A COMPARISON AND EVALUATION OF MOTION INDEXING ...

4.1 Scaling and Thresholding the DTW Score
Dynamic time warping tries to find the best matching occurrence of the query
in a given sequence. If both the query sequence and the sequence to be searched are
synchronized, there is a frame by frame match. However, if the given sequence is
performed faster or slower than the query, the query is shrunk or enlarged to match
the other sequence. This is very common in motion sequencing as humans rarely have
movements at a uniform pace. Hence, a minor warp is always expected.
In cases where the actions being compared differ greatly, the cost of matching
future consecutive frames in the sequences may be very high, compared to keeping
one sequence frozen and warping large lengths along the other. This results in long
horizontal or vertical paths in the matching cost matrix. To ensure these matches are
rejected, we can associate a penalty for following non-diagonal steps.
In our implementation, we keep count of the number of non-diagonal steps made
in the matching path. We later increase the cost obtained by an amount proportional
to these counts. These also depend on the actual length of the match. We use
regression to determine the proportionality constants and dependence on length. We
obtain these values for all the motion files in the database, and store them in a matrix
A = [C1 | C2 | C3 | C4 | C5], where C1 is a column with DTW score, C2 is a column
with warp along sequence 1, C3 is a column with warp along sequence 2, C4 is a
column with length of DTW match, and C5 is a column with a constant 1.
For a correct DTW match, we expect the score to be around a value Y + , and
for an incorrect match, we expect it to be around a value Y − . We create a column
vector B, where ith row is Y + if the query matches the ith sequence, else ith row is
Y − . In our case, we chose Y + = 0 and Y − = 100. We use MATLAB’s regression
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