  In this work, we propose a novel node splitting method for regression trees
and incorporate it into the regression forest framework. Unlike traditional
binary splitting, where the splitting rule is selected from a predefined set of
binary splitting rules via trial-and-error, the proposed node splitting method
first finds clusters of the training data which at least locally minimize the
empirical loss without considering the input space. Then splitting rules which
preserve the found clusters as much as possible are determined by casting the
problem into a classification problem. Consequently, our new node splitting
method enjoys more freedom in choosing the splitting rules, resulting in more
efficient tree structures. In addition to the Euclidean target space, we
present a variant which can naturally deal with a circular target space by the
proper use of circular statistics. We apply the regression forest employing our
node splitting to head pose estimation (Euclidean target space) and car
direction estimation (circular target space) and demonstrate that the proposed
method significantly outperforms state-of-the-art methods (38.5% and 22.5%
error reduction respectively).
