A Similarity Measure for Motion Stream Segmentation and Recognition (Chuanjun 2005)

Summary:
The paper proposes a similarity measure to deal with problems in recognizing and segmenting motion streams. Specifically, the problems dealt with are differing lengths of motion duration, different variations in attributes of similar motions, and the fact that motion streams are continuous with no obvious "pause" at which to segment. The model presented represents a motion by a matrix in which columns correspond to joint angles and rows correspond to samples in time. Singular value decomposition is applied to two of these motion matrices of varying rows to determine a measurement of similarity. Eigenvalues and eigenvectors of the matrices representing both streaming motion input and known motion patterns are calculated and compared. The more similar two matrices are, the closer their eigenvectors are to being parallel and the closer their eigenvalues are to being proportional to each other.
The measurement of similarity is referred to as k Weighted Angular Similarity (kWAS). Data was collected from both a CyberGlove and a Vicon motion capture system to test the performance of the kWAS measurement. Although the first two eigenvalues (k = 2 in terms of kWAS) account for more than 95% of the sums of all the eigenvalues, considering the first two eigenvectors was not sufficient to recognize gestures at an acceptable rate. Increasing the value of k to six increased the accuracy of recognition for CyberGlove data to 94% and motion capture data to 94.6%. These results were higher than two other similarity measures called Eros and MAS.

Discussion:
Not only was the kWAS measure more accurate, it required about the same running time as the MAS measurement and was twice as fast as the Eros measurement. It might be interesting to see how the speed of kWAS is affected by changing the value of k - especially in the context of comparing it with the other measurements, if they have variables that can be adjusted which affect their running time.
Since the proposed measure of similarity does not take into account the order patterns were executed in, it is unable to distinguish gestures which pass through the same positions at different times. For instance, performing a gesture normally and exactly in reverse would be identical in terms of the kWAS similarity measure.