Key Frame-Based Activity Representation Using Antieigenvalues

Many activities may be characterized by a sequence of key frames that are related to important changes in motion rather than dominant characteristics that persist over a long sequence of frames. To detect such changes, we define a transformation operator at every time instant, which relates the past to the future states. One of the useful quantities associated with numerical range of an operator is the eigenvalue. In the literature, eigenvalue-based approaches have been studied extensively for many modeling tasks. These rely on gross properties of the data and are not suitable to detect subtle changes. We propose an antieigenvalue based measure to detect key frames. Antieigenvalues depend critically on the turning of the operator, whereas eigenvalues represent the amount of dilation along the eigenvector directions aligned with the direction of maximum variance. We demonstrate its application to activity modeling and recognition using two datasets: a motion capture dataset and the UCF human action dataset.