document: 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 .
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