Null-Space representation for view-invariant motion trajectory classification-recognition and indexing-retrieval

This paper presents a novel classification/retrieval system for motion events based on a perfect view invariant representation of motion trajectories and a linear classifier algorithm. Specifically, Null Space Invariant (NSI) matrix representation for motion trajectories has been derived. The proposed view invariant representation based on the NSI operator is invariant to affine transformations and preserves the null space matrix. We use principal component null space analysis (PC-NSA) for indexing and classification of the NSI operator for recognition and retrieval of motion events. We rely on PC-NSA to determine the distance of the query trajectory to the centroid of each class, which is a statistical information vector in the PCNSA algorithm representing the corresponding motion class. Our results show that NSI provides a powerful approach to motion event recognition and retrieval that is invariant to affine transformations due to camera motion.