Rotation invariant distance measures for trajectories

For the discovery of similar patterns in 1D time-series, it is very typical to perform a normalization of the data (for example a transformation so that the data follow a zero mean and unit standard deviation). Such transformations can reveal latent patterns and are very commonly used in datamining applications. However, when dealing with multidimensional time-series, which appear naturally in applications such as video-tracking, motion-capture etc, similar motion patterns can also be expressed at different orientations. It is therefore imperative to provide support for additional transformations, such as rotation. In this work, we transform the positional information of moving data, into a space that is translation, scale and rotation invariant. Our distance measure in the new space is able to detect elastic matches and can be efficiently lower bounded, thus being computationally tractable. The proposed methods are easy to implement, fast to compute and can have many applications for real world problems, in areas such as handwriting recognition and posture estimation in motion-capture data. Finally, we empirically demonstrate the accuracy and the efficiency of the technique, using real and synthetic handwriting data.