A COMPARISON AND EVALUATION OF MOTION INDEXING ...

CHAPTER 4
DYNAMIC TIME WARPING TECHNIQUES
This chapter provides a brief overview of Dynamic Time Warping (DTW) and
the process of threshold selection. The threshold plays an important role in determin-
ing the matches in the algorithm. The latter part of chapter describes two techniques
to index motion data using Dynamic Time Warping. Both these techniques have been
refered from the book, Information retrieval for music and motion [16].
The Dynamic Time Warping algorithm can be explained as an algorithm that
calculates an optimal warping path to correspond two time series. The algorithm
calculates both warping path values between the two series and the distance be-
tween them using dynamic programming. Formally, consider two numerical sequences
(a1, a2, · · · , an) and (b1, b2, · · · , bm) which are of different length (n = m). The algo-
rithm starts with the calculation of local distances between the elements of the two
sequences. These distances can be of different types depending on the data and appli-
cation. Euclidian distance is the most commonly used distance. The local distances
are stored in a distance matrix D which has n rows and m columns. Each element
of the matrix Dis given by:
dij =| ai − bj |, i = {1, n} , j = {1, m} .
For i = 1, · · · · · · , n and j = 1, · · · · · · , m, where all denotes a local distance. The
next step in the DTW algorithm is to determine the matching cost matrix C. This is
performed using the local distances matrix D and by computing the minimal distance
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