An efficient indexing scheme may greatly facilitate the retrieval of information. I create an indexing structure that can provide easier, faster and more robust retrieval of human motion data without directly comparing high dimensional motion sequences at all.
My indexing structure is constructed in a feature space, with each feature point representing a motion segment. The closeness of points is measured via the Euclidean distance. The closer the two feature points, the more similarity in behaviors between the two motion segments represented by the feature points. The goal is to group
together the closest feature points, i.e., motion segments with similar behaviors. I partition a data set into a hierarchy using a divisive clustering method. I start from the root node corresponding to a whole data set of feature vectors and recursively partition the data evenly into two subsets until the number of the feature points at the node is less than a preset threshold. At each internal node, I conduct PCA and then project the data points onto the first principal axis, i.e. the eigenvector with the largest eigenvalue. Next, I split the data around the median of the projected data. Splitting by the median typically results in a more balanced tree structure. It is also more robust against outliers.
Pruning is a popular strategy to speed up a query process by avoiding expensive searches on apparently unmatched sequences in a database. I take an approach similar to the OBB-Trees (Gottschalk et al., 1996). At each node I compute PCA out of the data points in the feature space, and then form a minimum bounding rectangle (MBR) in thek-dimensional space spanned by the leadingkeigenvectors. This typically results in a MBR with a tighter bound of the enclosed data instance. Figure 6.2 illustrates the hierarchical indexing structure, where the feature points are clustered divisively, and the corresponding MBRs are constructed accordingly to each partition level. The partition process continues until a desired granularity is reached at every leaf node.
Once a motion database and the associated indexing structure are established, sub- sequent updates are allowed and can be done either dynamically or in a batch mode. A batch mode update is recommended to be done only when a significant amount of new data become available and must be added to the database. In this case the indexing hierarchy has to be rebuilt all over again using the feature points of both the old data and the new data. A dynamic update, on the other hand, can be done at any time in between the batch mode updates, with an assumption that the data being updated are small in size as compared to the current database, so that the distribution of the database will not change dramatically with the new data being added. Now I describe two dynamic operations, insertion and deletion, respectively.
Dynamic Insertion. A dynamic insertion adds in feature points, one at a time, to the indexing tree. When a new motion sequence becomes available and needs to be added to an existing motion database as well as the associated index hierarchy, I first segment the motion sequence into motion segments of single behaviors. Then for each motion segment, a feature vector is derived from the mean vector, and the covariance matrix of the poses in the segment. Then I project this new feature vector to the lower-dimensional indexing space. The projection then becomes a new feature point in
the indexing space and is ready for the dynamic insertion. Starting from the root node, I recursively insert the feature point to the most appropriate node. At each node, with the associated cluster of feature points, I perform a dynamic insertion as follows:
1. Subtract the cluster mean of a node from the feature point to be inserted. 2. Project the mean-centered feature point to the principal component space spanned
by the principal component axes associated with the cluster.
3. Check if the projection of the feature point is out of the original minimum bound- ing rectangle. If so, I update the boundaries of the affected minimum bounding rectangle to include the inserted feature point. If the node is an internal node, meaning it has two children, I then project the inserted feature point to the prin- cipal space of each child cluster. I then insert the feature point to the child node whose minimum bounding rectangle increases the least after inserting the feature point. The update stops if the node is a leaf node.
Dynamic Deletion. First, I simply delete the feature point from the leaf node to which it belongs. I then update the minimum bounding rectangle if any of its boundaries are affected (decreased) by the deletion of the feature point. Next, I find its parent node and perform the same deletion operation. The process continues until the root node is reached.