentation happens.
To find the next boundary, the whole algorithm is restarted on the rest of the
motion. The output of this technique is the same as the first one: The segment
boundaries in terms of their frame numbers.
2.1.5 Indexing of Segments
Segments are obtained as a result of the above segmentation techniques for a
motion sequence. The indexing of two motion sequences involves the indexing of
their respective segments. Therefore, indexing uses the information retrieved during
the PCA analysis step of segmentation. When all segments are derived, we store the
dimension r, the start frame, and the end frame for each segment. Our algorithm for
indexing can be described as:
1. Combine two segments from different motions by concatenating the second seg-
ment to the first segment. Suppose the first segment is a m × D matrix and the
second segment is a n×D matrix, the combined segment becomes a (m+n)×D
matrix. Then use the r1 from the first segment to calculate the preserved infor-
mation , Er1, for the combined segment.